FACTOR MODELS OF DOMESTIC AND FOREIGN INTEREST RATES WITH STOCHASTIC VOLATILITIES

Abstract

We consider a two‐country economy under the nonarbitrage assumption and where volatilities are stochastic. Assuming the existence of state variables, we show that, under some mild volatility assumptions, the model is actually fully specified. In particular, both term structure dynamics and the exchange rate process can be given endogeneously under the risk‐neutral probability. We then derive the exact dependence of the zero‐coupon bonds and the exchange rate on the underlying state variables. As a result, some closed‐form solutions can be proposed for the derivative assets as futures and options written on foreign zero‐coupon bonds.

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