Systematic jump risks in a small open economy: simultaneous equilibrium valuation of options on the market portfolio and the exchange rate

Abstract

The valuation of stock options and currency options has witnessed an explosion of new development in the past 20 years. These models, set up either in a partial equilibrium or a general equilibrium framework, have certainly enriched our understanding of option valuation in one way or the other. However, the main drawback of these models is that stock options and currency options are analyzed in separate contexts. The co-movement of the stock market and the currency market is absent from the option valuation analysis. Such co-movement is extremely important and is best illustrated by the Southeast Asian financial crisis. To overcome this drawback, this paper uses an equilibrium model to investigate the joint dynamics of the exchange rate and the market portfolio in a small open monetary economy with jump-diffusion money supplies and aggregate dividends. It is shown that the exchange rate and the market portfolio are strongly correlated since both are driven by the same economic fundamentals. Furthermore, options on the exchange rate and the market portfolio are evaluated in the same equilibrium context. The analysis shows that parameters describing the same economic fundamentals have very different effects on currency and stock options