The Reflection Principle And The Using In Pricing Of Financial Derivatives

Along with the development of China's financial market reforms, all kinds of financial products to more and more in our daily lives; the pricing of financial products has become an issue of increasing concern. The problem of barrier options and lookback options was tackled by Kunimoto and Ikeda (1992) and Geman and Yor (1996) who proposed accurate algorithms developed in a continuous-time setting under the usual assumptions of the Black-Scholes analysis. Both these model are based on the assumption of a continuous monitoring of the option contract. This means the underlying asset price has touched or crossed the barriers. However, in many cases this assumption is not realistic and only a discrete monitoring of the contract is possible. In these situations a discrete-time algorithm is needed to give the correct answer to the problem of pricing barrier options. This paper bases on the Cox-Ross-Rubinstein's binomial tree model, extending the Boyle-Lau algorithm, and using the reflection principle for random walk theory, to solve pricing problem of some special options and some financial derivatives. In this framework, the underlying asset process is a random walk and the price of financial derivatives is determined as the discounted value of the payoff at maturity under the risk-neutral probability measure. At last through the comparison with the continues-time model reflects the good nature of these methods tackled by computers.