As for the improvement of the numerical method, the first step is to introduce the Brownian bridge method, which makes it unnecessary to simulate the stock price at all times and save it to the end of the whole calculation. Thus it is saving the storage space and improving the calculation speed effectively. Based on the brown bridge method, the backward simulation of stock price can be realized. Because the stock price distribution at any intermediate time is known based on the initial and final value of the stock price, the stock price distribution at any intermediate time is known, so that only the stock price at two moments participating in the calculation is required to be saved in the iterative steps of each time point.
Secondly, the variable control method, which is one of the variance reduction techniques, is used to reduce the width of the confidence interval of the statistical estimation, so as to improve the estimation accuracy. European option is selected as Y in two specific examples of option pricing. It is found that the square difference obtained by using the variable control method is much smaller than that by using the variable control method(Duan, 2010).
Time all can exercise the option, but in the actual transaction of American options don’t always have the characteristics of some standard (Merton, 1977). Especially in the stock option market is limited to a specific date for the period of validity of the options rather than at any time to exercise the option. Namely the price has the characteristics of path dependence (Merton, 1973). It can be seen that the pricing of Bermuda options not only has important theoretical value, but also has important practical significance.
But because of the complexity of the characteristics of path dependence, option pricing is relatively difficult, less about the study of literature (Kou, 2002). By adopting the method of partial differential equations with jump diffusion is discussed in a permanent option pricing problem , but he only solution as a periodic solution of the mathematical model of continuous. However, it gave no general continuous Bermuda option pricing formula under the market model.
They extended the insurance actuarial method to the pricing problem of foreign exchange option and Asian option, etc. Because the advantages of the insurance actuarial model without any conditional assumptions made the application of this method extremely broad. This article uses the actuarial method of insurance to give the Bermuda option pricing formula under the continuous market model and gives the corresponding empirical analysis (Quigg, 2012).