The Convertible Option And Its Pricing Analysis

It is considered option has extensive prospect because it is widely used in hedging of the underlying asset and avoiding the risk and speculation. Since the appearance of Black-Scholes pricing formula at the beginning of 1970's, the option market has been developed quickly. Now option market has become an important part of international finance market. With the development of financial market, how to design new options base on the practical problem and give it a reasonable price is a important research content of option theory.In this paper we proposes a kind of exotic option ,convertible option , when the market develops in different directions that expect with investors , the option can be transferred from call option to a put option , or transfer from put option to a call option. Because there is much uncertainty in the realistic market, the investor is very difficult to know the future price of the underlying asset will be rise or drop, so we will face the risk in various degrees under many circumstances when buy in the call or put options, however, the new option can reduce risk and increase income in a certain extent because of its convertibility.Under the assumptions of Black-Scholes model, we research the convertible barrier option by Martingale method and Monte Carlo method. There are four parts in the paper, some knowledge about options are firstly introduced in the chapter 1. In the chapter 2, the pricing formula of the new option is obtained with the help of the Martingale method and the theory of the stopping, and the price of the new option is analyzed by compare it to the standard European options. Analysis result...