Monte Carlo Simulation Method For Pricing Inflation-Indexed Derivatives

As a new type of derivative securities, inflation-indexed derivatives in the international markets gains extensive attention. The pricing method of this kind of products has become an important topic in the research area. With the U.S. subprime mortgage crisis , inflation become the most important concern in the international economy and the primary control target all over the world. In the beginning of 2010, the central bank issued a series of monetary policy, adjusting the benchmark interest rates and reserve requirements, then reduced the money supply and kept CPI staying at a reasonable level. Inflation as the "one of three carriages" , there are great influence in the economy. In fact, besides some adjustment from the monetary policy, issuing inflation-indexed securities in the financial market will be an allternative way to keep from inflation risk and protect the value of assets. As inflation-indexed securities are a new class of complex derivatives, their research and development need a lot of financial engineering technical support, especially in the designing , pricing, risk control. So, no matter from the macro economic Angle or micro financial Angle, the use of financial engineering technology to pricing inflation-index derivatives has its important theoretical and practical significance.This paper selects feasible and complex inflation-indexed derivatives, including inflation-indexed European call option, and inflation-indexed European swaption as the research objects, chooses proper models of underlying assets and Markov Chain Monte Carlo method (MCMC method) of estimation parameters.At last, we use Monte Carlo simulation method and improved method——Antithetic Variate technique to price the products, showing the process to price inflation-index derivatives. It will be helpful for investors and issuers to understand inflation-index derivatives,and provide corresponding theoretical analysis basis for providers and demanders.Firstly, this paper puts forward the traditional value structure of inflation-index derivatives, using the general form of swaps, options to prepare parameters estimation and pricing process.Secondly, on the basis of characteristics analysis, this paper analyse the underlying asset of inflation-indexed derivatives——inflation rate and corresponding nominal interest rate, real interest rate and propose general diffusion models and jump-diffusion models. Interest rate is based on Vasicek-jump model while inflation rate is based on HJM-jump model.Thirdly, we use MCMC method for parameter estimation and the conclusion is either nominal interest rate, real interest rates or inflation rate, jump-diffusion model is better than general diffusion model, with minimum deviation of historical data, fitting the highest degree, so that be more reasonable and convincing .Lastly, based on jump-diffusion models, we use Monte Carlo simulation method to price inflation-indexed European call option and inflation-indexed European swaption, showing Monte Carlo simulation theory and empirical research, and gaining the two product value. For general weaknesses of Monte Carlo simulation method of volatility, more simulation times, it is proposed the improvement techniques of reduction variance——Antithetic Variate technique and Control Variate technique , including the principles and pricing process and gets the conclusion: compared to general Monte Carlo method , reduction variance technique have less simulation times, less volatility , therefore, be more suitable for complex options in actual use.Through the inflation-index derivatives theory research and empirical pricing simulation technology, this paper can reach the following conclusion: first of all, the selection of the reasonable underlying variables model is the primary factor; Secondly, the use of MCMC method to estimate parameter and the comparison of the result to choose reasonable model, making much more precise pricing value; Again, Monte Carlo simulation method and the improved technology on inflation-indexed derivatives pricing can get a more reasonable results; Finally, the inflation-index derivatives provide a decisive means to avoid inflation risk and stable asset value.