A Study On The Valuation Of Lookback Options In A Jump-diffusion Model

An option is a contract that gives the holder the right (but not the obligation) to buy or sell an underlying asset by a certain time for a predetermined price after paying off the option premium. Since tens of years, option develops at very fast speed as the way of keeping away risk and edging. So the study of option's question becomes important content in modern finance, but the option pricing is the core of the all the questions.On the foundation of standard contract, more different characteristics exotic finance derivatives were designed in order to satisfy the finance market and the different investor especial needs, and keep away the risk which many investors might face. One of them is the lookback options, they are path dependent options whose payoffs depend on the maximum or minimum of underlying asset price attained over a certain period of time. It is more complicated to price the lookback options, because of the path dependence.This paper mostly studies one of the valuations of floating strike price lookback options in a jump-diffusion model, by using the stochastic analysis, partial differential equation and general Ito formula. Firstly, we introduce effective methods of option pricing: A -edging principle and option replicating principle. Secondly, on the foundation of the option pricing model of floating strike lookback options, under the basic assumption of B-S option pricing model. We mostly discuss the following work: (1) We study the option pricing in a jump-diffusion process and set up the option pricing model;(2) Under the assumption of the diffusion process model we study the option pricing when there is transaction cost in the transaction and we set up the option pricing model;(3) We farther our discussing question, study option pricing in an inefficient finance market, that is, with the assumption that the underlying asset pricing is a jump-diffusion process and there is transaction cost in the transaction, we derive the differential equation of the option pricing model finally.