Strongly Path Dependent Option Pricing Under CIR Stochastic Interest Rate Model

The time to maturity value of strongly path dependent option not only depends on the underlying asset’s price at the maturity day, but also on the whole (part) path of underlying asset within the validity period. This kind of option can be divided into Asian Option which the value of depends on the average price and Lookback Option which the value of depends on the largest (small) price. Because of strong path dependence, compared with European Option, the price of Asian Option is cheaper. Lookback Option’s value, which is also strongly dependent on the path of the underlying asset before its maturity day, is so high that it’s very expensive. Because of its strong path dependence, its pricing problem becomes extremely complicate.At the same time, when we consider the option pricing question, the market is instability even if the short-term interest rate is constantly changing. So the hypothesis, which can make the problem becomes relatively simple, that interest rate is invariable in option term of validity is insufficient to meet the practical application. Therefore, interest rate uncertainty can be added in the study of option pricing.On the basis of CIR stochastic interest rate model, this paper obtains the pricing models of Asian Option and Lookback Option including the factor of advance execution, and then calculates their numerical solutions by Finite Difference Method. To illustrate this approach, an example is given at the last part of each question calculated the final solution by MATLAB.