RMB Currency Options Pricing In Quantum Finance

Traditional option pricing method is to use partial differential equation to obtain option price,but with the development of quantum finance,research on?applying Feynman path integral in quantum mechanics to financial derivatives pricing is increasing.Because Feynman path integral can not only simplify the option pricing process and has the advantages over obtaining analytical solution and numerical solution of option price,but also it is easy to expand to high-dimensional option pricing model.Feynman path integral can provide more complicated options pricing with a new research idea.In addition,Chinese foreign exchange market officially launch options trading of RMB currency options on April 1,2011 and it adopts the G-K model to price(assuming that exchange rate following geometric Brownian motion),but considering real situation in current foreign exchange market,using a mean reversion process to describe the change of the exchange rate would be more appropriate.Based on the above background,this article from the perspective of quantum finance,applying Feynman path integral to construct RMB currency options pricing model,in order to be able to provides a more generalized analysis framework and reasonable pricing model for RMB currency options pricing.First,this paper introduces the two expression forms of quantum mechanics including schrodinger wave mechanics and Feynman path integral,this paper expounds that the Langevin Equation and Planck equation in Physics are equivalent to stochastic differential equations and partial differential equations in financial derivatives pricing.Lately,this paper discusses why and how to use the above two expression forms to option pricing.Secondly,using the Feynman path integral to reconstruct the classical G-K model and use the Gaussian integral and the Fourier transform to solve the pricing result,which consistent with the traditional method;Considering the actual situation in current market,exchange rates are assumed to be a mean reversion process and build the corresponding path integral foreign exchange option pricing model(called simply MRL model)and using the one dimensional haRmonic oscillator in the quantum mechanics to calculate the analytical solution.Then,this paper makes a theoretical comparison between the above two models,founding that the foreign exchange option price of G-K model is always greater than the foreign exchange option price of MRL model and the price difference increases with the option maturity increasing.Finally,this paper carries out empirical analysis,founding that RMB exchange rate follows a mean reversion process.Then this paper estimates the parameters of the two models of parameters and calculates the prices of RMB currency options of the above two models when the variables in the two models are consistent,founding that RMB currency options price of the G-K model is always greater than MRL model,so if market is still using the G-K model for options pricing will overestimate the real price of RMB currency options,MRL model will be more suitable for the current RMB currency options pricing.