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Option Pricing Model When Stock Pricing Process Is A Jump-Diffusion Process

Posted on:2007-04-14Degree:MasterType:Thesis
Country:ChinaCandidate:Y F YangFull Text:PDF
GTID:2179360185458455Subject:Applied Mathematics
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Option pricing theory is always one of the kernel problems on financial mathematics. Together with the portfolio selection theory, the capital asset pricing theory, the effectiveness theory of market and acting issue, it is regarded as one of the five theory modules in modern finance. The domestic and foreign scholars have done a great deal of researches on Black-Scholes model and obtained many results which is instructive to financial practice. However the appearance of important information will cause the stock price to a kind of not continual jumps. A mass of finance practice has indicated that there is a serious warp between the hypothesis of Black-Scholes model about the underlying asset price and the realistic markets. Therefore, many scholars put forward many new kinds of option pricing models by relaxing some assuming conditions of Black-Scholes model. Option pricing theory with jump-diffusion is one of them.This article considers that price of underlying asset price obeys jump-diffusion process, because in the reality the stock price jumps do not necessarily obey the Poisson process, jump process generalized conforms to the actual situation of stock price movement, and other influential factors has also been considered.This dissertation is intended to study option-pricing theory with jump-diffusion, so as to establish the mathematic module of option pricing with jump-diffusion process by means of mathematical tools such as martingale theory and stochastic analysis, and deduces the option pricing equation.In detail we have made main conclusions as follows:(1) Under the hypothesis of underlying asset price being driven by a jump-diffusion process and the jump process is count process that more general than Poisson process. Using martingale method, European option and put-call parity is analyzed.(2) Under the hypothesis of underlying asset price being driven by ajump-diffusion process that is a count process discussed the option pricing when interest rate is random variable, we obtain the pricing formula of European call option.(3) Establish the option-pricing model when exercise price is random variable. The option-pricing model is options to exchange one asset to another. Pricing formula of European option is also given.(4) Considering dividend, we establish the option-pricing model with jump-diffusion process. Under the hypothesis of continuous dividend, if the continuous dividend rate is p, and regular payment dividend, we get European call and put option pricing formula and their parity.
Keywords/Search Tags:Option pricing, Jump-diffusion process, Count Process, Martingale method, Stochastic interest rate, Dividend
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