Abstract: Exchange rate,as the representation of the external price of a country’s currency,is a crucial part of the macroeconomic operation in China.In the macro field,exchange rate functions to connect the currency market,the foreign exchange market,and the macroeconomy,exerting significant influence on individuals’ and enterprises’ savings,credit,and investment behaviors.In the micro aspect,exchange rate serves as an important benchmark and target for asset pricing,derivative product design,risk management,arbitrage,and speculation.With the comprehensive opening of China’s financial market and the gradual progress of RMB’s free convertibility,the links among the currency market,the capital market,and the foreign exchange market are becoming closer and closer,resulting in a complex dynamic feedback system where exchange rate and other economic variables interact and influence each other.In the context of the current economic globalization,foreign exchange derivatives,as a common derivative instrument,are a comprehensive trading variety that combines investment,value preservation,and risk hedging functions.Compared with mature foreign derivative markets and their operational mechanisms,China is still in its infancy in this regard.For example,the current types of exchange rate financial derivatives in China are relatively limited and far from meeting market demand.Given this situation,it is imperative to develop China’s derivatives market,and the core of this task is to conduct in-depth research on the pricing principles of derivative products and implement them.Specifically,in line with the objectives of this paper,proper pricing of currency derivatives can not only hedge the profit risks of multinational enterprises,but also generate investment returns in the foreign exchange market,providing an important foundation and powerful tool for Chinese enterprises and institutions to participate in international financial market competition.Additionally,it can offer a scientifically rational reference for investors’ investment decisions and risk management,thus having significant practical implications in the flourishing development of China’s financial market.Therefore,this paper aims to closely connect with  cutting-edge theoretical research on exchange rate stochastic models internationally,with the goal of constructing excellent and practical currency derivative pricing models and methods.

The focus of exchange rate modeling lies In improving the empirical fitting effect of the model to the implied volatility surface,so as to better apply it to the development of China’s foreign exchange market.This paper aims to jointly model exchange rates and interest rates,derive analytical formulas for European option prices,and test their empirical fitting effect.In our model,the exchange rate and its volatility process are extended from the Heston model by introducing a jump term in the exchange rate process,while both domestic and foreign interest rate processes use the two-factor stochastic interest rate model (CIR).Our model incorporates three important empirical features:the correlation between exchange rates and their volatility,the presence of jumps in the exchange rate process,and stochastic interest rate processes.These features are beneficial for the development of complex exchange rate derivatives with longer maturities and help to expand the variety of Chin’s exchange rate derivative products.One important consideration is the examination of the correlation between exchange rates and their volatility with domestic and foreign interest rates.The model involves four processes,and if all of them are interconnected,the model becomes overly complex.Therefore,it is necessary to reasonably assume the correlation coefficient matrix.We assume that there is no correlation between domestic and foreign interest rates and exchange rates and their volatility.This modeling approach is selected based on empirical evidence,and it allows for the derivation of analytical formulas for various related derivative prices.These formulas can then be efficiently implemented using Fourier transform methods,thereby enabling efficient calibration of model parameters.The focus of this work is to ensure accuracy,efficiency,and stability in the implementation of the formulas,which can be tested by comparing the results with those generated by Monte Carlo simulations.

There is extensive discussion on what constitutes a good stochastic exchange rate model.Some argue that a successful exchange rate stochastic model should be able to generate appropriate implied volatility surfaces that are qualitatively consistent with market data.Others argue that a successful exchange rate stochastic model should be able to generate model prices for derivatives that are close to observed market prices.Often,models are selected through numerical optimization and goodness-of-fit or difference-related measures,as well as information criteria.This paper takes the latter view and uses a loss function constructed from exchange rate option prices,implied volatilities of exchange rate options,and zero-coupon bond yields to calibrate exchange rate model parameters via numerical optimization methods.

The findings of this paper have significant theoretical and practical implications.The four-factor model obtained satisfactory calibration results when using Monte Carlo simulation data for parameter calibration,demonstrating the effectiveness and robustness of the calibration method.Furthermore,when fitting real RMB/USD exchange rate option data,the model exhibited good performance.Additionally,besides exchange rate option data,the four-factor model also achieved a good fit with Chinese and US government bond data,which suggests its potential applicability in jointly modeling interest rates and exchange rates and pricing relevant derivatives,thereby contributing to the development of China’s foreign exchange market.