Research On Risk Measurement Of Options

In modern financial theories and practices, options are a kind of financial derivative tools which has the most complex theories, the most flexible application, the most completed function, but meanwhile, it also results in the fact that options are frequently used in speculation because of it's characteristic of high financial lever, low bargaining cost, the convenience of completing the business transaction and high fluidity, and then it becomes an efficient instrument for speculation. When options are increasingly used in speculation but not for the purpose of hedging, they will bring about risk themselves for requirement of avoiding the risk. Therefore, how to efficiently control the market risk in financial market especially in the financial derivative market has become a burning question for various which are in possession of assets.In the text, option pricing and its risk measuring are the key points in this thesis. We use the popular risk metrics Value at Risk( VaR) and coherent risk measuring technique Conditional Value at Risk(CVaR) to conduct the formulas of VaR and CVaR for European options on dividend-paying securities based on the derivation VaR for European options without dividend-paying, furthermore, we generalize the one-dimension condition to multidimensional condition and measure the market risk of index option separately by using VaR and CVaR. Finally, this text takes the Shanghai and Shenzhen 300 index as the underlying asset of index options and simulates the market risk of our country based on its historical closing price. In addition, since our nation does not have option market, this text can be considered as the perspective research and theoretically and practically provides certain references for researcher and designer of financial derivatives of our country. This text mainly has six chapters as follows:In the first chapter, Elaborate the background and significance of this topic, and introduce the present instance both home and broad and the basic writing idea and main contents. In the second chapter, we introduce the definition, features and categories of options, and the Black-Scholes option pricing model, and elaborate the definition and calculation method of VaR which is the risk measuring technique of options, and then introduce the coherent risk measuring technique CVaR due to the disadvantages of VaR.In the third chapter, we introduce the analytical and approximate methods of computing VaR of options, and point out the inadequacy of the calculation of VaR for options in the existing literature, we deduce the formula of VaR of options after the correction. Meanwhile, this text uses CVaR to measure the market risk for European options without dividend-paying. Considering that options are a kind of financial derivative tools having the characteristic of nonlinear curvature, this text presents the Delta-Gamma approximate formula of the utmost losses of options in the small time interval during the period of holding options.In the fourth chapter, we deduce the computational expression VaR for European options on three types of dividend-paying securities on the basis of derivation VaR for European options without dividend-paying.In the fifth chapter, we firstly give the pricing formulas of index options under two kinds of assumptions of the movement of underlying asset, and with VaR and CVaR, we measure the market risk of index options, and give the computational formulations of the utmost losses and extreme average loss under the given the confidence level of index options, finally, we simulate the market risk of index options of China with the underlying asset- the Shanghai and Shenzhen 300 index.The sixth chapter concludes and presents the emphases which we study further.