Abstract:
We decompose the three-month LIBOR rate into the OIS forward rate and the “discrete loss rate”, which represents the risk-free component and the default-risk component, respectively, and model them simultaneously using some popular dynamics for interest rates. In particular, we adopt the CEV dynamics with stochastic volatility and establish the dual-curve version of the combined LIBOR market model and stochastic alpha beta rho (LMM-SABR) model. LIBOR of other tenors can be constructed by properly making use of the risk premiums associated to LIBOR panel review. Closed-form pricing formulae are developed for caplets and swaptions under the dual-curve SABR model, along the approach of heat kernel expansion.
Biography:
Lixin Wu earned his PhD in applied mathematics from UCLA in 1991. He co-developed the PDE model for soft barrier options and the finite-state Markov chain model for credit contagion. He is, perhaps, best known in the financial engineering community for a series of works on market models, including an optimal calibration methodology for the standard market model, a market model with square-root volatility, a market model for credit derivatives, a market model for inflation derivatives. He has published a book, "Interest Rate Modeling: Theory and Practice" through Chapman Hall. His recent research interests include a dual-curve SABR market model for post crisis derivatives markets and the topic of xVA.