The Research Of Pricing Crack Spread Options Based On Fourier Transform

In recent years, with the developments of the global financial market, options and other financial derivatives are attracting considerable attention. Due to increasing demand, more and more types of options will be traded. Option has become one of the main investment tools for many market participants, especially in the commodities markets. Crack spread option is closely related to the energy commodities markets, and its payoff is the difference between fuel oil and crude oil. It is widely used in hedging and many scholars do research on pricing crack spread options. But the law of price movements in commodities markets is different from financial securities markets. Affected by storage costs and seasonal factors, the price behavior in commodities markets has special characteristic, like mean-reversion and seasonality. Thus, it is difficult to pricing the options under the framework of traditional B-S theory.In order to meet the actual price behavior of the commodities markets, here the ASubClR (Additive Subordinate Cox-Ingersoll-Ross) model is adopted to study the pricing problem. The model is time-inhomogeneous and mean-reverting, and it is helpful to capture the implied volatility surface of future options and implied correlation coefficient of spread options. Using the Fourier transform method, we can price options by finding the moment generating function of the price variable. Lastly, we get the pricing formula of one-factor future options, two-factor future options and spread options.In empirical example, we use C++ and MATLAB programming language to implement all option pricing formula. We compare our method with eigenfunction expansion approach of Li Jing. Using the same parameters, we calculate option prices for 40 different strike prices of each option expiration time. The conclusion is that our Fourier transform approach is faster than Li Jing’s. At the same time, another empirical example with certain parameters of crack spread options is offered, which verifies the feasibility of the method.