A Study On Option Pricing With A Kind Of Renewal Jump-diffusion Process

Financial derivative is a new type of risk management of financial instruments. Options are the most basic financial derivatives, and that the options theoretical research one of the priorities is determining how the growing complexity of the options value. Black-Scholes pricing formulas came out after 1973,the improvement on B-S model was paid constant attention by researchers. In 1976,Merton first proposed the jump-diffusion option pricing model, and then, a large number of domestic and foreign research vigorous jump - diffusion conducted.This dissertation thesis in Merton on the basis of the Poisson jump, promotion for the more general jump process- a special kind of renewal jump-diffusion process. That is the case time interval, and T₁, T₂,... for the mutual independence and obedience Gamma distribution F(α,λ) (a＞0,λ＞0) with the sequence of random variables. In this model, consider the types of options pricing, and corresponding results.The work done by two points in the dissertation is following:Firstly, consider in this model stock dividend payment of the situation, build up stochastic differential equation under the circumstance of the market no arbitrage based on stochastic analysis and martingale theory.The European call option pricing equation and call-put parity are deduced under the contingent claim by means of martingale measure pricing method.Secondly, derive the pricing formulas of the two exotic options-capped calls and deductible calls under the stochastic interest rates by martingale method with the risk-neutral hypothesis.