Cross-Currency Equity Swaps in the BGM Model

Abstract

n equity swap entails a sequence of exchanges of the return on a specified equity portfolio against a payment computed in a different way on the same notional principal. Valuation models exist, but those with a floating leg tied to a short-term interest rate are not so easy to use. The BGM (Brace-Gatarek-Musiela) model is a useful way to model short-rate dynamics for this purpose. Further complications occur when the swap legs are denominated in different currencies and/or notional principal varies over time. In this article, the authors develop very general valuation models for multi-currency equity swaps with floating-leg payoffs based on BGM short rates, as well as possible amortization of notional principal.