Study On The Strong Path-dependent Options

In the international financial derivatives market, options have developed rapidly. In recent years, a number of exotic options appear,and the strong path-dependent options are one of them.The strong path-dependent options mainly include two categories lookback options and Asian options.The payoff of this kind of the strong path-dependent options depends not only on the underlying asset price, but also on the mark of the underlying asset price in the whole or part of the effective period of options.This paper introduces several generalized models based on the B-S European option pricing model:CEV model, B-P hybrid driven model, the CEV and the B-P hybrid driven model.In CEV model, the underlying asset price volatility is not constant, but the elasticity of volatility is constant; B-P hybrid driven model considers that the underlying asset price may randomly jump up when it follows geometric Brownian motion; CEV and dividends paid and B-P hybrid driven model considers the situation of the previous two models.The three models make the stochastic processes followed by the underlying asset price be more closer to reality.On the basis of the previous studies, the author has researched the pricing of lookback options and Asian options under the three kinds of promotion models. We get the pricing model of lookback options and Asian options by the no-arbitrage principle and risk neutral pricing under these models and study the numerical solution of the arithmetic average Asian options with the discrete dividends payment through the binomial tree pricing model. This can make us compare the influence of three kinds of promotion pricing models to price options better.