| As a fastest growing financial derivatives instrument, foreign exchange options are favored by various countries and economies because of its good hedging effect, though they do not have a very long history. Scholars keep researching and improving on its pricing model. Under the assumption of volatility was a constant, we can get the corresponding closed form solution of the European option value, derived from the traditional mean-reverting lognormal model. And applying this model to the pricing of foreign exchange options, they will show the nature that foreign exchange rates are always fluctuate around its mean value within certain ranges, so its effect of pricing is good. In this paper, we improve the assumption that volatility was a constant, proposing the price-dependent mean-reverting lognormal model in which the volatility is a function of underlying asset. Based on the data, using the methods of non-parametric estimation, we value the volatility. Then substitute the estimation results into the model and the corresponding numerical solutions can be derived. Specific works are as follows:Section1introduces the current development of foreign exchange options and financial derivatives, the properties of mean-reverting model are also included; Section2illustrates the mean-reverting lognormal model, its mathematical derivation, and the importance of stochastic volatility in improving the accuracy of the pricing model; Section3mainly presents the wavelet estimation methods, we can use this to value the diffusion coefficient of the model; Section4of this paper shows the process of deriving the price-dependent mean-reverting lognormal formulas and derives the corresponding numerical solution. The boundary conditions of the solution and its stability and compatibility are proved; Section5shows the empirical analysis we can get from the data using the methods described in the section above. And conclusions are drawn as follows:the price-dependent mean-reverting lognormal model has a high accuracy in pricing when the volatility of the underlying assets is high. |
