Pricing The Single Point Multiple Level Reset Call Option With Martingale Theory

"Option" is considered to be a successful example of creative practice world finance market of the 20th Century. Although options have been firstly traded in American Chicago Board Option Exchange since 1973, almost nobody could, at that time, foresee that they would bring about huge influence on practice and financial and banking theory in the following several decades. Now option market has become an important part of international finance market. Under such background, research and application of option pricing theory, currently, set off a new climax of innovation in the field of financial theory.A new kind of reset option will be introduced in this paper, and we are going to give out the expression in multi-integration form with the method of martingale theory and stochastic analysisThis new kind of option, single point multiple level reset option, based on the research of the theory before, I constitute a brand new kind of reset option. Inspired by the convertible bonds'exchange regulation, a new stage of the reset is added to the option besides of the basic principle, which can be more helpful to prevent the arbitrage of the speculator controlling the asset price by means of great amount contract than the original reset option. The aim of our research is actually to show the fair price of the option in the risk neutral probability measure with Girsanov theorem. The new option just break the ordinary thought of the reset option, and much knowledge of stochastic differential equation and the Multiplication Formula in probability space will be necessary for solving the pricing problem, setting out some creative work.