A PDE Pricing Framework for Cross-Currency Interest Rate Derivatives with Target Redemption Features

Abstract

We propose a general framework for efficient pricing via a partial differential equation (PDE) approach for exotic cross‐currency interest rate (IR) derivatives, with strong emphasis on long‐dated foreign exchange (FX) IR hybrids, namely Power Reverse Dual Currency (PRDC) swaps with a FX Target Redemption (FX‐TARN) provision. The FX‐TARN provision provides a cap on the FX‐linked PRDC coupon amounts, and once the accumulated coupon amount reaches this cap, the underlying PRDC swap terminates. Our PDE pricing framework is based on an auxiliary state variable to keep track of the total accumulated PRDC coupon amount. Finite differences on uniform grids and the Alternating Direction Implicit (ADI) method are used for the spatial and time discretizations, respectively, of the model‐dependent PDE corresponding to each discretized value of the auxiliary variable. Numerical examples illustrating the convergence properties of the numerical methods are provided.