Spread Option Pricing And Hedging

In the modern financial markets, option pricing occupies a high place. And as one of the important means of hedging strategy, Spread option pricing has successfully and strongly been brought into focus.In the existing literature, all the Spread option pricing models are based on the assumption that assets subject to pure geometric Brownian motion. However, there are so important events in the actual operating process that the prices of the underlying assets and its derivatives have sharply jumps in the capital markets. Apparently the previous method can not cope with the occurrence of these abrupt phenomena. Therefore, Poisson jump is introduced from this aspect in this paper as real as possible to restore the scene over the process of assets changing.In this paper, the cases without jumps and with jumps in the Spread option and Digital Spread option pricing are taken into account. First of all, in the presence of no jumps, log prices of two assets are assumed to be jointly normal distribution. The exercise boundary is defined to be the minimal standardized log price of asset one for the option to be in the money as a function of the standardized log price of asset two. Under the conditions,Spread option pricing and Digital Spread option pricing formulas are derived. Secondly,the price formulas obtained are analyzed. And then, the reduction tools of Spread option and Digital Spread option price formulas—Pearson N proposition and Margrabe equation are described. Finally, the monotonicity and convexity of exercise boundary are analyzed.It can be seen that the existence of a closed form formula for exchange options results from the linearity of the exercise boundary and the conditional moneyness when the spread is zero. Eventually the minimalist analytic solutions of target options are obtained.On the other hand, the jump elements are added and Spread option and Digital Spread option pricing formulas under jump-diffusion models are analyzed and simplified. And the conclusion that the jumps can be eliminated is drawn. Furthermore, the prices of Spread option and Digital Spread option pricing formulas under jump-diffusion models are obtained through the conclusion. Considering the operability of results, the binomial tree method under the constraint to analyzing Spread option and Digital Spread option prices is used, which can be to derive that the prices of option in the initial moment are weighted average of discount of returns in the expiration date and confirm that numerical solution of the option price converge to the analytical solution. Finally, examples are used to validate the models, and sensitive factors of affecting the Spread option prices are intuitively analyzed with comparison.