The Optimal Arbitrage Strategy In Stock Index Futures

This article is concentrated on the pricing of American option which appeared in stockindex futures market. It's composed of seven parts below,Firstly, review Literature and issues.Secondly, Expatiating the concepts of threes kinds of American option and connectionamong them.Thirdly, Mainly narrating framework of mould of pricing of stock index futures, including the interpretation of differential equations and main boundary conditions.Fourthly, we describe the transaction data of current and futures stock market in TaiWan in 2007-2008 and also estimate parameters from historical data of every contract.Fifthly, we obtain the value of three kinds of American option corresponding to the different s(t) at every time point before expiration of future contracts by solving the differential eguation from the derivatives as well as using the estimated parameter we got in part 4 above. So we can determine four symmetrical boundaries of manipulation and perform sensitivity analysis of factors which affect value of option.Sixthly, To practice arbitrage on the basis of four boundary, we establish and close out positions by using simulated data, then compare the final return to simple arbitrage strategy's.Seventhly, Making a summary and raising the deficiency of this article.Coming to the conclusion below, following,(1) There will be three kinds of American arbitrage option derived from the stochastic volatility ofε(t), which are the option of closing out long arbitrage position before expiration, closing out short arbitrage position before expiration and the option of establishment of new arbitrage position. These three options are impacted by the time to expiration, volatility, trade cost and the boundary ofε(t).(2) We can get four boundary of manipulation by pricing of three kinds of American Options using Numerical Methods. The return we got on the basis of new arbitrage strategy will surpass the return of simple arbitrage strategy that we maintain arbitrage position till the expiration of future contract.(3) Under the circumstances of high fluctuation rate, If we set the boundaries ofε(t) close to trade cost of establishment of arbitrage positions, it won't affect the stability of the optimal arbitrage strategy return.