Cross-currency equity swaps in the BGM model

Under the arbitrage-free framework of the HJM model (Heath, Jarrow and Morton [1992]), this article simultaneously extends the BGM model (Brace, Gatarek and Musiela [1997]) from a singlecurrency economy to a cross-currency case and incorporates the stock price dynamics under the martingale measure. The resulting model is very general for pricing almost every kind of cross-currency equity swap traded in over-The-counter markets. Pricing formulas for equity swaps with hedged or unhedged exchange rate risk are derived using either a constant or a variable notional principal. The calibration procedure, hedging strategies, and numerical examples are also provided.