The informational content of implied volatility and its prediction power is evaluated for time horizons of one month. The study covers the period of November 2007 to November 2013 for the two indices S&P500 and OMXS30. The findings are put in relation to the corresponding results for past realized volatility. We find results supporting that implied volatility is an efficient, although biased estimator of realized volatility. Our results support the common notion that implied volatility predicts realized volatility better than past realized volatility, and that it also subsumes most of the informational content of past realized volatility.

The aim of this thesis is a development of a new class of financial models with random parameters, which are computationally efficient and have the same level of performance as existing ones. In particular, this research is threefold. I have studied the evolution of storable commodity and commodity futures prices in time using a new random parameter model coupled with a Kalman filter. Such a combination allows one to forecast arbitrage-free futures prices and commodity spot prices one step ahead. Another direction of my research is a new volatility model, where the volatility is a random variable. The main advantage of this model is high calibration speed compared to the existing stochastic volatility models such as the Bates model or the Heston model. However, the performance of the new model is comparable to the latter. Comprehensive numerical studies demonstrate that the new model is a very competitive alternative to the Heston or the Bates model in terms of accuracy of matching option prices or computing hedging parameters. Finally, a new futures pricing model for electricity futures prices was developed. The new model has a random volatility parameter in its underlying process. The new model has less parameters, as compared to two-factor models for electricity commodity pricing with and without jumps. Numerical experiments with real data illustrate that it is quite competitive with the existing two-factor models in terms of pricing one step ahead futures prices, while being far simpler to calibrate. Further, a new heuristic for calibrating two-factor models was proposed. The new calibration procedure has two stages, offline and online. The offline stage calibrates parameters under a physical measure, while the online stage is used to calibrate the risk-neutrality parameters on each iteration of the particle filter. A particle filter was used to estimate the values of the underlying stochastic processes and to forecast futures prices one step ahead. The contributory material from two chapters of this thesis have been submitted to peer reviewed journals in terms of two papers: • Chapter 4: “A fast calibrating volatility model” has been submitted to the European Journal of Operational Research. • Chapter 5: “Electricity futures price models : calibration and forecasting” has been submitted to the European Journal of Operational Research.

Este trabalho tem por objetivo verificar a eficácia do modelo parametrizado SVI (Stochastic Volatility Inspired), apresentando-o como um método alternativo à construção da volatilidade implícita para opções de ações e de índice no mercado brasileiro. Primeiramente, o conceito financeiro de opção e sua teoria de precificação são apresentados, incluindo os modelos de Black-Scholes e Heston, a importância da volatilidade implícita e seu comportamento estocástico e detalhando o funcionamento de cada parâmetro do modelo SVI (Stochastic Volatility Inspired). Um algoritmo é desenvolvido em cima da base teórica, assim como sua implementação computacional. Além disso, são feitos experimentos com dados de mercado reais e seus resultados analisados e comparados com os de publicações anteriores. / This work aims to verify the efficiency of parameterized SVI (Stochastic Volatility Inspired) model, presenting it as an alternative method to construct the implied volatility for stock and index options in Brazilian market. First, the financial option concept and its pricing theory are presented, including Black-Scholes and Heston models, the importance of implied volatility and its stochastic behavior and detailing the operation of each parameter of the SVI (Stochastic Volatility Inspired) model. An algorithm is developed on top of the theoretical basis, as well as its computational implementation. In addition, experiments are performed with real market data and their results are analyzed and compared with those of previous publications.

Este trabalho tem por objetivo verificar a eficácia do modelo parametrizado SVI (Stochastic Volatility Inspired), apresentando-o como um método alternativo à construção da volatilidade implícita para opções de ações e de índice no mercado brasileiro. Primeiramente, o conceito financeiro de opção e sua teoria de precificação são apresentados, incluindo os modelos de Black-Scholes e Heston, a importância da volatilidade implícita e seu comportamento estocástico e detalhando o funcionamento de cada parâmetro do modelo SVI (Stochastic Volatility Inspired). Um algoritmo é desenvolvido em cima da base teórica, assim como sua implementação computacional. Além disso, são feitos experimentos com dados de mercado reais e seus resultados analisados e comparados com os de publicações anteriores. / This work aims to verify the efficiency of parameterized SVI (Stochastic Volatility Inspired) model, presenting it as an alternative method to construct the implied volatility for stock and index options in Brazilian market. First, the financial option concept and its pricing theory are presented, including Black-Scholes and Heston models, the importance of implied volatility and its stochastic behavior and detailing the operation of each parameter of the SVI (Stochastic Volatility Inspired) model. An algorithm is developed on top of the theoretical basis, as well as its computational implementation. In addition, experiments are performed with real market data and their results are analyzed and compared with those of previous publications.

Nowadays, financial derivatives play an increasingly important role in the global financial system, and options are popular structural financial derivatives, which attract much attention from academia and the industry. China Financial Futures Exchange (CFFEX) initiated the CSI 1000 index future and CSI 1000 index option in the Chinese market on July 22, 2022, which indicates a trend of acceleration in financial innovations in China’s financial market. This dissertation focuses on the volatility models in option pricing and modern numerical procedures that approximate option prices. In this dissertation, different stochastic volatility models, for example, the Black–Scholes model and the Heston stochastic volatility model, are introduced and applied to price in not only European options but also exotic options, which possess complicated payoff structures. Moreover, a comprehensive empirical analysis is conducted to demonstrate these option pricing algorithms based on the recent data of CSI 1000 index options in the Chinese market. / Business Administration/Finance

This dissertation consists of two parts. In the first chapter, we examine the relative performance of four options-based investment strategies versus a buy-and-hold strategy in the underlying stock. Specifically, using ten stocks widely held in 401(k) plans, we examine monthly returns from strategies that include a long stock position as one component. These strategies are long stock, covered call, protective put, collar, and covered combination. Ignoring early exercise for simplicity, we find that the covered combination and covered call strategies generally outperform the long stock strategy, which in turn generally outperforms the collar and protective put strategies regardless of the performance measure considered. Clearly, from the first chapter, strategies that involve writing options, in general, outperform the ones buying options. The second chapter provides a detailed study of the conditions where option writers can maximize returns while minimizing risk. The nonlinear nature of time value decay in options suggests that, theoretically, holding short positions only when the speed of time decay is high might improve the performance of option writing strategies. We examine monthly returns from five option strategies without a position in the underlying asset. These strategies are: short straddle, short strangle, short guts, “crash-neutral” short straddle, and long iron butterfly. The results from two portfolios are compared: a “benchmark” portfolio using standard SPX options that expire the following month and a weekly portfolio using SPXW options that expire at the end of the weekly holding period. The short strangle strategy with weekly options consistently outperforms the other strategies with both standard and weekly options, even after accounting for transaction costs. This finding suggests that short-dated out-of-the-money options can be useful in improving the risk-return characteristics of an option writing strategy. In an effort to improve the performance of the short straddle strategy, this chapter introduces an extremely short holding period portfolio, by stitching together three weekly option expirations into one week. Although the straddle still underperforms relative to the short strangle, the performance of the short straddle is improved by entering the market 15 minutes before the close and by using the extremely short holding period portfolios.

The impact of the introduction of derivatives on the underlying stock is a debatable topic among the researchers. The issue is quite controversial as contradictory results have been obtained by researchers in various stock markets. The purpose of this study is to examine the volatility and the liquidity effect on the underlying stock after the introduction of index options. We have investigated volatility and liquidity effect by collecting sample data from the stock markets of India, Korea, Taiwan, Hong Kong, Japan, Thailand, Malaysia and Singapore, only markets which are offering index options in Asia.   Applying the generalized autoregressive conditional heteroscedasticity (GARCH) model, we have examined the conditional volatility of intraday (high frequency) returns for each stock market, before and after the introduction of index options. We have also examined the liquidity effect through t-test and Wilcoxon Signed Rank Test. We used t-test to determine the mean differences between the trading volume of pre-index and post-index options periods.    By comparing the estimated parameters and the coefficient of conditional volatility in pre and post period of index options introductions, we have examined that the derivatives trading dramatically increases the persistence of the conditional volatility for all the selected stock markets. We also observed mixed evidence in context to liquidity effect. In the stock exchanges of Hong Kong, Japan, Korea, Taiwan and Thailand, we found that the respective markets become more liquid in the post index options periods in contrast to pre index options period. In these markets trading volume increased significantly after the introduction of index options.  On the other hand, India, Malaysia and Singapore stock markets show no liquidity effect in the post-index option period.   Finally, the empirical results of our study conclude that the introduction of index options on the selected Asian stock markets have increased in stock return volatility and liquidity on the underlying stocks.

In this study a two-part mixed probability density function was derived which described the relative changes in the Standard and Poor's 100 Stock Index over various intervals of time. The density function is a mixture of two different halves of normal distributions. Optimal values for the standard deviations for the two halves and the mean are given. Also, a general form of the function is given which uses linear regression models to estimate the standard deviations and the means. The density functions allow stock market participants trading index options and futures contracts on the S & P 100 Stock Index to determine probabilities of success or failure of trades involving price movements of certain magnitudes in given lengths of time.

This thesis examines the application of neural networks in the context of option pricing. Throughout the thesis, different architecture choices and prediction parameters are tested and compared in order to achieve better performance and higher accuracy in option valuation. Two different volatility forecast mechanisms are used to compare neural networks performance with Black Scholes parametric model. Moreover, the performance of a neural network is compared also to more advanced modular neural networks. A new technique of adding rational prediction assumptions to neural network prediction is tested and the thesis shows the importance of adding virtual options fulfilling these assumptions in order to achieve better training of the neural network. This method comes out to increase the prediction power of the network significantly. The thesis also shows the neural network prediction outperforms the traditional parametric methods. The size and number of hidden layers in a neural network is tested with an emphasis to provide a benchmark and a structured way how to choose neural network parameters for future applications in option pricing. JEL Classification C13, C14, G13 Keywords Option pricing, Neural networks, Modular neu- ral networks, S&P500 index options Author's e-mail vach.dominik@gmail.com...

Since the introduction of derivatives to the financial markets, volatility trading has emerged as a method for investors to make money in every market condition. In parallel with introducing derivatives to the financial markets, hedging methods have emerged and are today essential instruments for the liquidity providers active in the markets. The most commonly used hedging method is delta hedging which cancels out the directional risk in the option. Hedging the vega risk with dispersion trading seems to be both a profitable and accurate hedging method. This thesis examines the effectiveness of dispersion trading for reducing the vega risk in OMXS30 options. This is investigated by backtesting a strategy based on going short OMXS30 index volatility and long volatility on a tracking portfolio with a zero net vega. This investigation aims to determine if the dispersion trading strategy can be a reliable risk management tool. It was found that vega could accurately be hedged using dispersion trading. However, when considering the bid-ask spread, the strategy did not show profitability over the simulated period. Weighting the portfolio more in favour of companies with smaller bid-ask spreads did not show improved profitability. / Sedan introduktionen av derivat på de finansiella marknaderna har volatilitetshandel dykt upp som en metod för investerare att tjäna pengar i alla marknadsförhållanden. Parallellt med introduktionen av derivat på de finansiella marknaderna har säkringsmetoder vuxit fram och är idag väsentliga instrument för de likviditetsgivare som är verksamma på marknaderna. Den vanligaste säkringsmetoden är delta säkring som tar bort den riktade risken i optionen. Att säkra vegarisken med spridningshandel tycks vara både en lönsam och pålitlig säkringsmetod. Detta examensarbete syftar till att undersöka effektiviteten av att använda en spridningshandel för att minska vegarisken i OMXS30-optioner. Metoden involverar att simulera en strategi baserad på att vara kort volatilitet i OMXS30 och lång volatilitet på en spårningsportfölj på historisk data. Genom denna undersökning strävas det efter att avgöra om strategin för spridningshandel kan vara ett tillförlitligt verktyg för riskhantering. Det visade sig att vega kunde säkras med hjälp av spridningshandel. Strategin visade sig vara lönsam under den simulerade perioden men när köp- och sälj-spreadarna i de enskilda aktieoptioner inkluderades var det inte längre lönsamt att utföra metoden. Att vikta portföljen mer till förmån för företag med mindre köp- och sälj-spread visade inte på förbättrad lönsamhet.