A Research Of Spread Option Pricing

With the continuous development of economic globalization, financial mathematics as anew multidisciplinary is increasingly attaching importance to the financial sector and theapplied mathematics society. Option pricing theory has been the main theory of financialmathematics, and spread options of this study is based on two different asset prices to obtainfinancial derivative gains by the purchase of two goods (such as crude oil and refined fuels,electricity prices and fuel prices), and utilize the difference between the two prices as theunderlying asset.Since1973, Black and Scholes have made some assumptions based on no arbitrageprinciples and published a seminal paper on options pricing[1], by solving a partial differentialequation to obtain the European option price. The famous Black-Scholes option pricing modelis recognized as a very important tool, but this model also has a lot of practical problems. Forexample, a very important assumption in the Black-Scholes option pricing model is that assetprice follows geometric Brown motion, volatility is a constant, therefore it cannot be capturedin the use of the financial markets in the key features of the experience, there is a deviationempirical test, ignoring the implied volatility in practice.In1993, Heston introduced a dynamic random fluctuation to extend the B-S model,better simulating the volatility in the option price smile and smirk changes[2]. Bates in1996combines stochastic volatility and jumps[3], making the simulation of long-term andshort-term option volatility smile with greater flexibility.This paper is a review about the Spread Option Pricing problem, which introducesthe spread option pricing problem of a series of research tools and methods development. Thefull text is divided into five parts, the first part introduces research background of thispaper and the main significance of the problem, the problem of option pricing is used as thecore of the theory of financial mathematics, that has a long history, for exampledetailed introduces some achievements of experts and scholars at home and abroad in theresearch field of the option pricing theory. In the second part, the background knowledge inthis paper are given, the important definitions and theorems such preliminary knowledge. Inthe third part, the Black-Scholes model as the starting point, it introduces the developmentprocess of spread option model, spread option pricing model is generated and then gives a Poisson process models with jumps and produced in the form ofCIR random fluctuations. The fourth part is obtained by comparing the numerical calculationto model the conclusion. The fifth part is the conclusion, a brief summary of the advantagesand disadvantages and development expectation model.