Option Pricing And Risk Management Under Time Varing Variance

Option pricing and risk management are the most important fields of option research.After Black & Scholes published the famous option pricing model in 1973, option pricing theory has became an academic research focus. But the assumption of constant of volatility don't match the market real situation. Many positive research on stock volatility shows that the volatility is variable. As a result of many unduly simplified assumptions of B-S model, many scholars started to modify the B-S model, such as the"stochastic volatility option model","stochastic interest rate option model"and"stochastic volatility and poisson jump diffusion option model". Many scholars devoted themselves to investigate the issue about whether the free-restricted models outperform B-S model. Most empirical results indicated that the free-restricted models outperform B-S model.Option pricing and risk management under time varing variance has been deeply developed on theory and empirical aspect of overseas. In the domestic, the relative research is scanty because of the underdevelopment of the financial derivative, especially on empirical research.Considerable theoretical work has been devoted to option replication in the presence of transaction cost, and several competing methods have been advocated to improve the dynamic hedging risk-return tradeoff. Very little is known on the subject from an empirical standpoint.This paper attempts to provide a systematic comparison of the four popular methods of option hedging in the presence of transaction cost within a unified mean-variance framework, and using an extensive data set of simulated asset prices. In the presence of proportional transaction costs and constant volatility, the optimal control or delta move-based approach clearly dominates other types of strategies, including time-based strategies and strategies based on moves in the underlying asset.This paper examines the out-of-sample performance of two common extensions of the Black-Scholes framework, namely a GARCH and a stochastic volatility option pricing model. It attempts to employ the models to empirically examine the pricing of our stock market related warrants. When analyzing the observed prices, GARCH clearly dominates both stochastic volatility and the benchmark B-S model.This paper study the option pricing and risk management under time varing variance systemically and deeply first time. The research expects to provide some useful information for further study.The innovation of this paper including :1. The most comprehensive analysis on NGARCH, EGARCH and GJR-GARCH model and apply into Chinese market for the first time.2. Considering the local market situation, change the GARCH and SV model. The modified model can match real option market better.3. Propose the framework of general factor and Chinese factor based on the price difference. The Chinese factor is the important one causing the difference.4. There is seldom research on hedging strategy. The paper is the first time on this field and analysis multi-factor hedging strategy.5. About the GARCH and SV model, this paper is the most comprehensive one in this field.The first chapter is exordium, which introduce the background, objective and framework. The second chapter discuss the literature based on B-S model and the modules of reducing the restrict on B-S model. The third chapter introduces many model, including GARCH family model and stochastic volatility option pricing model. It also discuss the effect of alterable parameters. The fourth chapter is empirical analysis based on B-S model and stochastic volatility option pricing model. It discuss the reason of difference and bring forward to some suggestion of how to improve efficiency.The fifth chapter concentrate on the impact of all kinds of risk management, including the constant of volatility and stochastic volatility. The last chapter presents the conclusion and potential research aspect.The empirical conclusions are:1. Overall, the real market price is much higher than the model price. The higher situation is seldom.2. Some GARCH model performance is better than HESTON model and B-S model. That means GARCH family is a proper choice of pricing model.3. For buying option, the gap of model price and the real market price is smaller along with the duration is coming. The advantage of move-based methods over time-based methods increases with reduced drift of the underlying asset and increased volatility of the underlying asset. Move-based strategies are hurt by the introduction of stochastic volatility.Because the difference is large, the paper analysis the several reasons, including the lack of option, the strict restrict of security company, no oversell system ect, . These factors impact the B-S formula applicability. The relative suggestion is to increase the supply of the derivative and consummate the institution.Under the united mean-variance framework, this paper analysis four kinds of hedging strategy. The conclusion is: Whalley-Wilmott is the best one, Delta is the second, Leland is the third one and B-S model is the last one.Overall, the conclusion is that the more complex option pricing models, such as GARCH and SV can improve on the B-S methodology only for the purpose of pricing, but not for dynamic hedging.