Study Of Pricing On LOOKBACK SPREAD Option Of Stock Price Index Based On Empirical Distribution

Financial derivatives are financial instruments based on traditional financial products,and have higher returns and risks compared with its underlying asset. Investors oftenonly care about its higher returns but ignore its enormous risks, which triggered the U.S.financial crisis. TMeanwhile, as financial instruments, investment instruments, hedgingtools, financial derivatives enrich types of financial products and make the financialmarkets more active. Therefore, an objective judge on the financial instruments isnecessary. In this paper, we choose and construct an option pricing model of arepresentative option-Lookback Spread Option whose revenue is higher and volatility isalso larger than the general Lookback Option.TIn the paper, firstly, select 7 stock price indexes among the international stock markets,and get the basic statistical characteristics of them; secondly, use the least square methodas a standard to fit the empirical distribution of the range earning of the stock price indexby applying Matlab software, and identify the non-center F distribution as empiricaldistribution of the range earning of the stock price index. Then, referring to the principlesof B-S option pricing model, construct an option pricing model based on the empiricaldistribution using the risk-neutral pricing method and explain the parameters of themodel indetail. Next, make a simple derivation of B-S option pricing formula on theLookback Spread Option, and make a detailed instruction of the two importantparameters in the model: the volatility(σ) and risk-free interest rate( f r ). Finally, takingShanghai Composite Index for example, calculate the prices of Lookback Spread Optionunder the classical B-S model and the empirical distribution model, and analyze thesimilarities and differences of the prices and make a brief analysis of the reasons for thisphenomenon.