Pricing Research Of Options On Stock Index Futures

In our country has just launched stock index futures background, this article discusses the pricing of financial derivatives, especially options on stock and stock index futures.Fractal characteristics of financial markets, such as the asymmetry and the long memory features, have been proved by many empirical researches, this paper introduces fractional Brownian motion (FBM) to describe these characteristics of underlying asset, as FBM can well explain these features in the financial markets, at the same time, considering the jump variation of the underlying assets caused by some unexpected events, besides of continuous changes gradually, the paper adds Poisson jump process to reflect such a leap of mutations. Based on the assumption that the underlying asset follows a stochastic model which is conditioned by FBM and Poisson jump process, this paper studies on options pricing on stocks and stock index futures.Focuses on using three different methods such as partial differential pricing, risk-neutral pricing and actuarial pricing methods to solve the pricing model of option on stock index futures, then receives corresponding option pricing formulas, finally gives an explanation for the result that three formulas are identical in nature. This paper on pricing of stock index futures options doesn't use general commodity futures option pricing methods, instead, it bases on the stock index evolution to launch stock index futures evolution, and then introduces stock index futures option pricing formula.Although China has not yet introduced in the stock index futures options, and this paper is advanced research in reality, I believe this theory will have some guidance to the development of China's futures market.