Equilibrium Valuation of Currency Options in a Small Open Economy
The log-normal Garman and Kohlhagen (1983) currency option model usually creates pricing biases when matched with the market prices. The observed price bias pattern is generally consistent with the mixed jump-diffusion distribution for exchange rates. Various studies have provided evidence of jump risks in exchange rate movements. This paper argues that the jump risk in the exchange rates may be correlated with the market. Thus an equilibrium framework is needed to price the systematic jump components in currency option prices. I propose an equilibrium model to investigate the dynamics of the exchange rate in a small open monetary economy with stochastic jump-diffusion processes for both the money supply and aggregate dividend. It is shown that the exchange rate is affected by government monetary policies, aggregate dividends and the level of investment in foreign assets. As a result, the exchange rate exhibits more discontinuities than stock prices as empirically documented. Since the jump in the exchange rate is correlated with aggregate consumption, the jump risk in the exchange rate derived from aggregate dividend must be priced for currency options. I further derive the foreign agents' risk-neutral valuation of the European currency option and provide restrictions to ensure the parity conditions in currency option market. In general, these restrictions depend on the agent's risk preference.
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