Study On Pricing Lookback Option Under The Log Student's T-distribution With Jumps

The classical Black-Scholes option pricing formulas took Brown motion as driven noise.But a lot of empirical researches showed that the density function of stock yields presentedthe character of high peak and fat tails. So researchers established the hyperbolic distribution,Pareto distribution, Student's t-distribution and stochastic volatilities model of stock returnsto reflect the real dynamics of stock price on the market as accurate as possible. The Student'st-distribution was especially discovered to fit extremely well the distribution of logarithmicstock returns. Therefore, there are essentially theoretical and practical significances to studythe problem of options pricing under the Student's t-distribution model.Financial institutions designed many new options whose trading ways were moreconvenient and flexible and trading prices were more suitable, and lookback option was oneof these options. Lookback option's returns depend on the dynamics of stock price strongly inthe effective period and lookback option is one typical kind of strong path dependent options.So it is very significant to study the theories of this option in detail. The paper mainly studiesthe related problems of lookback option pricing under the log Student's t-distribution withjumps.The core parts of this paper are in chapter three and four. Chapter three mainly studiesthe problem of lookback option pricing under the log Student's t-distribution with jumps. Themethods are divided into three steps:(1) The model assumptions are proposed by combiningwith behavioral finance related theories, the partial differential equations which the optionprice satisfies are deduced by using conditional delta hedging, and the theoretical prices oflookback option are given.(2) The close-form solutions of lookback option's market pricesare got by using a minimal mean-square-error hedging, and they are in agreement with theasset prices' mean reversion viewpoint of behavioral finance.(3) A new estimated method ofvolatility parameter σ based on Value-at-Risk (VaR) is proposed such that the pricing erroris in accord with the risk preferences of investors. Chapter four studies the parities relationbetween floating lookback options and fixed lookback options.The innovation points of this paper are:(1)The problem of lookback option pricing under the log Student's t-distribution withjumps is studied comprehensively. (2)The local information assumption is proposed on the basic of scale invariance.(3) The method of minimal mean-square-error hedging is put forward and the close-formsolutions of lookback option's market prices under the log Student's t-distribution with jumpsare obtained.(4) A new estimated method of volatility parameter σ based on Value-at-Risk (VaR) isproposed.(5) The parities relation between floating lookback options and fixed lookback optionsare given in detail.