| As financial markets flourish,so do trading risks.In order to meet the demand for trading and avoiding risk,a large number of derivative products emerged,Op-tions become better financial derivatives because of their flexible contract mecha-nism.Asian options for its maturity date returns depends on the average price of underlying asset over a period of time,which make it not only cheaper,but can ease the speculation and hedge risk,therefore it is highly welcomed by investors.As the classic model,Black-Scholes option pricing model is widely used in the option pricing,but this model is derived based on numerous ideal assumptions(such as asset returns volatility is a constant),which is far from real financial market.In fact,the volatility of asset returns will fluctuate over time,with the characteristics of volatility aggregation.GARCH model is widely used in predicting the volatility of asset returns.The value of Asian option is influenced by the change of the price path of the underlying asset,and it has strong path dependence.Monte Carlo method can simulate the price changes of financial assets better,and its advantages are obvious in the pricing of path dependent options.Therefore,the Monte Carlo method is used to solve the pricing of GARCH model Asian option.The Monte Carlo method is simple in thought,convenient in calculation,the standard error of the estimate is also given when the estimated value is simulated.However,Monte Carlo method is not very efficient in calculation.In order to achieve certain precision,a lot of simulation is needed.Some variance reduction techniques such as Antithetic variables,control variables and importance sampling techniques are often used to reduce the simulation variance.In addition,the Quasi-Monte Carlo method based on low discrepancy sequences can impprove the error convergence rate from O(N-1/2)to O(N-1)(N is path numbers of simulation),is also a kind of method commonly used.In this paper,we discuss the pricing of arithmetic average Asian option based on GARCH model under the Monte Carlo method.It provides some ideas and methods for Asian options pricing.This paper is divided into five parts.The first chapter introduces the research background,methods and contents of the article.The second chapter deduces the classic Black-Scholes option pricing formula,and gives the analytic solution of the geometric average Asian option based on B-S model.In the third chapter,the GARCH model and Monte Carlo method are briefly introduced,then Monte Carlo simulation is used to solve the price of the arithmetic average Asian option of GARCH model.The fourth and fifth chapters are the improved parts of Monte Carlo method.The fourth chapter introduces Monte Carlo variance reduction technique,and the numerical results show that the best variance reduction effect can be obtained when the stock price is selected as control variable.In chapter 5,Quasi-Monte Carlo method is applied to the simulated pricing of arithmetic mean Asian options in different dimensions.The empirical results show that Quasi-Monte Carlo method does improve the accuracy of simulation error.the low difference sequence of Sobol has the best performance.Finally,this paper combines the above two methods,and the numerical simulation results show that the combination of variance reduction technique and Quasi-Monte Carlo method can improve the error accuracy of the simulation estimate.The main innovation points of this paper:1.The GARCH model is combined with the classic Black-Scholes option pric-ing model to modify and improve the volatility of the asset yield of B-S model.2.The variance reduction technique and Quasi Monte Carlo method are ap-plied to the pricing of arithmetic average Asian option of GARCH model respec-tively,and combine the two methods,obtaining the better results.3.In different dimensions,selecting the appropriate low difference sequence and control variable technology to combine.which can improve Monte carlo simulation error accuracy and convergence rate. |
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