Pricing Exchange Rate Options and Quanto Caps in the Cross-Currency Random Field LIBOR Market Model

TL;DR

This paper introduces a novel arbitrage-free cross-currency LIBOR market model driven by a two-parameter random field, providing new pricing formulas for Quanto caps, cross-currency swaps, and exchange rate options.

Contribution

It develops a new random field LIBOR market model for cross-currency derivatives and derives both approximate and exact pricing formulas within this framework.

Findings

Derived an approximate closed-form formula for Quanto caps.

Established an exact pricing formula for exchange rate options.

Demonstrated the model's applicability to cross-currency derivatives.

Abstract

We develop an arbitrage-free random field LIBOR market model to price cross-currency derivatives. The uncertainty of the forward LIBOR rates of our cross-currency model is driven by a two time parameter random field instead of a finite dimensional Brownian motion. To demonstrate the applications of this model, we develop an approximate closed-form pricing formula for Quanto caps and cross-currency swaps. Further, we derive an exact pricing formula for an exchange rate option in the random field setting.