A Multicurve Cross-Currency LIBOR Market Model

Abstract

After the dawn of the August 2007 financial crisis, banks became more aware of financial risk leading to the appearance of nonnegligible spreads between LIBOR and OIS rates and also between LIBOR of different tenors. This consequently led to the birth of multicurve models. This study establishes a new model; the multicurve cross-currency LIBOR market model (MCCCLMM). The model extends the initial LIBOR Market Model (LMM) from the single-curve cross-currency economy into the multicurve cross-currency economy. The model incorporates both the risk-free OIS rates and the risky forward LIBOR rates of two different currencies. The established model is suitable for pricing different quanto interest rate derivatives. A brief illustration is given on the application of the MCCCLMM on pricing quanto caplets and quanto floorlets using a Black-like formula derived from the MCCCLMM.

Valuation of Quanto Caps and Floors in a Calibrated Multi-Curve Cross-Currency LIBOR Market Model

“…Under the multi-curve framework, one curve is used to generate future cashflows while the other one is used to discount the generated future cashflows. So far, many models have already been proposed in practice (see [11] [14]- [27] and so on).…”

“…Our main interest in this paper is in pricing quanto caps and floors using the multi-curve cross-currency LIBOR market model (MCCCLMM) dynamics introduced in [27]. The model parameters are first calibrated to exactly match the market observable cap prices.…”