Option Pricing For Jump Model In Dual Currency Market

The main research of this paper is option pricing problems for jump modelin dual currency market, The primary Black–Scholes model is no longer applicablewhen the price of risk assets jump in fnancial market. This paper discusses theEuropean option and American option pricing.We get explicit expression of European option pricing under the assumptionsthat the price of risk asset follows Poisson process and the jump-range is constant.Then we construct a new measure Q which is equivalent to the original marketmeasure P by using Girsanov theorem with jump and multiple-factor. Then weprove the measure Q is risk neutral. European option pricing formula for the jumpmodel is obtained with the help of the martingale approaches.We cannot get explicit expression of American option pricing. In this chapter,the American option model is slightly change to compare with European optionmodel for simple calculation, but they have the same essence. We need to discusswhether the jump risk is calculated in the price of American option for single jumpof risk asset is negligible for the market. Then a free boundary problem about theprice of American option is deduced by taking diferent-hedge strategies throughpartial diferential method.This model has certain practical signifcance and can be used to hedge riskwhen asset price jumps or other emergence occurs.