Research On Pricing Of Exchange Rate Linked Financial Products Based On Hierarchical MC

The pricing of wealth management products has been highly concerned by many scholars and financial professionals at the whole world.the interest rate and exchange rate vary so fast above people`s intention,including many unexpected accidents on different condition,so it needs more and higher tool to price the financial derivatives.Among commonly used financial derivatives pricing method,the MC simulation method proofs more effective and more precise,which is a numerical method for solving the option price by simulating the underlying asset price movement.the general function of MC is to randomly generate the possible path of the underlying asset price in a risk-neutral system,and to obtain the expected value of the option income,discount it at a risk-free rate,and final price the corresponding option.As a statistical method,the MC method has become an important computing tool for solving problems in many fields,applying at aerospace,physics,engineering,and finance.There are also a wide range of applications in terms of investment risk.However,there is a deficiency in the MC method,that is,the accuracy and volatility of the simulation result are excessively dependent on the number of paths of the simulation,and the convergence speed is slow,and the true value can only be effectively approximated by increasing the number of simulations.The layered MC can effectively utilize the generated pseudo-random sequence to improve the calculation accuracy of the simulation.Based on the hierarchical MC method,this paper studies the pricing of exchange-linked financial products,and obtains the following research results:(1)A statistical analysis of the exchange rate data from Sina Finance Network from October 30,2017 to December 2,2017 obtained a stochastic model of exchange rate suitability.The efficiency and estimation accuracy of the MC simulation method are analyzed.It is concluded that the accuracy of the MC method improves from two aspects: increase the simulation path,reduce the variance of the fluctuation.(2)Introducing dual variable technology and control variable technology to carry out Monte Carlo simulation of wealth management products.The results show that compared with the ordinary Monte Carlo simulation,the introduction of dual variable technology and control variables can achieve the effect of variance reduction,and the pricing results can be obtained with less simulation times,which reduces the computational load of the computer and saves computing time.(3)Theoretically,the stratified MC sampling technique can improve the calculation accuracy of the simulation,and the effect of the stratified sampling variance reduction comparing with the pass value and the rough estimator variance is derived.The specific algorithm is applied to the pricing of financial products with linked exchange rate;and according to the derivation,the hierarchical probability weighting method,the hierarchical matching sample method and the optimal stratification method are found.The stratified matching sample method has a good effect of variance reduction.And the results of the research are applied to the pricing of options,so that the introduced methods can improve the accuracy of option simulation pricing.The effect of layered MC on improving precision is obvious,This paper will provide a certain theoretical basis for investors.