Monte Carlo Method In The Three Categories Of Financial Derivatives Pricing

Valuing and hedging securities, risk management, portfolio optimization andmodel calibra tion are four most concerned questions in the financial industry.Among them, pricing financial derivatives is the priority among priorities. The studyof pricing financial derivatives has occurred a historic breakthrough since optionpricing model of Black and Scholes was born, and it cases extensive attention. In thefinancial market today, the various kinds of derivatives not only in clude standardEuropean Option and American Option but also abundant exotic options and otherfinancial derivative instruments. These bring huge challenge for pricing financialderivatives.In essence, the difficulty of pricing is brought by higher dimension. It results inthat analyticalsolution for pricing model of financial derivatives can’t be obtained, so that thenumerical method is needed. Monte Carlo method is a numerical simulation methodbased on random number. The order of its convergence has nothing to do with thedimension of problem. Thus, Monte Carlo method has become the importantinstrument of computing high dimension problem of pricing financial derivatives. Inorder to overcome the slow convergence rate of Monte Carlo method, numerousvariance reduction techniques are widespread used along with the Monte Carlomethod developing. In this paper, the application of Monte Carlo method in pricingfinancial derivatives will be studied Through three fields, Asian foreign exchangeoption, Basket Option and credit default swaps. This paper is consisted of thefollowing six chapters:In chapter one, preface summarizes the background and meaning of theresearch, and it introduces development of correlational studies and the contents ofthis paper.In chapter two, overview the main idea and fundamental principles of MonteCarlo method and introduce its application in pricing problem of financial derivativesas well as its advantage. In chapter three, the mathematical model for pricing arithmetic average Asianforeign ex change option under stochastic interest rate and stochastic volatility wasestablished by properties of martingale. Because the obtained equation has not theexplicit solution, a simulation analysis is conducted by applying Monte Carlo methodcombined with the variance reduction techniques with controlling variables. Thesimulation variance is reduced effectively and the numerical re sults of the pricingproblem are obtained.In chapter four, we conduct a simulation analysis by applying Monte Carlomethod combined with the variance reduction techniques with multi-mean valuecontrol variate for pricing basket arithmetic average option under the assumption ofVasicek stochastic interest rate. we reduce the simulation error effectively and getthe numerical results of the pricing problem.In chapter five, we presents a study of the valuation for credit default swap ofcounterparty with credit rating. The default contagion model based on credit rating isbuilt by considering that counterparty default intensity is changing along with itscredit rating and also reference firm default intensity is impacted. Then pricing modelfor the value of CDS is obtained via analysing cash flow of different default situation.Finally Monte Carlo method is used to get the numerical solution and calculate theCVA.In chapter six, a summary of this paper is made and further research outlinesare provided.