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1
Antwi Baafi, Joseph. "The Nexus Between Black-Scholes-Merton Option Pricing and Risk: A Case of Ghana Stock Exchange." Archives of Business Research 10, no. 5 (May 24, 2022): 140–52. http://dx.doi.org/10.14738/abr.105.12350.
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Even though option pricing and its market activities are not new, in Ghana the idea of trading options is yet to be realized. One popular method in pricing options is known as Black-Scholes-Merton option pricing model. Even though option pricing activities are not currently happening on the Ghana Stock Exchange, authors looked at the possibilities and preparedness of the GES to start trading such financial instrument. The main objective of this study therefore was to know how Black-Scholes-Merton model could be used to help in appropriate option value and undertake a risk assessment of stocks on the exchange. This study basically used the black-Scholes formula in calculating the call and put option prices for 28 companies listed GES. The results showed that the price of call option for 18 out of 28 listed stocks showed a value of zero. Again, only seven (7) companies had a value for both call and put options. This means stocks of 21 companies cannot be an underlying asset for trading financial derivatives. Reason for this performance of stock is due to low volatility. The study recommends that policies to increase volatility on the stock market should be put in place in other to make option pricing possible.
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Blau, Benjamin M., T. Boone Bowles, and Ryan J. Whitby. "Gambling Preferences, Options Markets, and Volatility." Journal of Financial and Quantitative Analysis 51, no. 2 (April 2016): 515–40. http://dx.doi.org/10.1017/s002210901600020x.
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AbstractThis study examines whether the gambling behavior of investors affects volume and volatility in financial markets. Focusing on the options market, we find that the ratio of call option volume relative to total option volume is greatest for stocks with return distributions that resemble lotteries. Consistent with the theoretical predictions of Stein (1987), we demonstrate that gambling-motivated trading in the options market influences future spot price volatility. These results not only identify a link between lottery preferences in the stock market and the options market, but they also suggest that lottery preferences can lead to destabilized stock prices.
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Cremers, Martijn, and David Weinbaum. "Deviations from Put-Call Parity and Stock Return Predictability." Journal of Financial and Quantitative Analysis 45, no. 2 (February 19, 2010): 335–67. http://dx.doi.org/10.1017/s002210901000013x.
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AbstractDeviations from put-call parity contain information about future stock returns. Using the difference in implied volatility between pairs of call and put options to measure these deviations, we find that stocks with relatively expensive calls outperform stocks with relatively expensive puts by 50 basis points per week. We find both positive abnormal performance in stocks with relatively expensive calls and negative abnormal performance in stocks with relatively expensive puts, which cannot be explained by short sale constraints. Rebate rates from the stock lending market directly confirm that our findings are not driven by stocks that are hard to borrow. The degree of predictability is larger when option liquidity is high and stock liquidity low, while there is little predictability when the opposite is true. Controlling for size, option prices are more likely to deviate from strict put-call parity when underlying stocks face more information risk. The degree of predictability decreases over the sample period. Our results are consistent with mispricing during the earlier years of the study, with a gradual reduction of the mispricing over time.
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Hoyyi, Abdul, Abdurakhman Abdurakhman, and Dedi Rosadi. "VARIANCE GAMMA PROCESS WITH MONTE CARLO SIMULATION AND CLOSED FORM APPROACH FOR EUROPEAN CALL OPTION PRICE DETERMINATION." MEDIA STATISTIKA 14, no. 2 (December 12, 2021): 183–93. http://dx.doi.org/10.14710/medstat.14.2.183-193.
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The Option is widely applied in the financial sector. The Black-Scholes-Merton model is often used in calculating option prices on a stock price movement. The model uses geometric Brownian motion which assumes that the data is normally distributed. However, in reality, stock price movements can cause sharp spikes in data, resulting in nonnormal data distribution. So we need a stock price model that is not normally distributed. One of the fastest growing stock price models today is the process exponential model. The process has the ability to model data that has excess kurtosis and a longer tail (heavy tail) compared to the normal distribution. One of the members of the process is the Variance Gamma (VG) process. The VG process has three parameters which each of them, to control volatility, kurtosis and skewness. In this research, the secondary data samples of options and stocks of two companies were used, namely zoom video communications, Inc. (ZM) and Nokia Corporation (NOK). The price of call options is determined by using closed form equations and Monte Carlo simulation. The Simulation was carried out for various values until convergent result was obtained.
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Stolorz, Beata. "Probability of Exercise of Option." Folia Oeconomica Stetinensia 6, no. 1 (January 1, 2007): 1–14. http://dx.doi.org/10.2478/v10031-007-0001-8.
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Probability of Exercise of Option To estimate the risk the investors take when investing their money in stocks or stock options one must study if the option is exercised or not. From the point of view of a call option writer, especially those uncovered, one should study the probability of the exercise of option by a holder. The method presented in the paper enables to estimate risk connected with investment in options. In the assessment of risk that is born when investing money in stocks or options it is interesting whether the option will be exercised or not. From the writers' point of view, particularly those without coverage, it could be necessary to analyse probability of the exercise of options by buyers. The described method allows to assess at any time of call option duration whether the investor can be certain of the result of their investment. It can be applied also for the option strategies. In the paper the author has attempted to estimate the risk of call option and to estimate the probability of profit achievement in the case of long strangle option application. Investors using option strategies are able to do preliminary analysis of options and to minimize risk of their investment through choosing a proper date and price of exercise.
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Bae, Kwangil. "Analytical Approximations of American Call Options with Discrete Dividends." Journal of Derivatives and Quantitative Studies 26, no. 3 (August 31, 2018): 283–310. http://dx.doi.org/10.1108/jdqs-03-2018-b0001.
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In this study, we assume that stock prices follow piecewise geometric Brownian motion, a variant of geometric Brownian motion except the ex-dividend date, and find pricing formulas of American call options. While piecewise geometric Brownian motion can effectively incorporate discrete dividends into stock prices without losing consistency, the process results in the lack of closed-form solutions for option prices. We aim to resolve this by providing analytical approximation formulas for American call option prices under this process. Our work differs from other studies using the same assumption in at least three respects. First, we investigate the analytical approximations of American call options and examine European call options as a special case, while most analytical approximations in the literature cover only European options. Second, we provide both the upper and the lower bounds of option prices. Third, our solutions are equal to the exact price when the size of the dividend is proportional to the stock price, while binomial tree results never match the exact option price in any circumstance. The numerical analysis therefore demonstrates the efficiency of our method. Especially, the lower bound formula is accurate, and it can be further improved by considering second order approximations although it requires more computing time.
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Szu, Wen-Ming, Yi-Chen Wang, and Wan-Ru Yang. "How Does Investor Sentiment Affect Implied Risk-Neutral Distributions of Call and Put Options?" Review of Pacific Basin Financial Markets and Policies 18, no. 02 (June 2015): 1550010. http://dx.doi.org/10.1142/s0219091515500101.
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This paper investigates the characteristics of implied risk-neutral distributions separately derived from Taiwan stock index call and put options prices. Differences in risk-neutral skewness and kurtosis between call and put options indicate deviations from put-call parity. We find that the sentiment effect is significantly related to differences between call and put option prices. Our results suggest the differential impact of investor sentiment and consumer sentiment on call and put option traders' expectations about underlying asset prices. Moreover, rational and irrational sentiment components have different influences on call and put option traders' beliefs.
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Broughton, John B., Don M. Chance, and David M. Smith. "Implied Standard Deviations And Put-Call Parity Relations Around Primary Security Offerings." Journal of Applied Business Research (JABR) 15, no. 1 (August 31, 2011): 1. http://dx.doi.org/10.19030/jabr.v15i1.5683.
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<span>This study examines the response of the options market to new security registrations and issuances. Two methods are employed to gauge option market response. The first involves the calculation of implied standard deviations (ISDs) around primary security registration and issuance dates. The second employs American put-call parity to simultaneously evaluate the relationship between put, call and stock prices around these dates. We find a statistically significant mean decrease in relative ISD five trading days before announcement of new stock issuances and a statistically significant mean increase in relative ISD one day before announcement of new debt issuances. Put-call parity tests provide evidence that the options market anticipates stock price decreases prior to announcements of both stock and debt issuance.</span>
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BUCKLEY, JAMES J., and ESFANDIAR ESLAMI. "PRICING STOCK OPTIONS USING BLACK-SCHOLES AND FUZZY SETS." New Mathematics and Natural Computation 04, no. 02 (July 2008): 165–76. http://dx.doi.org/10.1142/s1793005708001008.
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We use the basic Black-Scholes equation for pricing European stock options but we allow some of the parameters in the model to be uncertain and we model this uncertainty using fuzzy numbers. We compute the fuzzy number for the call value of option with and without uncertain dividends. This fuzzy set displays the uncertainty in the option's value due to the uncertainty in the input values to the model. We also correct an error in a recent paper which also fuzzified the Black-Scholes equation.
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Chauhan, Arun, and Ravi Gor. "COMPARISON OF THREE OPTION PRICING MODELS FOR INDIAN OPTIONS MARKET." International Journal of Engineering Science Technologies 5, no. 4 (July 20, 2021): 54–64. http://dx.doi.org/10.29121/ijoest.v5.i4.2021.203.
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Black-Scholes option pricing model is used to decide theoretical price of different Options contracts in many stock markets in the world. In can find many generalizations of BS model by modifying some assumptions of classical BS model. In this paper we compared two such modified Black-Scholes models with classical Black-Scholes model only for Indian option contracts. We have selected stock options form 5 different sectors of Indian stock market. Then we have found call and put option prices for 22 stocks listed on National Stock Exchange by all three option pricing models. Finally, we have compared option prices for all three models and decided the best model for Indian Options.
Motivation/Background:
In 1973, two economists, Fischer Black, Myron and Robert Merton derived a closed form formula for finding value of financial options. For this discovery, they got a Nobel prize in Economic science in 1997. Afterwards, many researchers have found some limitations of Black-Scholes model. To overcome these limitations, there are many generalizations of Black-Scholes model available in literature. Also, there are very limited study available for comparison of generalized Black-Scholes models in context of Indian stock market. For these reasons we have done this study of comparison of two generalized BS models with classical BS model for Indian Stock market.
Method:
First, we have selected top 5 sectors of Indian stock market. Then from these sectors, we have picked total 22 stocks for which we want to compare three option pricing models. Then we have collected essential data like, current stock price, strike price, expiration time, rate of interest, etc. for computing the theoretical price of options by using three different option pricing formulas. After finding price of options by using all three models, finally we compared these theoretical option price with market price of respected stock options and decided that which theoretical price has less RMSE error among all three model prices.
Result:
After going through the method described above, we found that the generalized Black-Scholes model with modified distribution has minimum RMSE errors than other two models, one is classical Black-Scholes model and other is Generalized Black-Scholes model with modified interest rate.
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EKSTRÖM, ERIK, and JOHAN TYSK. "OPTIONS WRITTEN ON STOCKS WITH KNOWN DIVIDENDS." International Journal of Theoretical and Applied Finance 07, no. 07 (November 2004): 901–7. http://dx.doi.org/10.1142/s0219024904002694.
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There are two common methods for pricing European call options on a stock with known dividends. The market practice is to use the Black–Scholes formula with the stock price reduced by the present value of the dividends. An alternative approach is to increase the strike price with the dividends compounded to expiry at the risk-free rate. These methods correspond to different stock price models and thus in general give different option prices. In the present paper we generalize these methods to time- and level-dependent volatilities and to arbitrary contract functions. We show, for convex contract functions and under very general conditions on the volatility, that the method which is market practice gives the lower option price. For call options and some other common contracts we find bounds for the difference between the two prices in the case of constant volatility.
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Tewari, Manish, and Pradipkumar Ramanlal. "Floating Rate Notes in High Rate Environment and the Stock Market Response." International Journal of Finance & Banking Studies (2147-4486) 11, no. 3 (October 13, 2022): 72–81. http://dx.doi.org/10.20525/ijfbs.v11i3.2020.
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Previous study finds that the firms with inferior growth options tend to issue callable bonds. Typically, these firms are characterized by stock underperformance. Previous study also finds that the floating rate as a superior alternative to the call provision, which is restrictive, when the interest rates are likely to fall. We study the long-term stock performance of floating rate notes (FRNs) issuing firms, issued when the interest rates are high. Stock overperformance would suggest floating rate as a preferred choice by the firms with high growth options rather the call option. We find that the FRNs are generally investment grade with extremely rare presence of a call option. We perform the analysis using Buy and hold abnormal return (BHAR) as the proxy for the long-term stock overperformance/underperformance. A sample of floating rate notes issued (1654) from 1992 to 2007, a period of high interest rates, reveals significant overperformance by the floating rate notes issuing firms in the high-rate paradigm. High growth firms, in the high-rate environment, significantly benefit from the floating rate provision which is less restrictive and less costly than the call option, which typically provides call protection period and pays a call premium. Floating rate provision better mitigates the interest rate risk for the firms in the high-rate environment. We find that the smaller, high growth, higher leverage, less profitable firms with greater agency issues benefit more from issuing FRNs in the high-rate environment. Our study has relevance to the stock portfolio construction and performance. We also perform a comparative analysis using the sample of floating rate notes issued (270) during 2008 to 2018, a period of low interest rates, and find stock underperformance. The implications are that the call option likely is a better choice for the firm since the firm preserves the right to forego exercising the option.
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Bae, Kwangil. "Research on the American Call Options on the Stocks Paying Multiple Dividends." Journal of Derivatives and Quantitative Studies 27, no. 3 (August 31, 2019): 253–74. http://dx.doi.org/10.1108/jdqs-03-2019-b0001.
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Cassimon et al. (2007) propose a pricing formula of American call options under the multiple dividends by extending Roll (1977). However, because these studies investigate the option pricing formula under the escrow model, there is inconsistency for the assumption of the stock prices. This paper proposes pricing formulas of American call options under the multiple dividends and piecewise geometric Brownian motion. For the formulas, I approximate the log prices of ex-dividend dates to follow a multivariate normal distribution, and decompose the option price as a function of payoffs and exercise boundaries. Then, I obtain an upper bound of the American call options by substituting approximated log prices into the both of the payoffs and the exercise boundaries. Besides, I obtain a lower bound of the price by substituting approximated price only into the exercise boundaries. These upper and lower bounds are exact prices when the amounts of dividends are linear to the stock prices. According to the numerical study, the lower bound produces relatively small errors. Especially, it produces small errors when the dividends are more sensitive to the stock price changes.
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Jiménez-Gómez, Miguel, Natalia Acevedo-Prins, and Miguel David Rojas-López. "Simulation hedge investment portfolios through options portfolio." Indonesian Journal of Electrical Engineering and Computer Science 16, no. 2 (November 1, 2019): 843. http://dx.doi.org/10.11591/ijeecs.v16.i2.pp843-847.
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<p>This paper presents two hedging strategies with financial options to mitigate the market risk associated with the future purchase of investment portfolios that exhibit the same behavior as Colombia's COLCAP stock index. The first strategy consists in the purchase of a Call plain vanilla option and the second strategy in the purchase of a Call option and the sale of a Call option. The second strategy corresponds to a portfolio of options called Bull Call Spread. To determine the benefits of hedging and the best strategy, the Geometric Brownian Motion and Monte Carlo simulation is used. The results show that the two hedging strategies manage to mitigate market risk and the best strategy is the first one despite the fact that the Bull Call Spread strategy is lower cost.</p>
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Li, Meng, Xuefeng Wang, and Fangfang Sun. "Proactive Hedging European Call Option Pricing with Linear Position Strategy." Discrete Dynamics in Nature and Society 2018 (September 17, 2018): 1–13. http://dx.doi.org/10.1155/2018/2087145.
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Proactive hedging option is an exotic European stock option designed for hedgers. Such option requires option holders to buy in (or sell out) the underlying asset (stock) and allows them to adjust the holdings of the underlying asset per its price changes within an option period. The proactive hedging option is an attractive choice for hedgers because its price is lower than that of classical options and because it completely hedges the risk of exposure for option holders. In this study, the underlying asset price movement is assumed to follow geometric fractional Brownian motion. The pricing formula for proactive hedging call options is derived with a linear position strategy by applying the risk-neutral evaluation principle. We use simulations to confirm that the price of this exotic option is always no more than that of the classical European option under the same parameters.
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Gerber, Hans U., and Elias S. W. Shiu. "Martingale Approach to Pricing Perpetual American Options." ASTIN Bulletin 24, no. 2 (November 1994): 195–220. http://dx.doi.org/10.2143/ast.24.2.2005065.
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AbstractThe method of Esscher transforms is a tool for valuing options on a stock, if the logarithm of the stock price is governed by a stochastic process with stationary and independent increments. The price of a derivative security is calculated as the expectation, with respect to the risk-neutral Esscher measure, of the discounted payoffs. Applying the optional sampling theorem we derive a simple, yet general formula for the price of a perpetual American put option on a stock whose downward movements are skip-free. Similarly, we obtain a formula for the price of a perpetual American call option on a stock whose upward movements are skip-free. Under the classical assumption that the stock price is a geometric Brownian motion, the general perpetual American contingent claim is analysed, and formulas for the perpetual down-and-out call option and Russian option are obtained. The martingale approach avoids the use of differential equations and provides additional insight. We also explain the relationship between Samuelson's high contact condition and the first order condition for optimality.
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Bae, Kwangil, Jangkoo Kang, and Hwa-Sung Kim. "Call options with concave payoffs: An application to executive stock options." Journal of Futures Markets 38, no. 8 (April 25, 2018): 943–57. http://dx.doi.org/10.1002/fut.21924.
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Christain, Onugu,, Davies, Iyai, and Amad, Innocent Uchenna. "A Numerical Approximation on Black-Scholes Equation of Option Pricing." Asian Research Journal of Mathematics 19, no. 7 (May 9, 2023): 92–105. http://dx.doi.org/10.9734/arjom/2023/v19i7682.
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This paper considered the notion of European option which is geared towards solving analytical and numerical solutions. In particular, we examined the Black-Scholes closed form solution and modified Black-Scholes (MBS) partial differential equation using Crank-Nicolson finite difference method. These partial differential equations were approximated to obtain Call and Put option prices. The explicit price of both options is found accordingly. The numerical solutions were compared to the closed form prices of Black-Scholes formula. More so, comparisons of other parameters were discussed for the purpose of investment plans. The computational results shows: increase in stock volatility increases the value of options, when the initial stock price is equal to its strike price the values of call option is higher than the put option. This informs the investor about the behavior of stock prices for the purpose of decision making. Finally, all simulation results presented graphically using MATLAB.
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MA, GUIYUAN, and SONG-PING ZHU. "Pricing American call options under a hard-to-borrow stock model." European Journal of Applied Mathematics 29, no. 3 (September 22, 2017): 494–514. http://dx.doi.org/10.1017/s0956792517000262.
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While a classic result by Merton (1973,Bell J. Econ. Manage. Sci., 141–183) is that one should never exercise an American call option just before expiration if the underlying stock pays no dividends, the conclusion of a very recent empirical study conducted by Jensen and Pedersen (2016,J. Financ. Econ.121(2), 278–299) suggests that one should ‘never say never’. This paper complements Jensen and Pedersen's empirical study by presenting a theoretical study on how to price American call options under a hard-to-borrow stock model proposed by Avellaneda and Lipkin (2009,Risk22(6), 92–97). Our study confirms that it is the lending fee that results in the early exercise of American call options and we shall also demonstrate to what extent lending fees have affected the early exercise decision.
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Yang, Ming, and Yin Gao. "Pricing formulas of binary options in uncertain financial markets." AIMS Mathematics 8, no. 10 (2023): 23336–51. http://dx.doi.org/10.3934/math.20231186.
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<abstract><p>Binary options have a payoff that is either a fixed value or nothing at all. In this paper, the generalized pricing formulas of binary options, including European binary call options, European binary put options, American binary call options and American binary put options, are investigated in uncertain financial markets. By applying the Liu's stock model to describe the stock price, the explicit pricing formulas of binary options are derived successfully. Besides, the corresponding numerical examples for the above four kinds of binary options are discussed in this paper.</p></abstract>
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Guo, Meiding. "Research On The Pricing Of Rainbow Option Based On The Geometric Brownian Motion Model: Case Of Pfizer & Walmart." BCP Business & Management 32 (November 22, 2022): 438–45. http://dx.doi.org/10.54691/bcpbm.v32i.2964.
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Trading financial derivatives become more and more popular in the modern life. The investor wants to purchase the financial derivative to receive more benefits. However, Option is the important component in the financial derivatives. Compared with Futures, Option can let investor feel more convenance since it acts as the contract. This research analyzes the price of the Rainbow Option in the Stock market. The Stock market includes two companies which are Pfizer and Walmart. The results shows that the Rainbow Option should be priced between max of call options and the sum of the options. It can testify the theory of rainbow Options‘ price successfully. Based on this research, the investor can understand the background and process of the rainbow Options‘ working. Combine with the feature of the rainbow options, the investor can make the proper investment decision in the different situations.
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Bae, Sung C., and Haim Levy. "The Valuation of Stock Purchase Rights as Call Options." Financial Review 29, no. 3 (August 1994): 419–40. http://dx.doi.org/10.1111/j.1540-6288.1994.tb00404.x.
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Schober, Peter, and Martin Wagener. "Arbitrage potential in the Eurex order book – evidence from the financial crisis in 2008." Risk Governance and Control: Financial Markets and Institutions 5, no. 4 (2015): 300–313. http://dx.doi.org/10.22495/rgcv5i4c2art4.
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In this paper we investigate the valuation efficiency of the Eurex market for DAX single stock options. As a measure of arbitrage potential we use an adapted version of Stoll’s put-call parity model. By calculating deviations from the theoretical fair put and call prices before and during the financial crisis in 2008, we find evidence for a decrease in market’s valuation efficiency. Valuation efficiency is even worse for German financial stocks for which short selling was restricted. Although considerable profit opportunities are found, only a small number turn out to be profitable after transaction costs are considered. Our research complements the existing research by investigating American type stock options on a fully electronic exchange in both, volatile and stable markets.
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Jaramillo-Restrepo, Juan Andrés, Miguel Jiménez-Gómez, and Natalia Acevedo-Prins. "Stock portfolio hedging with financial options." Indonesian Journal of Electrical Engineering and Computer Science 19, no. 3 (September 1, 2020): 1436. http://dx.doi.org/10.11591/ijeecs.v19.i3.pp1436-1443.
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<span lang="EN-US">The financial market currently offers derivative products whose characteristics allow investors to reduce the negative impact of natural market fluctuations on the value of their assets. Hedging with financial options is one of the possible strategies that an investor can implement in order to reduce the exposure or risk of their investments. This paper aims to assess the real impact of financial options as a hedging instrument on an investment portfolio made up of variable income assets of the Colombian market. The results show that for options with an upward trend, call options allow future losses to be hedged; on the other hand, for bearish trends, coverage is made with put options.</span>
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Chirima, Justin, Eriyoti Chikodza, and Senelani Dorothy Hove-Musekwa. "Uncertain Stochastic Option Pricing in the Presence of Uncertain Jumps." International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 27, no. 04 (July 23, 2019): 613–35. http://dx.doi.org/10.1142/s0218488519500272.
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In this paper, a new differential equation, driven by aleatory and epistemic forms of uncertainty, is introduced and applied to describe the dynamics of a stock price process. This novel class of differential equations is called uncertain stochastic differential equations(USDES) with uncertain jumps. The existence and uniqueness theorem for this class of differential equations is proposed and proved. An appropriate version of the chain rule is derived and applied to solve some examples of USDES with uncertain jumps. The differential equation discussed is applied in an American call option pricing problem. In this problem, it is assumed that the evolution of the stock price is driven by a Brownian motion, the Liu canonical process and an uncertain renewal process. MATLAB is employed for implementing the derived option pricing model. Results show that option prices from the proposed call option pricing formula increase as the jump size increases. As compared to the proposed call option pricing formula, the Black-Scholes overprices options for a certain range of strike prices and under-prices the same options for another range of exercise prices when the jump size is zero.
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PITRAYANI, NI KADEK LANI, KOMANG DHARMAWAN, and I. NYOMAN WIDANA. "PENENTUAN KONTRAK OPSI TIPE EROPA MENGGUNAKAN MODEL SIMULASI VARIANCE GAMMA (VG)." E-Jurnal Matematika 12, no. 3 (August 23, 2023): 182. http://dx.doi.org/10.24843/mtk.2023.v12.i03.p417.
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Options are used as a hedge against stock price uncertainty brought on by unstable stock prices fluctuation. The price of an option contract can be determined using a variety of approaches, one of which is the Variance Gamma. The purpose of this study is to compare the Black Scholes method with the Variance Gamma simulation model to determine the European call option contract price. The first thing that needs to be done is to figure out the moment variance gamma method. These parameters were used as initial values to get an idea of what the parameters that will be used in the simulation will be like. The European call option contract's price is calculated using the simulation results, which are then compared to the Variance Gamma simulation model and the Black Scholes model for the European call option contract. This study shows that the European call option contract's price, which was calculated using the Variance Gamma simulation, is less expensive than the Black Scholes contract's price.
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Zhang, Lidong, Yanmei Sun, and Xiangbo Meng. "European Spread Option Pricing with the Floating Interest Rate for Uncertain Financial Market." Mathematical Problems in Engineering 2020 (May 21, 2020): 1–8. http://dx.doi.org/10.1155/2020/2015845.
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In this paper, we investigate the pricing problems of European spread options with the floating interest rate. In this model, uncertain differential equation and stochastic differential equation are used to describe the fluctuation of stock price and the floating interest rate, respectively. We derive the pricing formulas for spread options including the European spread call option and the European spread put option. Finally, numerical algorithms are provided to illustrate our results.
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BÄUERLE, NICOLE, and DANIEL SCHMITHALS. "CONSISTENT UPPER PRICE BOUNDS FOR EXOTIC OPTIONS." International Journal of Theoretical and Applied Finance 24, no. 02 (March 2021): 2150011. http://dx.doi.org/10.1142/s0219024921500114.
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We consider the problem of finding a consistent upper price bound for exotic options whose payoff depends on the stock price at two different predetermined time points (e.g. Asian option), given a finite number of observed call prices for these maturities. A model-free approach is used, only taking into account that the (discounted) stock price process is a martingale under the no-arbitrage condition. In case the payoff is directionally convex we obtain the worst case marginal pricing measures. The speed of convergence of the upper price bound is determined when the number of observed stock prices increases. We illustrate our findings with some numerical computations.
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Anderson, Chris K., and Neil Brisley. "Employee Stock Options: An Up-and-Out Protected Barrier Call." Applied Mathematical Finance 16, no. 4 (October 2009): 347–52. http://dx.doi.org/10.1080/13504860902753251.
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Mo, Di, Neda Todorova, and Rakesh Gupta. "Implied volatility smirk and future stock returns: evidence from the German market." Managerial Finance 41, no. 12 (December 7, 2015): 1357–79. http://dx.doi.org/10.1108/mf-04-2015-0097.
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Purpose – The purpose of this paper is to investigate the relationship between option’s implied volatility smirk (IVS) and excess returns in the Germany’s leading stock index Deutscher-Aktien Index (DAX) 30. Design/methodology/approach – The study defines the IVS as the difference in implied volatility derived from out-of-the-money put options and at-the-money call options. This study employs the ordinary least square regression with Newey-West correction to analyse the relationship between IVS and excess DAX 30 index returns in Germany. Findings – The authors find that the German market adjusts information in an efficient way. Consequently, there is no information linkage between option volatility smirk and market index returns over the nine years sample period after considering the control variables, global financial crisis dummies, and the subsample test. Research limitations/implications – This study finds that the option market and the DAX 30 index are informationally efficient. Implications of the findings are that the investors cannot profit from the information contained in the IVS since the information is simultaneously incorporated into option prices and the stock index prices. The findings of this study are applicable to other markets with European options and for market participants who seek to exploit short-term market divergence from efficiency. Originality/value – The relationship between IVS and stock price changes has not been investigated sufficiently in academic literature. This study looks at this relationship in the context of European options using high-frequency transactions data. Prior studies look at this relationship for only American options using daily data. Pricing efficiency of the European option market using high-frequency data have not been studied in the prior literature. The authors find different results for the German market based on this high-frequency data set.
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Höcht, Stephan, Dilip B. Madan, Wim Schoutens, and Eva Verschueren. "It Takes Two to Tango: Estimation of the Zero-Risk Premium Strike of a Call Option via Joint Physical and Pricing Density Modeling." Risks 9, no. 11 (November 4, 2021): 196. http://dx.doi.org/10.3390/risks9110196.
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It is generally said that out-of-the-money call options are expensive and one can ask the question from which moneyness level this is the case. Expensive actually means that the price one pays for the option is more than the discounted average payoff one receives. If so, the option bears a negative risk premium. The objective of this paper is to investigate the zero-risk premium moneyness level of a European call option, i.e., the strike where expectations on the option’s payoff in both the P- and Q-world are equal. To fully exploit the insights of the option market we deploy the Tilted Bilateral Gamma pricing model to jointly estimate the physical and pricing measure from option prices. We illustrate the proposed pricing strategy on the option surface of stock indices, assessing the stability and position of the zero-risk premium strike of a European call option. With small fluctuations around a slightly in-the-money level, on average, the zero-risk premium strike appears to follow a rather stable pattern over time.
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Huang, Xiaoxia, and Xuting Wang. "Portfolio Investment with Options Based on Uncertainty Theory." International Journal of Information Technology & Decision Making 18, no. 03 (May 2019): 929–52. http://dx.doi.org/10.1142/s0219622019500159.
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In financial markets, there are situations where investors have the future stock prices according to the experts’ evaluations rather than historical data. Thus, the estimations of the stock prices contain much subjective imprecision instead of randomness. This paper discusses a portfolio investment with options in such a kind of situation. Treating the stock index price as an uncertain variable, we build an uncertain mean-chance portfolio model based on uncertainty theory and provide the equivalent form of the model. Furthermore, we make a comparison of the optimal expected return between portfolio investment with options and without options. An important conclusion is reached: The portfolio investment with options produces a no less expected return than that without options. In addition, we make sensitivity analysis and get two vital corresponding results. As an illustration, a numerical example is presented as well. The numerical results reveal that the options should be considered in portfolio investment. And the call option with maximum exercise price is most valuable per premium cost with the same exercise date.
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ALGHALITH, MOAWIA, CHRISTOS FLOROS, and THOMAS POUFINAS. "SIMPLIFIED OPTION PRICING TECHNIQUES." Annals of Financial Economics 14, no. 01 (February 13, 2019): 1950003. http://dx.doi.org/10.1142/s2010495219500039.
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In this paper we provide alternative methods for pricing European and American call and put options. Our contribution lies in the simplification attempted in the models developed. Such simplification is feasible due to our observation that the value of the option can be derived as a function of the underlying stock price, strike price and time to maturity. This route is supported by the fact that both the risk-free rate and the volatility of the stock are captured by the move of the underlying stock price. Moreover, looking at the properties of the Brownian motion, widely used to map the move of the stock price, we realize that volatility is well depicted by time. Last but not the least, the value of an option is an increasing function of both time and volatility. We find simplified option pricing formulas depending on the underlying asset (price and strike price) and the time to maturity only. We test our formulas against the S&P 500 index options; the advantage of the approach is that less simplifying assumptions are needed and much simpler methods are produced. We provide alternative formulas for pricing European- and American-type options.
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Kwark, Noe-Keol, Hyoung-Goo Kang, and Sang-Gyung Jun. "Can Derivative Information Predict Stock Price Jumps?" Journal of Applied Business Research (JABR) 31, no. 3 (May 1, 2015): 845. http://dx.doi.org/10.19030/jabr.v31i3.9222.
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<p>This study examines the predictability of jumps in stock prices using options-trading information, the futures basis spread, the cross-sectional standard deviation of returns on components in the stock index, and exchange rates. A stock price jump was defined as a large fluctuation in the stock price that deviated from the distribution thresholds of the past rates of return. This empirical analysis shows that the implied volatility spread between ATM call and put options was a significant predictor for both upward and downward jumps, whereas the volatility skew was less significant. In addition, the futures basis spread was moderately significant for downward stock price jumps. Both the cross-sectional standard deviation of the rates of return on component stocks in the KOSPI 200 and the won-dollar exchange rates were significant predictors for both upward and downward jumps.</p>
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Fadhilla, Putri, and Rudianto Artiono. "PENGGUNAAN STRATEGI HEDGING (LINDUNG NILAI) PADA PEMODELAN OPSI SAHAM KARYAWAN YANG MENGALAMI PERGERAKAN PERDAGANGAN SECARA STATIS DAN DINAMIS." MATHunesa: Jurnal Ilmiah Matematika 9, no. 3 (December 31, 2021): 532–41. http://dx.doi.org/10.26740/mathunesa.v9n3.p532-541.
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Abstrak
Artikel ini bertujuan untuk memodelkan opsi saham karyawan yang mengalami pergerakan perdagangan secara statis dan dinamis menggunakan strategi hedging (lindung nilai). Hedging (lindung nilai) merupakan tindakan yang dilakukan untuk melindungi aset ataupun hutang sebuah perusahaan dari exposure terhadap perubahan nilai tukar sehingga dapat mengurangi atau meniadakan resiko pada suatu investasi di bursa saham. Strategi ini digunakan untuk melindungi nilai keuangan jangka panjang pada aset non liquid seperti opsi saham. Opsi saham merupakan suatu perjanjian yang memungkinkan pemiliknya untuk melakukan call (menjual) atau put (membeli) suatu saham dengan harga yang telah ditentukan pada waktu tertentu. Salah satu jenis opsi saham adalah opsi saham karyawan. Pemegang opsi saham karyawan dapat memaksimalkan keuntungan dan meminimalkan kerugian dari aset yang diperjualbelikan dengan melakukan lindung nilai. Metode ini menggabungkan antara pergerakan perdagangan dinamis dari aset liquid yang saling berkorelasi dan posisi statis dalam opsi yang diperdagangkan di bursa saham. Strategi lindung nilai statis-dinamis ini mengarah pada masalah kontrol stokastik dan Persamaan Diferensial Parsial Hamilton-Jacobi-Bellman melalui serangkaian transformasi yang dapat dilakukan untuk menyederhanakan masalah dan menghitung strategi lindung nilai yang optimal. Penelitian ini menghasilkan model matematika yang dapat digunakan untuk menentukan harga yang wajar dari suatu opsi saham karyawan yang mengalami pergerakan perdagangan secara statis dan dinamis.
Kata Kunci: Opsi Saham Karyawan, Strategi Hedging, PDP Hamilton-Jacobi-Bellman.
Abstract
This article aims to model employee stock options that experience trading movements statically and dynamically using a hedging strategy. Hedging is an action taken to protect a company's assets or debts from exposure to changes in exchange rates so as to reduce or eliminate the risk of an investment in the stock market. This strategy is used to protect the long-term financial value of non-liquid assets such as stock options. A stock option is an agreement that allows the owner to call (sell) or put (buy) a stock at a predetermined price at a certain time. One type of stock options is employee stock options. Holders of employee stock options can maximize profits and minimize losses from the assets traded by hedging. This method combines dynamic trading movements of correlated liquid assets and static positions in options traded on the stock exchange. This static-dynamic hedging strategy leads to the problem of stochastic control and the Hamilton-Jacobi-Bellman Partial Differential Equation through a series of transformations that can be performed to simplify the problem and calculate the optimal hedging strategy. This research produces a mathematical model that can be used to determine the fair price of an employee stock option that experiences static and dynamic trading movements.
Keywords: Employee Stock Option, Hedging Strategy, PDE Hamilton-Jacobi-Bellman.
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Gardner, John C., and Carl B. McGowan Jr. "Valuing Coca-Cola And PepsiCo Options Using The Black-Scholes Option Pricing Model And Data Downloads From The Internet." Journal of Business Case Studies (JBCS) 8, no. 6 (October 29, 2012): 559–64. http://dx.doi.org/10.19030/jbcs.v8i6.7377.
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In this paper, we demonstrate how to collect the data and compute the actual value of Black-Scholes Option Pricing Model call option prices for Coca-Cola and PepsiCo.The data for the current stock price and option price are taken from Yahoo Finance and the daily returns variance is computed from daily prices.The time to maturity is computed as the number of days remaining for the stock option.The risk-free rate is obtained from the U.S. Treasury website.
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Guo, Xin, and Larry Shepp. "Some optimal stopping problems with nontrivial boundaries for pricing exotic options." Journal of Applied Probability 38, no. 3 (September 2001): 647–58. http://dx.doi.org/10.1239/jap/1005091029.
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We solve the following three optimal stopping problems for different kinds of options, based on the Black-Scholes model of stock fluctuations. (i) The perpetual lookback American option for the running maximum of the stock price during the life of the option. This problem is more difficult than the closely related one for the Russian option, and we show that for a class of utility functions the free boundary is governed by a nonlinear ordinary differential equation. (ii) A new type of stock option, for a company, where the company provides a guaranteed minimum as an added incentive in case the market appreciation of the stock is low, thereby making the option more attractive to the employee. We show that the value of this option is given by solving a nonalgebraic equation. (iii) A new call option for the option buyer who is risk-averse and gets to choose, a priori, a fixed constant l as a ‘hedge’ on a possible downturn of the stock price, where the buyer gets the maximum of l and the price at any exercise time. We show that the optimal policy depends on the ratio of x/l, where x is the current stock price.
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Guo, Xin, and Larry Shepp. "Some optimal stopping problems with nontrivial boundaries for pricing exotic options." Journal of Applied Probability 38, no. 03 (September 2001): 647–58. http://dx.doi.org/10.1017/s0021900200018817.
Full textAbstract:
We solve the following three optimal stopping problems for different kinds of options, based on the Black-Scholes model of stock fluctuations. (i) The perpetual lookback American option for the running maximum of the stock price during the life of the option. This problem is more difficult than the closely related one for the Russian option, and we show that for a class of utility functions the free boundary is governed by a nonlinear ordinary differential equation. (ii) A new type of stock option, for a company, where the company provides a guaranteed minimum as an added incentive in case the market appreciation of the stock is low, thereby making the option more attractive to the employee. We show that the value of this option is given by solving a nonalgebraic equation. (iii) A new call option for the option buyer who is risk-averse and gets to choose, a priori, a fixed constant l as a ‘hedge’ on a possible downturn of the stock price, where the buyer gets the maximum of l and the price at any exercise time. We show that the optimal policy depends on the ratio of x/l, where x is the current stock price.
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Biebuyck, Anton, and Johan H. Van Rooyen. "Valuing put options on single stock futures: Does the put-call parity relationship hold in the South African derivatives market?" Risk Governance and Control: Financial Markets and Institutions 4, no. 4 (2014): 107–19. http://dx.doi.org/10.22495/rgcv4i4c1art5.
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This study attempts to determine whether mispricing of options on single stock futures is present in the South African derivatives market. The valuation of options on single stock futures is considered through the put-call parity relationship. The theoretical fair values obtained, are compared to the actual market values over a period of three years, that is, from 2009 to 2011. Only put options are considered in this research.The results show that arbitrage put option opportunities do present themselves for the chosen shares. The actual put options were found to be underpriced in 5 out of 6 (83%) of the cases considered over the evaluation periods chosen. The mispricing was significant for both the BHP Billiton options with 100% and in the case of Sasol options (66%) of the time. Whether profitable arbitrage opportunities is possible, will depend on the magnitude of the mispricing and the transaction fees payable. Further, more extensive research may help identify tendencies which may be of use for the formulation of arbitrage strategies.
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Lee, Jaeram. "Information Contents of Order Flow Toxicity in the Options Market : The Case of KOSPI200 Index Options." Journal of Derivatives and Quantitative Studies 27, no. 4 (November 30, 2019): 365–400. http://dx.doi.org/10.1108/jdqs-04-2019-b0001.
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This study estimates the VPIN (volume-synchronized probability of informed trading) of the KOSPI200 index options, the measure of order flow toxicity suggested by Easley et al. (2012), for the first time. To apply the VPIN approach, options are categorized by their real-time moneyness. I examine the predictive power of VPIN for the future stock market volatility using time-series regression analysis. The empirical result shows that the toxic order flow measure estimated by price changes has more information than that estimated by the actual order imbalance. In general, put options contain more information than call options, and the toxic order flow measure of OTM (out-of-the-money) put options contains the most significant information about the future stock market volatility. In addition, the predictive power of toxic order flow measure is much significant in the highly volatile than in the stable market. The volatility predictability of toxic order flow measure declined significantly after the option multiplier increase, whereas it has gradually recovered over time.
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Megawati, Megawati, and Rudianto Artiono. "Pemodelan Opsi Saham Karyawan Menggunakan Pendekatan Top-Down." MATHunesa: Jurnal Ilmiah Matematika 9, no. 3 (December 31, 2021): 524–31. http://dx.doi.org/10.26740/mathunesa.v9n3.p524-531.
Full textAbstract:
Abstrak
Opsi saham merupakan suatu perjanjian yang memungkinkan pemiliknya untuk melakukan call (menjual) atau put (membeli) suatu saham dengan harga yang telah ditentukan pada waktu tertentu. Salah satu jenis opsi saham adalah opsi saham karyawan (OSK) atau yang lebih dikenal dengan Employee Stock Options (ESO). Pemegang OSK dapat melakukan exercise opsi lebih awal setelah melewati vesting period dan secara bertahap melakukan exercise terhadap opsi yang tersisa sebelum maturity time. Penelitian ini bertujuan untuk memodelkan harga opsi saham karyawan melalui suatu analisis fundamental yakni analisis yang mempelajari hal-hal yang berhubungan dengan kondisi keuangan atau perusahaan dan umumnya digunakan untuk menentukan saham yang ingin dijual atau dibeli dengan menggunakan pendekatan top-down. Pendekatan ini diperlukan oleh perusahaan yang memiliki saling ketergantungan antar unit operasi dalam rangka meningkatkan koordinasi antara manager dan karyawan. Perspektif perusahaan untuk menentukan harga OSK umumnya melibatkan banyak opsi dengan jangka waktu lama. Untuk menghitung harga OSK, disajikan dua metode numerik yaitu transformasi fast fourier dilanjutkan dengan metode beda hingga untuk memecahkan sistem persamaan diferensial parsial terkait dengan opsi vested dan unvested. Metode numerik yang diusulkan tidak hanya berlaku untuk pengeluaran harga OSK, tetapi juga berguna untuk memahami efek gabungan dari intensitas exercise dan risiko pemutusan hubungan kerja pada penentuan harga OSK.
Kata Kunci: Employee Stock Options, Pendekatan Top-down, Fast Fourier Transformation, Metode Beda Hingga.
Abstract
A stock option is an agreement that allows the owner to call (sell) or put (buy) a stock at a predetermined price at a certain time. One type of stock options is employee stock options (OSK) or better known as Employee Stock Options (ESO). OSK holders can exercise options earlier after the vesting period and gradually exercise the remaining options before maturity. This study aims to model the price of employee stock options through a fundamental analysis, namely an analysis that studies matters relating to the financial condition of the company and is generally used to determine which shares to sell or buy using a top-down approach. This approach is needed by companies that have interdependence between operating units in order to improve coordination between managers and employees. The company's perspective for pricing OSK generally involves many long-term options. To calculate the OSK price, two numerical methods are presented, namely the fast Fourier transformation followed by the finite difference method to solve the system of partial differential equations related to vested and unvested options. The proposed numerical method is not only applicable to OSK pricing, but is also useful for understanding the combined effect of exercise intensity and risk of termination of employment on OSK pricing.
Keywords: Employee Stock Options, Top-down Approach, Fast Fourier Transformation, Finite Difference Method.
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Ibrahim, Siti Nur Iqmal, Adem Kilicman, and Mohamed Faris Laham. "Analytical Formula of European-Style Power Call Options in an MFBM with Jumps Model." Journal of Engineering and Science Research 6, no. 6 (December 30, 2022): 84–87. http://dx.doi.org/10.26666/rmp.jesr.2022.6.8.
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Studies have shown that stock price process exhibits long-range dependence. To address this, many have introduced the mixed-fractional Brownian motion (MFBM) model to the stock price process. Under risk-neutral measure, this study provides an analytical formula for the price of European-style power call options in an MFBM environment with the inclusion of the jumps process. Modeling the stock price with MFBM and jumps process enables the capturing of long memory trend as well as discontinuity in the stock price process.
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Félix, Luiz, Roman Kräussl, and Philip Stork. "Single Stock Call Options as Lottery Tickets: Overpricing and Investor Sentiment." Journal of Behavioral Finance 20, no. 4 (January 22, 2019): 385–407. http://dx.doi.org/10.1080/15427560.2018.1511792.
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Ma, Guiyuan, Song-Ping Zhu, and Wenting Chen. "Pricing European call options under a hard-to-borrow stock model." Applied Mathematics and Computation 357 (September 2019): 243–57. http://dx.doi.org/10.1016/j.amc.2019.04.002.
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Pukthuanthong, Kuntara, and Thomas Walker. "On the pros and cons of employee stock options: What are the alternatives?" Corporate Ownership and Control 4, no. 1 (2006): 266–83. http://dx.doi.org/10.22495/cocv4i1c2p3.
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Despite theoretical validity, there is mixed empirical evidence on whether employee stock options align the interests of management and shareholders by turning managers into owners. Yet, recent accounting scandals, excessive payouts, and the public’s call for a proper recognition of stock option grants have produced considerable debate in boardrooms and the financial press about the desirability of using stock options. This paper provides an overview of the empirical research in the field and discusses the advantages and disadvantages of using stock options as part of an employee’s compensation package. In light of the recent accounting scandals, regulatory bodies have been hard pressed to change the accounting treatment and recognition of stock options. As a result, practitioners and academics are increasingly on the lookout for alternative forms of compensation tools. To aid in the ongoing discussion, we propose a number of alternative compensation tools that help alleviate some of the problems inherent in stock options, while still rewarding a manager for his performance and aligning management and shareholder incentives. While there is no clear-cut answer as to what compensation tool is best, our study should provide corporate managers with the necessary insights that are needed to choose the method that most closely meets their objectives. In addition, our study aims to open the door for further academic discussion that is required to address a number of questions that remain unanswered in this area
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Huang, Hong, and Yufu Ning. "Risk-Neutral Pricing Method of Options Based on Uncertainty Theory." Symmetry 13, no. 12 (December 1, 2021): 2285. http://dx.doi.org/10.3390/sym13122285.
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In order to rationally deal with the belief degree, Liu proposed uncertainty theory and refined into a branch of mathematics based on normality, self-duality, sub-additivity and product axioms. Subsequently, Liu defined the uncertainty process to describe the evolution of uncertainty phenomena over time. This paper proposes a risk-neutral option pricing method under the assumption that the stock price is driven by Liu process, which is a special kind of uncertain process with a stationary independent increment. Based on uncertainty theory, the stock price’s distribution and inverse distribution function under the risk-neutral measure are first derived. Then these two proposed functions are applied to price the European and American options, and verify the parity relationship of European call and put options.
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Kim, Suhkyong. "Financial Crisis, Put-Call Parity and Momentum Effect." Journal of Derivatives and Quantitative Studies 22, no. 1 (February 28, 2014): 141–59. http://dx.doi.org/10.1108/jdqs-01-2014-b0007.
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This study investigates the deviation from put-call parity in the KOSPI200 options market. The sample period is from January 2, 2006 to May 31, 2009. Due to the financial crisis in 2008, short sale of stocks had been prohibited from October 1, 2008 to May 31, 2009. The sample is divided into the pre-crisis period and the crisis period. The crisis period is the period during which short sale of stocks are prohibited. The summary statistics shows that the trading volume of KOSPI200 stocks doubled, but the trading volume of call options and that of put options declined to one half and one third from the pre-crisis period to the crisis period, respectively. The equation which relates the deviation of futures price to the deviation of put-call parity is derived and the deviation from put-call parity is analyzed by using two stage least square. This paper looks into not only the prior 60 day return's momentum effect, but also the intraday spot return's momentum effect. Evidence indicates that the intraday momentum does exist in options and stock prices. Empirical results show that the prior 60 day return's momentum effect is statistically insignificant during the pre-crisis period, but statistically significant during the crisis period whereas the intraday return's momentum effect is strongly significant for both of the periods. This result lends support to the argument that the deviation of futures price from its theoretical price is a component of the deviation from put-call parity. The sign and significance of the regression coefficient for momentum effects are consistent with Kim and Park (2011) and Kim (2012) again lending support to the validity of their regression equation. Overall, our results are consistent with the validity of the derived equation, Kim and Park (2011) and Kim (2013)’s rationale.
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Goard, Joanna, and Mohammed AbaOud. "Pricing European and American Installment Options." Mathematics 10, no. 19 (September 25, 2022): 3494. http://dx.doi.org/10.3390/math10193494.
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This paper derives accurate and efficient analytic approximations for the prices of both European and American continuous-installment call and put options. The solutions are in the form of series in time-to-expiry with explicit formulae for the coefficients provided. Unlike other solutions for installment options, no Laplace inverses are needed, and there is no need to solve complex, recursive systems or integral equations. The formulae provided fast yield and accurate solutions not just for the prices, but also for the critical boundaries. We also compare the solutions with those obtained using an existing method and show that it surpasses it delivering more correct option prices and critical stock prices.
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Seamer, Michael, and Adrian Melia. "Remunerating non-executive directors with stock options: who is ignoring the regulator?" Accounting Research Journal 28, no. 3 (November 2, 2015): 251–67. http://dx.doi.org/10.1108/arj-12-2013-0092.
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Purpose – This paper aims to investigate the incidence of remunerating Australian Securities Exchange (ASX)-listed non-executive directors (NEDs) with options and to determine whether companies that fail to adhere to NED remuneration recommendations share a common corporate governance profile. Despite corporate regulators condemning the practice of remunerating NEDs with stock options, there is a paucity of evidence regarding its prevalence in Australia. Design/methodology/approach – Focusing on ASX400 companies during 2008, a series of hypotheses relating NED stock option remuneration and corporate governance are tested using logistic regression. Findings – The study shows that the prevalence and quantum of NED option payments during 2008 was considerable with 73 of the ASX400 companies, including options in NED remuneration (option payers). Comparison of the corporate governance characteristics of option payers to that of a matched control group (non-option payers) highlighted both the existence and independence of the remuneration committee as critical in ensuring NED remuneration practices comply with regulator recommendations. Research limitations/implications – These results provide regulators and stakeholder groups with additional evidence to continue to call for corporate governance reforms to ensure that corporate remuneration practices are in the best interest of shareholders. Originality/value – This study is the first to highlight the extent to which Australian-listed company NED remuneration practices fail to comply with regulator recommendations and adds to the limited research on remuneration committee effectiveness.
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Shao, Zeyuan. "Pricing Technique for European Option and Application." Highlights in Business, Economics and Management 14 (June 12, 2023): 14–18. http://dx.doi.org/10.54097/hbem.v14i.8930.
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In financial mathematics, the pricing technique for derivatives is constantly debated. In this paper, the pricing technique of the European Option is mainly discussed, and the binomial tree (BN) model is first applied to the pricing process of European options. The previous results show that carbon credit index can be traded as an option, and BN model can correctly simulate the future price of call option constructed by consuming the carbon credit index. Secondly, the Black-Scholes (BN) model is also a crucial technique for pricing European options, and it is successfully applied to predicting the future three months' CSI 300 index option price. Finally, BN model is compared with BS model, and the result reflects that BN model can perform as well as BS model for pricing European Option When the step reaches 2000. However, the efficiency of the BN model is stable under low volatility. Under higher volatility, such as 1.5 sigmas, the required steps will increase to achieve the same accuracy level. For American options, the BN simulator of a put option is close to the actual value, but the call option simulator will fluctuate. For the stock-pricing process, both models estimate far above Monte-Carlo method. The result of this paper is to provide some clues for pricing European options with different methods.