Binary Option Pricing Under The Martingale Method

Option is an important financial hedging derivatives. The1997Nobel Prize in Economics was awarded to option pricing formula in-ventor. This shows the importance of option’s research. In recent years, many scholars have done lots of research using various methods in the underlying asset follows different models. In addition, compared with the standard exchange-traded products, there are new option products to meet the special needs of the market, sometimes they are attached to the bonds issued in order to increase the attractiveness of the market. Binary option is a discontinuous income option only when the price of the underlying asset more than the exercise price will have benefits. This paper first studied the underlying asset follows geometric Brownian motion, using of Girsanov theorem to measure transformation and the Bayes rule to eliminate random item, then got binary option pricing formula. Underlying asset follows a geometric Brownian motion, which means that the price of the underlying asset is a continuous process. But in the actual financial market stock prices will jump because of some unusual factors. To this end, we further investigated binary option pricing in jump-diffusion model, got the pricing formula. The pricing formula will be seen in the special case of geometric Brownian motion, compared to the latter for verification.