Research On Pricing And Risk Management Of Equity Derivatives

The research on pricing and risk management of equity derivatives is a comprehensive problem in academia and the practice. After the Subprime mortgage crisis in America, people pay more attention to the risk management of derivatives. The crisis is explosive by Credit Default Swap, which is priced on the assumption of house pricing will be rising continuously. Listed equity derivatives have little relationships with the crisis. While, the crisis still taught us the lesson. When we talk about equity derivatives, pricing and risk management are still the most important points, and that is why the paper started.In china, we have no equity derivatives now, and the investors can only earn from the stock price rising. The professional investors act coincidentally, and let the market fluctuate dramatically. It is concerned by the investors, the government, and the researchers that how to control the risk of the equity derivatives. Meanwhile, we must price correctly and efficiently in order to control the risk of the equity derivatives. Futures have symmetrical rights and responsibilities, so they are easier to give prices of the futures, while the options have more complicated pricing models since they have unsymmetrical rights and responsibilities. Black-Scholes Model and Monte Carlo Simulation are the basis of the option pricing, but in the practice, exotic options cannot be priced by the Black-Scholes Model, and the Monte Carlo Simulation is too slow to simulate millions of the paths. So it is the complicated question that how to price the exotic options fast and correctly.The paper started from the pricing of equity derivatives, and gave some new and practical method to measure the price and risk of the equity derivatives. Since the futures have symmetrical rights and responsibilities, the paper does not discuss the pricing of the futures, and concentrates on the pricing of the options, especially the exotic options. We use Crank-Nicolson Method and solve the Partial Difference Equation so that we get the closed form of the exotic options, and discuss the risk management with the price methods. Consequently, we concern the particularity in our nation's stock market, and give the method how to control risk better in the given conditions in our nation. As to the futures, we optimize the arbitrage model and the hedging model, and solve the problem that some stock has too low ratio in the stock portfolios. When we track on the stock index using empirical method, our optimized model shows the better results than the regular models.The paper uses several quantitative economic methods and gives some innovative ideas as follows.1. We solve the closed form of the path-dependent options, and find out the difference and the strengths and weaknesses between the closed form and Monte Carlo Simulation through empirical methods.2. We solve the American put options using Finite Difference Method (FDM) and find out the difference between the method and Monte Carlo Simulation.3. We solve the Greeks of the American put options using Finite Difference Method (FDM). Specially, Gamma should be dynamic configuration to be stable and accurate.4. In our nation's particular situation, we analyse the sensitivity of the Asian Option's volatility to the P&L and the money used. We make the P&L and money used stress tests in the higher accurate volatility, the sharp turbulence of the stock prices, and lass of liquity.5. We measured the best hedge ratios of the stock index futures through empirical methods, and found that the hedge ratio using ECM model is bigger than the OLS model, but the different range can be accepted. In practice, the samples should match the time period of the hedge. If we hedge for a short period of time, we should collect less samples; otherwise we should collect more samples.6. We enhance the hedge models with the proportion of the stock investment portfolios, and solved the problem that some stock maybe has too little proportion in the stock investment portfolios. In empirical practice of tracking stock indexes, our enhanced model is better than the old ones. At the same time, our enhanced model of arbitrage between the stock portfolio and the futures is better than the old ones through empirical test.Overall, we suggest that equity derivatives can enhance the accuracy of risk management through improve their pricing methods and efficiency in China. We should enhance our methods to control the risk better. It is much meaningful both to the academia and the practice. It is also meaningful to the governor of the stock market. Meanwhile, the professional investors like securities and funds, should do sensitivity analysis and stress test in our nation's special conditions, to manage the expected and unexpected risks. They can also use the optimize arbitrage model and hedging model to control the risk better, and get the rational earnings.Governors may request the professional investors to do the earning stress tests, the money occupied stress tests, and the sensitivity analysis as the paper says. Thus the governors can use the data to know and govern the professional investor's risks and behaviors.