Rozprawy doktorskie na temat „STOCK CALL OPTIONS”

Over 22 billion derivative contracts were traded on different stock exchanges globally during the year 2010 of which almost 50% were futures while the remaining 50% were options. An overall 25% increase in such contracts was registered as compared to those traded in the year 2009 (International Options Market Association (IOMA) Report, 2011).Investors often use a wide array of trading tools, market indicators and market trading strategies to get the best possible returns for the money that was invested. The main objective of this paper is to focus on the use of market sentiment indicators, specifically the Put-Call Ratio (PCR) as a predictor of returns for an investor.The Put-Call Ratio is defined as a ratio of the trading volume of put options to call options. It is called a sentiment indicator because it measures the “feelings” of option traders. Additionally, it has longed been viewed as an indicator of investors’ sentiment in the market (Put-Call Ratio, 2012) and is possibly the most favoured description of market psychology (James, 2011).
Dissertation (MBA)--University of Pretoria, 2012.
Gordon Institute of Business Science (GIBS)
unrestricted

Employee share options and Black Economic Empowerment deals are financial instruments found in the South African market. Employee share options (ESOs) are issued as a form of non-cash compensation to the employees of the company in addition to their salaries or bonuses. Its value is linked to the share price and since there is no downside risk for the employee his share option is similar to owning a call option on the stock of his employer. Black economic empowerment (BEE) deals in this report refer to those types of transactions structured by listed South African companies to facilitate the transfer of a portion of their ordinary issued share capital to South African individuals or groups who qualify under the Broad-Based Black Economic Empowerment Act of 2003 (“the Act”). This Act requires a minimum percentage of the company to be black-owned in order to address the disproportionate distribution of wealth amongst racial groups in South Africa due to the legacy of Apartheid. These transactions are usually structured in such a way to allow the BEE partner to participate in the upside of the share price beyond a certain level but not in the downside which replicates a call option on the share price of the issuing company. The cost of both ESOs and BEE deals has to be accounted for on the balance sheet of the issuing company at its fair-value. Neither of these instruments can be traded and their extended option lifetimes are features that distinguish these deals significantly from regular traded options for which liquid markets exist. This makes pricing them a non-trivial exercise. A number of types of mathematical models have been developed to take the unique structure features into account to price them as accurately as possible. Research by Huddart&Lang (1995&1996) has shown that option holders often exercise their vested options long before the maturity of the transactions but are unable to quantify a measure that can be used. The wide variety of factors influencing option holders (recent stock price movements, market-to-strike ratio, proximity of vesting dates, time to maturity, share price volatility and wealth of option holder) as well as little exercise data publicly available prevents the options from being priced in a consistent manner. Various assumptions regarding the exercise behaviour of option holders are used that are not based on empirical observations even though the option prices are sensitive to this input. This dissertation provides an overview of the models, inputs and exercise behaviour assumptions that are recognized in pricing both ESOs and BEE deals under IFRS 2 in South Africa. This puts the reader in a position to evaluate all pricing aspects of these deals. Furthermore, their structuring are also analysed in order to identify the general issues related to them. A number of methods to manage the pricing issue surrounding exercise behaviour on ESOs have been considered for the South African market. The ESO Upper Bound-methodology showed that for each strike there is a threshold at which exercise will occur and the employee can invest the after-tax proceeds in a diversified portfolio with a higher expected return than that of the single equity option. This approach reduces the standard Black-Scholes option value without relying on assumptions about the employee’s exercise behaviour and is a viable alternative for the South African market. The derived option value represents the cost of the option. Seven large listed companies’ BEE transactions are dissected and compared against one another using the fair-value of the transaction as a percentage of the market capitalization of the company. The author shows how this measure is a more equitable way of assigning BEE credits to companies than the current practice which is shareholding-based. The current approach does not reward the effort (read cost) that a company has undertaken to transfer shares to black South Africans but only focuses on the amount that is finally owned by the BEE participants. This leaves the transaction vulnerable to a volatile share price and leads to transactions with extended lock-in periods that do not provide much economic benefit to the BEE participants for many years. Other inefficiencies in the type of BEE transactions that have emerged in reaction to the BEE codes that have been published by the South African government are also considered. Finally the funding model that is often used to facilitate these deals is assessed and the risks involved for the funder (bank) is reflected on.
Dissertation (MSc)--University of Pretoria, 2011.
Mathematics and Applied Mathematics
unrestricted

PONTIFÍCIA UNIVERSIDADE CATÓLICA DO RIO DE JANEIRO
CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO
O presente estudo tem como objetivo mostrar a existência de cones de assimetria e curtose no mercado brasileiro de opções. Além disso, os coeficientes de assimetria e curtose são de suma importância para a aplicação do modelo de Corrado e Su (1996). As volatilidades implícitas calculadas pelo método inverso deste modelo serão sobrepostas aos cones de volatilidade, buscando oportunidades de compra ou de venda de volatilidade. Para efeito de comparação, o modelo de Black e Scholes também será utilizado para a extração de tais medidas de volatilidade implícita. Outra contribuição deste trabalho é mostrar se os efeitos do sorriso de volatilidade e da estrutura a termo da volatilidade são amenizados diante de operações realizadas com os cones de volatilidade, levando-se em consideração a volatilidade implícita calculada pelos diferentes modelos. Para isto, foram realizados testes estatísticos de eficiência, além de uma análise descritiva das variáveis mais importantes para uma correta análise do mercado de opções, em momentos de estabilidade e baixa volatilidade como o verificado no ano de 2010. O estudo mostra a existência de cones de assimetria e curtose no mercado brasileiro de opções e possibilidades de ganhos com as operações feitas através dos cones de volatilidade, porém os resultados obtidos pelos dois modelos não apresentaram diferenças estatisticamente significantes.
The present study aims to show the existence of skewness and kurtosis cones in the Brazilian market. In addition, the coefficients of skewness and kurtosis are of paramount importance for the application of the model of Corrado and Su (1996). The implied volatilities calculated by the inverse of this template will be superimposed to the cones of volatility, seeking opportunities to acquire or dispose of volatility. Comparison of Black and Scholes model will also be used for the extraction of such measures of implied volatility. Another contribution of this paper is to show the effects of the volatility smile and term structure of volatility are amenable before operations performed with the cones of volatility, taking into account the implied volatility calculated by different models. For this, statistical tests were performed, efficiency and a descriptive analysis of the most important variables for a correct analysis of the options market, in times of stability and low volatility as the year of 2010. The study showed the existence of skewness and kurtosis cones in the Brazilian market and gains possibilities with volatility cones operations, but the results obtained with the two models didn´t have significative statistics differences.

In computational finance, finite differences are a widely used tool in the valuation of standard derivative contracts. In a lower-dimensional setting, high accuracy and speed often characterize such methods, which gives them a competitive advantage against Monte Carlo methods. For option contracts with discontinuous payoff functions, however, finite differences encounter problems to maintain the order of convergence of the employed finite difference scheme. Therefore the timesteps are often computed in a conservative manner, which might increase the total execution time of the solver more than necessary.     It can be shown that for American call options written on dividend paying stocks, it may be optimal to exercise the option right before a dividend is paid out. The result is that yet another discontinuity is introduced in the solution and the timestep is often reduced to preserve the intrinsic convergence order. However, it is thought that at least in theory the optimal length of the timestep is an increasing function of the time elapsed since the last discontinuity occured. The objective thus becomes that of finding an explicit method for adjusting the timestep both at the dividend instants and between dividend instants. Keeping the discretization in space constant leads to a time non-equidistant finite difference problem.     The aim of this thesis is to propose a time non-equidistant numerical finite difference algorithm for valuation of American call options on stocks with dividends known in advance. In particular, an explicit formula is proposed for computing timesteps at the dividend instants and between dividend payments given a user-specified error tolerance. A portion of the report is also devoted to numerical stabilization techniques that are applied to maintain the convergence order, including Rannacher time-marching and mollification.

Essa dissertação tem como escopo principal a análise da natureza jurídica e do regime aplicável às opções de compra e venda de ações. Na primeira parte, foram verificados a função econômico-social e o posicionamento doutrinário, em sede de direito nacional e comparado, quanto à classificação das opções de compra ou venda, bem como seu contraste com outros instrumentos existentes, a fim de demonstrar seu caráter contratual sui generis à luz do direito pátrio. Na segunda parte, foram estudadas as principais características das opções de compra ou venda de ações, com especial enfoque nos requisitos subjetivos, objetivos e formais, a fim de determinar seu tratamento à luz no direito brasileiro. Por fim, foram objeto de investigação os efeitos práticos no âmbito societário, bem como o regime de sua tutela jurisdicional em caso de violação das obrigações (lato sensu) assumidas pelas partes.
This dissertation intends to analyze the legal nature and judicial treatment of call and put options having stocks as their underlying assets. In the first part, it was analyzed their economic and social function and doctrine, in terms of national and comparative law, regarding the classification of call and put options in general, as well as their contrast with other existing instruments, in order to demonstrate their contractual sui generis aspect under national law. In the second part, it was verified the main characteristics of call and put stock options, with particular focus on their subjective, objective and formal aspects for the purpose of determining their legal treatment under Brazilian law. Finally, their practical effects within the corporate field were object of analysis, as well as the ruling of their judicial protection upon a default of the obligations (lato sensu) assumed by the parties thereunder.

In this thesis, important theories in financial mathematics will be explained and derived. These theories will later be used to value financial derivatives. An analytical formula for valuing European call and put option will be derived and European call options will be valued under the Black-Scholes partial differential equation using three different finite difference methods. The Crank-Nicholson method will then be used to value American call options and solve their corresponding free boundary value problem. The optimal exercise boundary can then be plotted from the solution of the free boundary value problem. The algorithm for valuing American call options will then be further developed to solve the stock loan problem. This will be achieved by exploiting a link that exists between American call options and stock loans. The Crank-Nicholson method will be used to value stock loans and their corresponding free boundary value problem. The optimal exit boundary can then be plotted from the solution of the free boundary value problem. The results that are obtained from the numerical calculations will finally be used to discuss how different parameters affect the valuation of American call options and the valuation of stock loans. In the end of the thesis, conclusions about the effect of the different parameters on the optimal prices will be presented.
I det här kandidatexamensarbetet kommer fundamentala teorier inom finansiell matematik förklaras och härledas. Dessa teorier kommer lägga grunden för värderingen av finansiella derivat i detta arbete. En analytisk formel för att värdera europeiska köp- och säljoptioner kommer att härledas. Dessutom kommer europeiska köpoptioner att värderas numeriskt med tre olika finita differensmetoder. Den finita differensmetoden Crank-Nicholson kommer sedan användas för att värdera amerikanska köpoptioner och lösa det fria gränsvärdesproblemet (free boundary value problem). Den optimala omvandlingsgränsen (Optimal Exercise Boundary) kan därefter härledas från det fria gränsvärdesproblemet. Algoritmen för att värdera amerikanska köpoptioner utökas därefter till att värdera lån med aktier som säkerhet. Detta kan åstadkommas genom att utnyttja ett samband mellan amerikanska köpoptioner med lån där aktier används som säkerhet. Den finita differensmetoden Crank-Nicholson kommer dessutom att användas för att värdera lån med aktier som säkerhet. Den optimala avyttringsgränsen (Optimal Exit Boundary) kan därefter härledas från det fria gränsvärdesproblemet. Resultaten från de numeriska beräkningarna kommer slutligen att användas för att diskutera hur olika parametrar påverkar värderingen av amerikanska köpoptioner, samt värdering av lån med aktier som säkerhet. Avslutningsvis kommer slutsatser om effekterna av dessa parametrar att presenteras.

碩士
逢甲大學
財務金融學所
99
Research topics in options are numerous, such as market efficiency, option pricing, volatility smile, etc. However, this study focuses on the issue of put-call parity. This study follows Cremers and Weinbaum (2010) to investigate whether the deviations from the put-call parity of the Taiwan stock options contain any information for the predictability of future returns on individual stocks. This study uses the Taiwan call and put options on individual stocks with the same maturities, the same strike prices, and the same underlying stocks to calculate the implied volatility spreads, which are used as the surrogates of the deviations from put-call parities for the Taiwan stock options. Then, this study investigates whether the information contained in the implied volatility spreads is helpful to the prediction of future return on individual stocks. The sample period in this study covers November 2004 through November 2010, and is divided into two sub-periods, i.e., the ante period and the post period. The sample stocks are sorted into three portfolios based on their volatility spreads. Then this study examines the relationship between excess returns on portfolios and their market values, weights in market values, and betas, respectively. Using the same methodology, the sample stocks are sorted into three portfolios based on options trading volume, stock liquidity, stock industry, and corporation sizes, respectively. Then, this study investigates the relationship between excess returns on portfolios and their volatility spreads. The results indicate that deviations are more likely to occur in calls that are relatively more expensive than the corresponding puts, and the autocorrelation of volatility spreads has declined over time. This study finds that there are no significant abnormal returns on portfolios that are constructed based on the implied volatility spreads. However, four-week holding period returns are higher than one-week holding period returns for most of the portfolios. Moreover, returns on stocks in portfolios are positively correlated with the returns on the market portfolio. These evidences support that the Taiwan stock options market is efficient. Similar results are also found for portfolios that are based on options trading volume, stock liquidity, and corporation sizes, respectively. That is, no significant abnormal returns on these portfolios can be found. However, the evidence shows that the return predictability for the portfolio of the electronic industry is higher than that for the portfolio of non-electronic industry. In summary, the evidence shows that it is still difficult to use implied volatility spreads of options to predict future returns on individual stocks in the Taiwan options market. This is majorly due to the small number of the listing of individual stock options and the illiquidity of stock options in Taiwan. Key words: Put-Call Parity, Implied Volatility Spread, Taiwan Stock Options, Stock Return Predictability

碩士
中原大學
財務金融研究所
107
According to Cremers and Weinbaum (2010), I compute the implied volatility spread by option put-call parity theory. Then, I build strategy based on implied volatility spread, and compares it with OS, 52-week high, and contrary investment strategies to explore whether the investment performance of the implied-volatility-spread strategy is better than other strategies. Moreover, this study combines the implied-volatility-spread strategy with other strategies to form the two-dimensional investment strategy to explore whether the performance of two-dimensional implied-volatility-spread strategy is better than one-dimensional implied-volatility-spread strategy. The empirical results show that it needs more than one year of investment to get positive abnormal return by implied-volatility-spread strategy. Otherwise, it will only receive negative abnormal return when the investment horizon is less than one year. In addition, two-dimensional strategy improves bad performance of one-dimensional strategy. After combining the contrary 52-week high and contrary investment strategy with implied-volatility-spread strategy, I find that there is the best strategic effect when the holding period is 12. Nevertheless, the abnormal returns decrease after the holding period is 24.

碩士
朝陽科技大學
財務金融系碩士班
99
The data involved in this research were recorded form April 2009 to March 2010, during which 246 trade dates were marked. The transaction data with call options and put options at the same time within one minute in a day are the subject of this thesis. The "Put Call Futures Parity" pattern is employed to deduce the relations among option striking prices. "Least squares method" is then applied to conduct regression analysis, examining if efficiency exists regarding the fluctuation of striking prices in Taiwan Stock Index. Moreover, through spread strategy analysis, whether Taiwan Stock Index Options market is efficient is determined. Empirical results deomnstrate that the fluctuation of call option striking prices is slower than that of put option premiums. That is, put strategy shows greater efficiency. Spreads of call stragegy are wider than those of put strategy. As a result, interest arbitrage for call spread strategy is more likely to occur. Yet the transaction cost would not be covered, thus diminishing the possibility. The same results also indicate that both call and put striking prices are closely linked to the changes of the market, showing instantaneous dynamic equilibrium. This also proves that options market in Taiwan is efficient.

Derivatives are an important class of financial instruments that are central to today’s financial and trade markets. They offer various types of risk protection and allow innovative investment strategies. Derivatives markets have been in existence in India in some form or other for a long time. However, the ban on futures trading of many commodities was lifted starting in the early 2000s, and national electronic commodity exchanges were created. India’s tryst with derivatives began in 2000 when both the NSE and the BSE commenced trading in equity derivatives. In June 2000, index futures became the first type of derivate instruments to be launched in the Indian markets, followed by index options in June 2001, options in individual stocks in July 2001, and futures in single stock derivatives in November 2001. The turnover of derivatives on the NSE increased from Rs 23,654 million in 2000–2001 to Rs. 292,482,211 million in 2010–2011. Derivative products like index futures, stock futures, index options and stock options have become important instruments of price discovery, portfolio diversification and risk hedging in stock markets all over the world in recent times. An option is a financial instrument (Derivative) which gives holder of the option the right to do something, but holder does not have to exercise the right. The price of option is theoretically determined by many models like binomial method, Black –Scholes option pricing formula, put-call parity, Volatility jump model etc. out of which Black Scholes option pricing model is the most popular and widely used throughout the world. Black and Scholes developed closed-form formula to calculate the prices of European calls and puts, based on certain assumptions by showing how to hedge continuously the exposure on the short position of an option. Partial differential equation, derived by them, referred to as the Black–Scholes equation, governs the price of the option over time. Delhi School of Management, DTU Page vi This research, covering a period of five years from 2008 to 2012 gives the modern day perspective of Black Scholes implication on Call options pricing with sample covering the top 5 banks based on ET500 list of top 500 companies in India and compare it with the CNX Bank Nifty index that capture the movement of 12 most traded banks on NSE. This report covers some of the angles of an empirical study such as the sensitivity of the model to its variables, comparing the theoretical value of call option with the actual and understanding the deviation from the current market. Finally, this report tests the validity of the various assumptions of Black – Scholes model.

碩士
國立臺北大學
企業管理學系
95
Previous researchers usually use GARCH models in estimating volatility for evaluation of value at risk (VaR) performance. There are very few academic articles talked about that interaction with assets would affect the VaR on these assets. A 744 daily data of Taiwan stock indexes of spot, futures, and call options ranging from Jan. 1, 2004 to Dec. 31, 2006 were collected. In this study, Tri-EGARCH models were adopted in estimating volatility. The estimated volatility is then estimated VaR using Monte Carlo Simulation method. We established a control model to estimate VaR which simply using Monte Carlo Simulation method. The VaR performances of these two models are compared using back-testing and Lopez loss function. There are four purpose of this study. First, using Tri-EGARCH analyzes three markets to discover how interaction affect rate of return in these three markets. To apply conditional variance equation describes volatility clustering and volatility spilling effect in these markets which is second purpose. Third purpose is to confirm that asymmetric effect existence whether or not. Forth purpose, the main purpose, is to establish estimating method using Tri-EGARCH and Monte Carlo Simulation method, and to confirm its’ performance. The result which is research in how interaction affect rate of return in these three markets is showed that spot market will be positive affected by futures about one day ago. Futures will be positive affected by spot and itself about two days ago. Call option will be negative affected by itself about one day and two days ago, others are not significant. And the result which is research with second purpose is showed that three markets all have volatility clustering and volatility spilling effect. The research into the effect of asymmetric effect, we find the effect is opposite of Tri-EGARCH model and single EGARCH model using in these three markets. The result on model of estimating VaR is showed that Tri-EGARCH model estimating performance is the best whether in back-testing or Lopez loss function.

碩士
南台科技大學
財務金融系
95
With the fast growth of the financial derivatives market in Taiwan, more and more investors are involved in futures and option trading. There are much higher trading risks in derivatives than spot market; therefore, this study focus on how to construct an effective trading strategy to raise the probability of positive return, and to reduce the trading risk. This study focuses on the specific feature of options, time value. An index futures and an index option are used to construct the trading strategies. Two strategies are mainly concerned. Strategy 1: long a futures and short a call. Strategy 2: short a futures and short a put. Taiwan Stock Index Futures and Index Option are used to analysis them. The period was from 2003 to 2005. Use description statistic and t-test to treat of return with hold-to-maturity and rolling, and compare with the different exercise price of option and to construct a basic model. The empirical result shows that using Strategy 1 mostly makes significant profit, and use the rolling strategy is better than the hold-to-maturity strategy. When considering the exercise price of the options, it is suggested to choose those second in the money because those have low trading risk. Use Strategy 1 and rolling the options, the probability of positive return of Strategy 1 is about 74%, and the average annul return is about 64.7% without transaction cost.