Pricing Options on Trend-Stationary Currencies: Applications to the Chinese Yuan

Abstract

The Black-Scholes option pricing model assumes, among other things, that stock prices followa lognormal distribution. Other writers have extended this assumption to currency options. However, the work in currency options has mainly assumed floating exchange rates. Options on currencies such as the Chinese yuan and Peruvian sol, which historically have followed a steadily increasing trend over considerable periods of time, would be priced incorrectly given this assumption. To address this lack in the literature, a closed-form version of a model with a trend-stationary, stochastic volatility exchange rate is derived, using both a linear and quadratic trend. The results show that the model more accurately prices currency options such as the ones on the yuan and creates lower percentage hedging errors from the computed prices compared with the Garman-Kohlhagen and Heston models. The model will help institutions to more accurately hedge their foreign exchange risk in a world in which the yuan's, and other similar currencies', value is increasingly important.