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Journal articles on the topic 'Option Pricing'

Author: Grafiati

Published: 4 June 2021

Last updated: 7 September 2023

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1

Jensen, Bjarne Astrup, and Jørgen Aase Nielsen. "OPTION PRICING BOUNDS AND THE PRICING OF BOND OPTIONS." Journal of Business Finance & Accounting 23, no. 4 (June 1996): 535–56. http://dx.doi.org/10.1111/j.1468-5957.1996.tb01025.x.

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2

Li, Feng. "Option Pricing." Journal of Derivatives 7, no. 4 (May 31, 2000): 49–65. http://dx.doi.org/10.3905/jod.2000.319134.

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3

Lord, Richard. "Option pricing." Journal of Banking & Finance 10, no. 1 (March 1986): 157–61. http://dx.doi.org/10.1016/0378-4266(86)90028-2.

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4

Mitra, Sovan. "Multifactor option pricing: pricing bounds and option relations." International Journal of Applied Decision Sciences 3, no. 1 (2010): 15. http://dx.doi.org/10.1504/ijads.2010.032238.

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5

Blake, D. "Option pricing models." Journal of the Institute of Actuaries 116, no. 3 (December 1989): 537–58. http://dx.doi.org/10.1017/s0020268100036696.

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6

Guo, Yuanyuan. "Comparative Analysis of the Application of Monte Carlo Model and BSM Model in European Option Pricing." BCP Business & Management 32 (November 22, 2022): 43–48. http://dx.doi.org/10.54691/bcpbm.v32i.2856.

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At present, the expansion of China's domestic options market brings positive factors and risks, and in order to avoid risks, it is crucial to choose a suitable model for option pricing. This article provides an example of an option for the underlying asset of the SSE 50 ETF. Using the BSM model and the Monte Carlo model for the selected option pricing, and comparing the actual option price. It is found that the pricing efficiency of the Monte Carlo model is higher than that of the BSM model when the number of simulations reaches 30,000 times in the call option, and there is little difference between the two in the put option pricing. It is recommended to prefer the Monte Carlo model when pricing call options and the more convenient BSM model when pricing put options.

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7

Ryszard, Kokoszczyński, Sakowski Paweł, and Ślepaczuk Robert. "Which Option Pricing Model Is the Best? HF Data for Nikkei 225 Index Options." Central European Economic Journal 4, no. 51 (April 1, 2019): 18–39. http://dx.doi.org/10.1515/ceej-2018-0010.

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Abstract In this study, we analyse the performance of option pricing models using 5-minutes transactional data for the Japanese Nikkei 225 index options. We compare 6 different option pricing models: the Black (1976) model with different assumptions about the volatility process (realized volatility with and without smoothing, historical volatility and implied volatility), the stochastic volatility model of Heston (1993) and the GARCH(1,1) model. To assess the model performance, we use median absolute percentage error based on differences between theoretical and transactional options prices. We present our results with respect to 5 classes of option moneyness, 5 classes of option time to maturity and 2 option types (calls and puts). The Black model with implied volatility (BIV) comes as the best and the GARCH(1,1) as the worst one. For both call and put options, we observe the clear relation between average pricing errors and option moneyness: high error values for deep OTM options and the best fit for deep ITM options. Pricing errors also depend on time to maturity, although this relationship depend on option moneyness. For low value options (deep OTM and OTM), we obtained lower errors for longer maturities. On the other hand, for high value options (ITM and deep ITM) pricing errors are lower for short times to maturity. We obtained similar average pricing errors for call and put options. Moreover, we do not see any advantage of much complex and time-consuming models. Additionally, we describe liquidity of the Nikkei225 option pricing market and try to compare the results we obtain here with a detailed study for Polish emerging option market (Kokoszczyński et al. 2010b).

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8

Behera, Prashanta kumar, and Dr Ramraj T. Nadar. "Dynamic Approach for Index Option Pricing Using Different Models." Journal of Global Economy 13, no. 2 (June 26, 2017): 105–20. http://dx.doi.org/10.1956/jge.v13i2.460.

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Option pricing is one of the exigent and elementary problems of computational finance. Our aims to determine the nifty index option price through different valuation technique.Â In this paper, we illustrate the techniques for pricing of options and extracting information from option prices. We also describe various ways in which this information has been used in a number of applications. When dealing with options, we inevitably encounter the Black-Scholes-Merton option pricing formula, which has revolutionized the way in which options are priced in modern time. Black and Scholes (1973) and Merton (1973) on pricing European style options assumes that stock price follows a geometric Brownian motion, which implies that the terminal stock price has a lognormal distribution. Through hedging arguments, BSM shows that the terminal stock price distribution needed for pricing option can be stated without reference to the preference parameter and to the growth rate of the stock. This is now known as the risk-neutral approach to option pricing. The terminal stock price distribution, for the purpose of pricing options, is now known as the state-price density or the risk-neutral density in contrast to the actual stock price distribution, which is sometimes referred to as the physical, objective, or historical distribution.

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9

Stamatopoulos, Nikitas, Daniel J. Egger, Yue Sun, Christa Zoufal, Raban Iten, Ning Shen, and Stefan Woerner. "Option Pricing using Quantum Computers." Quantum 4 (July 6, 2020): 291. http://dx.doi.org/10.22331/q-2020-07-06-291.

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We present a methodology to price options and portfolios of options on a gate-based quantum computer using amplitude estimation, an algorithm which provides a quadratic speedup compared to classical Monte Carlo methods. The options that we cover include vanilla options, multi-asset options and path-dependent options such as barrier options. We put an emphasis on the implementation of the quantum circuits required to build the input states and operators needed by amplitude estimation to price the different option types. Additionally, we show simulation results to highlight how the circuits that we implement price the different option contracts. Finally, we examine the performance of option pricing circuits on quantum hardware using the IBM Q Tokyo quantum device. We employ a simple, yet effective, error mitigation scheme that allows us to significantly reduce the errors arising from noisy two-qubit gates.

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10

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.

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11

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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12

Li, Songsong, Yinglong Zhang, and Xuefeng Wang. "The Sunk Cost and the Real Option Pricing Model." Complexity 2021 (September 30, 2021): 1–12. http://dx.doi.org/10.1155/2021/3626000.

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Although the academic literature on real options has grown enormously over the past three decades, hitherto an accurate real option pricing model has not been developed for investment decision analyses. In this paper, we propose a real option pricing model based on sunk cost characteristics, which can estimate the value of real options more accurately. First, we explore the distinctive features that distinguish real options from financial options. The study shows that the distinguishing feature of the real options is the sunk cost, which does not exist in the financial options. Based on the sunk cost characteristic of real options, we find that the exercise conditions of real and financial options are different. Second, we introduce the sunk cost into the intrinsic value function of real options and establish a new real option pricing model. Finally, this paper also discusses the properties of the intrinsic value function and pricing model of real options. We find that the application of the Black–Scholes option pricing model will overestimate the value of real options.

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13

Amin, Kaushik. "Option Pricing Trees." Journal of Derivatives 2, no. 4 (May 31, 1995): 34–46. http://dx.doi.org/10.3905/jod.1995.407926.

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14

Madan, Dilip B., and Wim Schoutens. "Conic Option Pricing." Journal of Derivatives 25, no. 1 (August 31, 2017): 10–36. http://dx.doi.org/10.3905/jod.2017.25.1.010.

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15

Bieta, Volker, Udo Broll, and Wilfried Siebe. "Strategic Option Pricing." Economics and Business Review 6 (20), no. 3 (2020): 118–29. http://dx.doi.org/10.18559/ebr.2020.3.7.

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In this paper an extension of the well-known binomial approach to option pricing is presented. The classical question is: What is the price of an option on the risky asset? The traditional answer is obtained with the help of a replicating portfolio by ruling out arbitrage. Instead a two-person game from the Nash equilibrium of which the option price can be derived is formulated. Consequently both the underlying asset’s price at expiration and the price of the option on this asset are endogenously determined. The option price derived this way turns out, however, to be identical to the classical no-arbitrage option price of the binomial model if the expiration-date prices of the underlying asset and the corresponding risk-neutral probability are properly adjusted according to the Nash equilibrium data of the game.

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16

Carvalho, Vitor H., and Raquel M. Gaspar. "Relativistic Option Pricing." International Journal of Financial Studies 9, no. 2 (June 18, 2021): 32. http://dx.doi.org/10.3390/ijfs9020032.

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The change of information near light speed, advances in high-speed trading, spatial arbitrage strategies and foreseen space exploration, suggest the need to consider the effects of the theory of relativity in finance models. Time and space, under certain circumstances, are not dissociated and can no longer be interpreted as Euclidean. This paper provides an overview of the research made in this field while formally defining the key notions of spacetime, proper time and an understanding of how time dilation impacts financial models. We illustrate how special relativity modifies option pricing and hedging, under the Black–Scholes model, when market participants are in two different reference frames. In particular, we look into maturity and volatility relativistic effects.

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17

Wang, Tai-Ho. "Nonlinear Option Pricing." Quantitative Finance 15, no. 1 (July 14, 2014): 19–21. http://dx.doi.org/10.1080/14697688.2014.931594.

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18

McCauley, J. L., G. H. Gunaratne, and K. E. Bassler. "Martingale option pricing." Physica A: Statistical Mechanics and its Applications 380 (July 2007): 351–56. http://dx.doi.org/10.1016/j.physa.2007.02.038.

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19

Bandi, Chaithanya, and Dimitris Bertsimas. "Robust option pricing." European Journal of Operational Research 239, no. 3 (December 2014): 842–53. http://dx.doi.org/10.1016/j.ejor.2014.06.002.

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20

Chalasani, P., S. Jha, and I. Saias. "Approximate Option Pricing." Algorithmica 25, no. 1 (May 1999): 2–21. http://dx.doi.org/10.1007/pl00009280.

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21

Lin, Yueh-Neng, and Chien-Hung Chang. "VIX option pricing." Journal of Futures Markets 29, no. 6 (June 2009): 523–43. http://dx.doi.org/10.1002/fut.20387.

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22

Husmann, Sven, and Neda Todorova. "CAPM option pricing." Finance Research Letters 8, no. 4 (December 2011): 213–19. http://dx.doi.org/10.1016/j.frl.2011.03.001.

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23

Bhat, Aparna, and Kirti Arekar. "Empirical Performance of Black-Scholes and GARCH Option Pricing Models during Turbulent Times: The Indian Evidence." International Journal of Economics and Finance 8, no. 3 (February 26, 2016): 123. http://dx.doi.org/10.5539/ijef.v8n3p123.

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Exchange-traded currency options are a recent innovation in the Indian financial market and their pricing is as yet unexplored. The objective of this research paper is to empirically compare the pricing performance of two well-known option pricing models – the Black-Scholes-Merton Option Pricing Model (BSM) and Duan’s NGARCH option pricing model – for pricing exchange-traded currency options on the US dollar-Indian rupee during a recent turbulent period. The BSM is known to systematically misprice options on the same underlying asset but with different strike prices and maturities resulting in the phenomenon of the ‘volatility smile’. This bias of the BSM results from its assumption of a constant volatility over the option’s life. The NGARCH option pricing model developed by Duan is an attempt to incorporate time-varying volatility in pricing options. It is a deterministic volatility model which has no closed-form solution and therefore requires numerical techniques for evaluation. In this paper we have compared the pricing performance and examined the pricing bias of both models during a recent period of volatility in the Indian foreign exchange market. Contrary to our expectations the pricing performance of the more sophisticated NGARCH pricing model is inferior to that of the relatively simple BSM model. However orthogonality tests demonstrate that the NGARCH model is free of the strike price and maturity biases associated with the BSM. We conclude that the deterministic BSM does a better job of pricing options than the more advanced time-varying volatility model based on GARCH.

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24

Hong, Jingqi. "Progress of the Study on the Models of Option Pricing." BCP Business & Management 39 (February 22, 2023): 147–53. http://dx.doi.org/10.54691/bcpbm.v39i.4057.

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Option pricing, a core part of options trading, has been fruitfully researched over the years. This article reviews the history of the emergence and advancement of option pricing in terms of a thorough classification of the widely used option pricing models and their empirical studies that follow. The three option pricing models are summarized, including the Black-Scholes pricing model, the tree diagram model, and the Monte Carlo simulation techniques, which have all represented significant progress in the field of option pricing theory. Moreover, the differences between various pricing models are analyzed and compared to show their applications and to provide an outlook on future work in this theory. It is vital to carry out some research on option pricing in order to better suit the preferences of investors. In order to meet the continuous development of financial markets, valuation of financial derivative securities is the key to effective investment in risky assets.

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25

Hoque, Ariful, Felix Chan, and Meher Manzur. "Modeling Volatility in Foreign Currency Option Pricing." Multinational Finance Journal 13, no. 3/4 (December 1, 2009): 189–208. http://dx.doi.org/10.17578/13-3/4-2.

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26

BRANGER, NICOLE, and CHRISTIAN SCHLAG. "OPTION BETAS: RISK MEASURES FOR OPTIONS." International Journal of Theoretical and Applied Finance 10, no. 07 (November 2007): 1137–57. http://dx.doi.org/10.1142/s0219024907004585.

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This paper deals with the problem of determining the correct risk measure for options in a Black–Scholes (BS) framework when time is discrete. For the purposes of hedging or testing simple asset pricing relationships previous papers used the "local", i.e., the continuous-time, BS beta as the measure of option risk even over discrete time intervals. We derive a closed-form solution for option betas over discrete return periods where we distinguish between "covariance betas" and "asset pricing betas". Both types of betas involve only simple Black–Scholes option prices and are thus easy to compute. However, the theoretical properties of these discrete betas are fundamentally different from those of local betas. We also analyze the impact of the return interval on two performance measures, the Sharpe ratio and the Treynor measure. The dependence of both measures on the return interval is economically significant, especially for OTM options.

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27

Gradojevic, Nikola, Dragan Kukolj, and Ramazan Gencay. "Clustering and Classification in Option Pricing." Review of Economic Analysis 3, no. 2 (September 30, 2011): 109–28. http://dx.doi.org/10.15353/rea.v3i2.1458.

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This paper reviews the recent option pricing literature and investigates how clustering and classification can assist option pricing models. Specifically, we consider non-parametric modular neural network (MNN) models to price the S&P-500 European call options. The focus is on decomposing and classifying options data into a number of sub-models across moneyness and maturity ranges that are processed individually. The fuzzy learning vector quantization (FLVQ) algorithm we propose generates decision regions (i.e., option classes) divided by ‘intelligent’ classification boundaries. Such an approach improves generalization properties of the MNN model and thereby increases its pricing accuracy.

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28

Ross, Sheldon M., and J. George Shanthikumar. "PRICING EXOTIC OPTIONS." Probability in the Engineering and Informational Sciences 14, no. 3 (July 2000): 317–26. http://dx.doi.org/10.1017/s0269964800143037.

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We show that if the payoff of a European option is a convex function of the prices of the security at a fixed set of times, then the geometric Brownian motion risk neutral option price is increasing in the volatility of the security. We also give efficient simulation procedures for determining the no-arbitrage prices of European barrier, Asian, and lookback options.

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29

Visagie, Jaco. "On the interchangeability of barrier option pricing models." South African Statistical Journal 52, no. 2 (2018): 157–71. http://dx.doi.org/10.37920/sasj.2018.52.2.4.

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An important question when modelling option prices is which of the multitude of option pricing models to use. In this paper, the calculation of barrier option prices is considered. These exotic options are found in many financial markets the world over. It is demonstrated numerically that it is possible to replicate (with a high degree of accuracy) the barrier option prices obtained from one model by making use of a different model; these models are referred to as ‘interchangeable’. Tests for the interchangeability of barrier option pricing models are developed and applied. However, the tests developed are not specific to barrier option pricing models and can also be applied to the prices of other exotic options.

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30

Singh, Akash, Ravi Gor Gor, and Rinku Patel. "VALUATION OF EUROPEAN PUT OPTION BY USING THE QUADRATURE METHOD UNDER THE VARIANCE GAMMA PROCESS." International Journal of Engineering Science Technologies 4, no. 5 (September 23, 2020): 1–5. http://dx.doi.org/10.29121/ijoest.v4.i4.2020.101.

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Dynamic asset pricing model uses the Geometric Brownian Motion process. The Black-Scholes model known as standard model to price European option based on the assumption that underlying asset prices dynamic follows that log returns of asset is normally distributed. In this paper, we introduce a new stochastic process called levy process for pricing options. In this paper, we use the quadrature method to solve a numerical example for pricing options in the Indian context. The illustrations used in this paper for pricing the European style option. We also try to develop the pricing formula for European put option by using put-call parity and check its relevancy on actual market data and observe some underlying phenomenon.

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31

DOKUCHAEV, NIKOLAI. "MULTIPLE RESCINDABLE OPTIONS AND THEIR PRICING." International Journal of Theoretical and Applied Finance 12, no. 04 (June 2009): 545–75. http://dx.doi.org/10.1142/s0219024909005348.

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We suggest a modification of an American option such that the option holder can exercise the option early before the expiration and can revert later this decision to exercise; it can be repeated a number of times. This feature gives additional flexibility and risk protection for the option holder. A classification of these options and pricing rules are given. We found that the price of some call options with this feature is the same as for the European call. This means that the additional flexibility costs nothing, similarly to the situation with American and European call options. For the market model with zero interest rate, the price of put options with this feature is also the same as for the standard European put options. Therefore, these options can be more competitive than the standard American options.

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32

Ou, Shubin, and Guohe Deng. "Extremum Options Pricing of Two Assets under a Double Nonaffine Stochastic Volatility Model." Mathematical Problems in Engineering 2023 (February 1, 2023): 1–20. http://dx.doi.org/10.1155/2023/1165629.

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In this paper, we consider the pricing problem for the extremum options by constructing a double nonaffine stochastic volatility model. The joint characteristic function of the logarithm of two asset prices is derived by using the Feynman–Kac theorem and one-order Taylor approximation expansion. The semiclosed analytical pricing formulas of the European extremum options including option on maximum and option on minimum of two underlying assets are derived by using measure change technique and Fourier transform approach. Some numerical examples are provided to analyze the pricing results of extremum options under affine model, nonaffine model, Black–Scholes model, and the influences of some model parameters on the option. Numerical results show that the analytical pricing formulas have higher computational efficiency and accuracy than those of Monte Carlo simulation method. Also, results of sensitivity analysis report that the nonaffine models are more effective than other existing models in capturing the effect of volatility on option pricing.

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33

Yin, Xiaocui. "Correlation Financial Option Pricing Model and Computer Simulation under a Stochastic Interest Rate." Wireless Communications and Mobile Computing 2022 (August 10, 2022): 1–9. http://dx.doi.org/10.1155/2022/6745980.

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With the continuous expansion of the consumer interest rate market today, the risks brought by interest rate fluctuations have had a huge and far-reaching impact on the financial markets of many countries and it is becoming more and more important to simulate the pricing of financial options. In the traditional pricing model of financial options, the pricing standard of the pricing model is generally set as a financial product with random disturbance characteristics and the market price of its transaction does not follow the arbitrage principle of financial product pricing. It is easy to generate errors and cause risks, and the accuracy of traditional financial option pricing models is not high, and the simulation time is long, which greatly reduces the rate of financial transactions. To improve the accuracy of option pricing models, this paper uses computer simulation technology to simulate the pricing of correlated financial options under stochastic interest rates. From the four aspects of error, risk parameters, success rate, and simulation time, it is tested to observe the influence of computer simulation technology on the financial option pricing model. The final results show that by using computer simulation technology, the error of the correlation financial option pricing model under the random interest rate is reduced, the success rate is improved, the risk parameter is reduced by 3.03%, and the simulation time is reduced by 0.605 seconds.

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34

DIA, BAYE M. "A REGULARIZED FOURIER TRANSFORM APPROACH FOR VALUING OPTIONS UNDER STOCHASTIC DIVIDEND YIELDS." International Journal of Theoretical and Applied Finance 13, no. 02 (March 2010): 211–40. http://dx.doi.org/10.1142/s0219024910005747.

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This paper studies the option pricing problem in a class of models in which dividend yields follow a time-homogeneous diffusion. Within this framework, we develop a new approach for valuing options based on the use of a regularized Fourier transform. We derive a pricing formula for European options which gives the option price in the form of an inverse Fourier transform and propose two methods for numerically implementing this formula. As an application of this pricing approach, we introduce the Ornstein-Uhlenbeck and the square-root dividend yield models in which we explicitly solve the pricing problem for European options. Finally we highlight the main effects of a stochastic dividend yield on option prices.

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35

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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36

Kim, Sol. "The Best Option Pricing Model for KOSPI 200 Weekly Options." Korean Journal of Financial Studies 51, no. 5 (October 31, 2022): 499–521. http://dx.doi.org/10.26845/kjfs.2022.10.51.5.499.

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This study finds the best option pricing model for KOSPI 200 weekly options. It examines the in-sample pricing, out-of-sample pricing and hedging performances of the short-term options with a maximum maturity of seven days or less, which have not been analyzed in previous studies. The Black and Scholes (1973) model, Ad Hoc Black-Scholes model, and stochastic volatility and jumps models are compared. As a result, one of the Ad Hoc BlackScholes models, the absolute smile model using the strike price as an independent variable shows the best performance. However, its performance is not significantly different from that of the Black and Scholes (1973) model. In the early days of the KOSPI 200 weekly options market, it is confirmed that the Black and Scholes (1973) model continues to show the excellent performance in pricing and hedging options.

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37

Singh, Vipul Kumar. "Pricing competitiveness of jump-diffusion option pricing models: evidence from recent financial upheavals." Studies in Economics and Finance 32, no. 3 (August 3, 2015): 357–78. http://dx.doi.org/10.1108/sef-08-2012-0099.

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Purpose – The purpose of this paper is to investigate empirically the forecasting performance of jump-diffusion option pricing models of (Merton and Bates) with the benchmark Black–Scholes (BS) model relative to market, for pricing Nifty index options of India. The specific period chosen for this study canvasses the extreme up and down limits (jumps) of the Indian capital market. In addition, equity markets keep on facing high and low tides of financial flux amid new economic and financial considerations. With this backdrop, the paper focuses on finding an impeccable option-pricing model which can meet the requirements of option traders and practitioners during tumultuous periods in the future. Design/methodology/approach – Envisioning the fact, the all option-pricing models normally does wrong valuation relative to market. For estimating the structural parameters that governs the underlying asset distribution purely from the underlying asset return data, we have used the nonlinear least-square method. As an approach, we analyzed model prices by dividing the option data into 15 moneyness-maturity groups – depending on the time to maturity and strike price. The prices are compared analytically by continuously updating the parameters of two models using cross-sectional option data on daily basis. Estimated parameters then used to figure out the forecasting performance of models with corresponding BS and market – for pricing day-ahead option prices and implied volatility. Findings – The outcomes of the paper reveal that the jump-diffusion models are a better substitute of classical BS, thus improving the pricing bias significantly. But compared to jump-diffusion model of Merton’s, the model of Bates’ can be applied more uniquely to find out the pricing of three popularly traded categories: deep-out-of-the-money, out-of-the-money and at-the-money of Nifty index options. Practical implications – The outcome of this research work reveals that the jumps are important components of pricing dynamics of Nifty index options. Incorporation of jump-diffusion process into option pricing of Nifty index options leads to a higher pricing effectiveness, reduces the pricing bias and gives values closer to the market. As the models have been tested in extreme conditions to determine the dominant effectuality, the outcome of this paper helps traders in keeping the investment protected under normal conditions. Originality/value – The specific period chosen for this study is very unique; it canvasses the extreme up and down limits (jumps) of the Indian capital market and provides the most apt situation for testifying the pricing competitiveness of the models in question. To testify the robustness of models, they have been put into a practical implication of complete cycle of financial frame.

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Lin, Wensheng. "Black-Scholes Model’s application in rainbow option pricing." BCP Business & Management 32 (November 22, 2022): 500–507. http://dx.doi.org/10.54691/bcpbm.v32i.2988.

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In this paper, we use excel as a tool to explore the pricing of rainbow options and their advantages based on the Black-Scholes Model. Two-color rainbow options are mainly explored in the paper, in which the underlying stocks are Apple and ExxonMobil. Simulating the price of two stocks is performed through Excel. Return on the corresponding European options and rainbow options is obtained after that. Next, the differences between the return on rainbow options and European options and pricing on rainbow option are analyzed. Finally, sensitivity analysis is carried out to further explore rainbow option pricing.

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Zeng, Xianglong. "Comparison of the Pricing Model for Different Types of options." BCP Business & Management 38 (March 2, 2023): 3337–42. http://dx.doi.org/10.54691/bcpbm.v38i.4295.

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Contemporarily, option is one of the widely used underlying assets to hedge the risks and construct portfolio in finance field. As a matter fact, with different regulations and trading rules of various transaction center around the world, there are plenty of types of options. On account of the differences in the trading rules, the option pricing models vary a lot. On this basis, this study will select three common types of options (i.e., European option, American option, and Asian Option) in order to detailly demonstrate the differences in the pricing. To be specific, the formulae as well as the empirical analysis will be presented to vividly prove the statement. According to the analysis, the differences between the pricing procedure and models will be exhibited. In addition, the current drawbacks for the models will be illustrated and suggestions for further study will be clarified accordingly. Overall, these results shed light on guiding further exploration of option pricing from the theoretical as well as empirical sides.

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MITOV, GEORGI K., SVETLOZAR T. RACHEV, YOUNG SHIN KIM, and FRANK J. FABOZZI. "BARRIER OPTION PRICING BY BRANCHING PROCESSES." International Journal of Theoretical and Applied Finance 12, no. 07 (November 2009): 1055–73. http://dx.doi.org/10.1142/s0219024909005555.

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This paper examines the pricing of barrier options when the price of the underlying asset is modeled by a branching process in a random environment (BPRE). We derive an analytical formula for the price of an up-and-out call option, one form of a barrier option. Calibration of the model parameters is performed using market prices of standard call options. Our results show that the prices of barrier options that are priced with the BPRE model deviate significantly from those modeled assuming a lognormal process, despite the fact that for standard options, the corresponding differences between the two models are relatively small.

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Wang, Meini, Panjie Wang, and Yuyi Zhang. "An empirical study of down-and-out put option pricing based on Geometric Brownian Motion and Monte Carlo Simulation: evidence from crude oil and E-mini Nasdaq-100 futures." BCP Business & Management 26 (September 19, 2022): 804–9. http://dx.doi.org/10.54691/bcpbm.v26i.2041.

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Option, an instrument of significant financial values in the modern market, is of growing importance. In the case of pricing the option, pricing exotic option remains the problem, since none of the practical methods have been developed as a corresponding way of solution. In order to address the existing issue, this paper examines the feasibility of down-and-out put option pricing based on Geometric Brownian Motion and Monte-Carlo Simulation. Specifically, the stock prices will be calculated through the Geometric Brownian Motion certain while the underlying asset price and down-and-out put option price will be obtained by Monte-Carlo simulations. Two typical underlying assets are selected as the investigation target to validate the pricing feasibility: Crude Oil Futures and E-mini Nasdaq-100 futures. According to the analysis, the barrier option price is lower than a European option, and the barrier option is always cheaper than a European option with the same parameters. These results shed light on the seeking of a method in pricing exotic options.

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Fabbiani, Emanuele, Andrea Marziali, and Giuseppe De Nicolao. "vanilla-option-pricing: Pricing and market calibration for options on energy commodities." Software Impacts 6 (November 2020): 100043. http://dx.doi.org/10.1016/j.simpa.2020.100043.

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Martinkutė-Kaulienė, Raimonda. "EXOTIC OPTIONS: A CHOOSER OPTION AND ITS PRICING." Business, Management and Education 10, no. 2 (December 20, 2012): 289–301. http://dx.doi.org/10.3846/bme.2012.20.

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Financial instruments traded in the markets and investors’ situation in such markets are getting more and more complex. This leads to more complex derivative structures used for hedging that are harder to analyze and which risk is harder managed. Because of the complexity of these instruments, the basic characteristics of many exotic options may sometimes be not clearly understood. Most scientific studies have been focused on developing models for pricing various types of exotic options, but it is important to study their unique characteristics and to understand them correctly in order to use them in proper market situations. The paper examines main aspects of options, emphasizing the variety of exotic options and their place in financial markets and risk management process. As the exact valuation of exotic options is quite difficult, the article deals with the theoretical and practical aspects of pricing of chooser options that suggest a broad range of usage and application in different market conditions. The calculations made in the article showed that the price of the chooser is closely correlated with the choice time and low correlated with its strike price. So the first mentioned factor should be taken into consideration when making appropriate hedging and investing decisions.

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Liu, David, and An Wei. "Regulated LSTM Artificial Neural Networks for Option Risks." FinTech 1, no. 2 (June 2, 2022): 180–90. http://dx.doi.org/10.3390/fintech1020014.

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This research aims to study the pricing risks of options by using improved LSTM artificial neural network models and make direct comparisons with the Black–Scholes option pricing model based upon the option prices of 50 ETFs of the Shanghai Securities Exchange from 1 January 2018 to 31 December 2019. We study an LSTM model, a mathematical option pricing model (BS model), and an improved artificial neural network model—the regulated LSTM model. The method we adopted is first to price the options using the mathematical model—i.e., the BS model—and then to construct the LSTM neural network for training and predicting the option prices. We further form the regulated LSTM network with optimally selected key technical indicators using Python programming aiming at improving the network’s predicting ability. Risks of option pricing are measured by MSE, RMSE, MAE and MAPE, respectively, for all the models used. The results of this paper show that both the ordinary LSTM and the traditional BS option pricing model have lower predictive ability than the regulated LSTM model. The prediction ability of the regulated LSTM model with the optimal technical indicators is superior, and the approach adopted is effective.

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45

Yin, Zhao, and Chang Tan. "The Differential Algorithm for American Put Option with Transaction Costs under CEV Model." Journal of Systems Science and Information 2, no. 5 (October 25, 2014): 401–10. http://dx.doi.org/10.1515/jssi-2014-0401.

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AbstractThis paper mainly studies the American put option pricing with transaction costs in the CEV process. The specific Crank-Nicolson form of numerical solution is obtained by the finite difference method. On this basis, Hong Kong stock CKH option is selected as the object to estimate option price. Finally, by comparing with the actual price, the American put option pricing model is verified as reasonable. This paper is significant to the rational pricing and the institutional construction of the upcoming stock options in mainland China.

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Aljedhi, Reem Abdullah, and Adem Kılıçman. "Fractional Partial Differential Equations Associated with Lêvy Stable Process." Mathematics 8, no. 4 (April 2, 2020): 508. http://dx.doi.org/10.3390/math8040508.

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In this study, we first present a time-fractional L e ^ vy diffusion equation of the exponential option pricing models of European option pricing and the risk-neutral parameter. Then, we modify a particular L e ^ vy-time fractional diffusion equation of European-style options. Further, we introduce a more general model based on the L e ^ vy-time fractional diffusion equation and review some recent findings associated with risk-neutral free European option pricing.

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Jin, Yunguo, and Shouming Zhong. "Pricing Spread Options with Stochastic Interest Rates." Mathematical Problems in Engineering 2014 (2014): 1–11. http://dx.doi.org/10.1155/2014/734265.

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Although spread options have been extensively studied in the literature, few papers deal with the problem of pricing spread options with stochastic interest rates. This study presents three novel spread option pricing models that permit the interest rates to be random. The paper not only presents a good approach to formulate spread option pricing models with stochastic interest rates but also offers a new test bed to understand the dynamics of option pricing with interest rates in a variety of asset pricing models. We discuss the merits of the models and techniques presented by us in some asset pricing models. Finally, we use regular grid method to the calculation of the formula when underlying stock returns are continuous and a mixture of both the regular grid method and a Monte Carlo method to the one when underlying stock returns are discontinuous, and sensitivity analyses are presented.

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Liu, Zhaopeng. "Option Pricing Formulas in a New Uncertain Mean-Reverting Stock Model with Floating Interest Rate." Discrete Dynamics in Nature and Society 2020 (November 3, 2020): 1–8. http://dx.doi.org/10.1155/2020/3764589.

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Options play a very important role in the financial market, and option pricing has become one of the focus issues discussed by the scholars. This paper proposes a new uncertain mean-reverting stock model with floating interest rate, where the interest rate is assumed to be the uncertain Cox-Ingersoll-Ross (CIR) model. The European option and American option pricing formulas are derived via the α -path method. In addition, some mathematical properties of the uncertain option pricing formulas are discussed. Subsequently, several numerical examples are given to illustrate the effectiveness of the proposed model.

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Chang, Shih-Kang, and Latha Shanker. "OPTION PRICING AND THE ARBITRAGE PRICING THEORY." Financial Review 21, no. 3 (August 1986): 17. http://dx.doi.org/10.1111/j.1540-6288.1986.tb00681.x.

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Chang, Jack S. K., and Latha Shanker. "OPTION PRICING AND THE ARBITRAGE PRICING THEORY." Journal of Financial Research 10, no. 1 (March 1987): 1–16. http://dx.doi.org/10.1111/j.1475-6803.1987.tb00470.x.

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