Dual-Curve SABR-LMM Market Model for Post-Crisis Interest Rate Derivatives Markets
This chapter discusses the discrete loss rate, and then define London Interbank Offer Rates (LIBOR) rates in terms of the overnight-index-swap forward rates and the discrete loss rates, as well as the extension of the standard LIBOR market model. It introduces the dual-curve SABR-LMM model and develop the closed-form pricing of caplets under the approach of heat kernel expansion. Before the 2007-2008 financial crisis, forward rates were considered free of default risk, and the modeling of interest-rate derivatives was carried out with a single LIBOR curve, typically the three-month curve. Bianchetti makes use of the currency analogy and derives quanto convexity corrections to the valuation formulas under the standard LIBOR market model. A hybrid Heath–Jarrow–Morton (HJM)-LIBOR market model is proposed in Moreni and Pallavicini, where the HJM framework is used to obtain a model for multiple curves using a single family of Markov driving processes.