Abstract
A three-factor exchange-rate diffusion model that includes three stochastically-dependent Brownian motion processes, namely, the domestic interest rate process, volatility process and return process is considered. A linear regression approach that derives explicit expressions for the distribution function of log return of foreign exchange rate is derived. Subsequently, a closed form workable formula for the call option price that has an algebraic expression similar to a Black-Scholes model, which facilitates easier study, is discussed.
Highlights
A foreign exchange rate depends on the supply and demand dynamics of a currency
The exchange rate is a function of trade balance, the interest rate differential and differential inflation expectations between the two countries [1] [2]
Foreign exchange rate option modeling is the subject of several well-known papers and in chapters within [3] [4] [5] [6]
Summary
A foreign exchange rate depends on the supply and demand dynamics of a currency. The exchange rate is a function of trade balance, the interest rate differential and differential inflation expectations between the two countries [1] [2]. The proposed three-factor exchange-rate diffusion model is discussed, such that the stochastic volatility process and the stochastic domestic interest rate process each have a stochastically dependent Brownian motion return process. Foreign exchange rate option modeling is the subject of several well-known papers and in chapters within [3] [4] [5] [6]. Leveraging Heston’s model [4] for this application would introduce complexity due to the need to numerically integrate conditional characteristic functions obtained as solutions of nonlinear pdf to derive the call option prices. The method suggested in this paper results in Black-Scholes type formula for call option pricing, which is computable. We provide concluding remarks and suggestions for future direction
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