Stochastic Skew in the Interest Rate Cap Market

Abstract

AbstractThe term structure of interest rates cannot be used to fully explain and hedge the prices of interest rate derivatives. Unspanned stochastic volatility improves the accuracy of interest rate derivatives valuation but is still inadequate to capture the variation of skews in the implied volatility surface. In this study, we document the stochastic variation of implied volatility skews in the interest rate cap market. To develop a term structure model that is consistent with the empirical phenomena, we incorporate the Wishart process into the standard LIBOR market model, namely, the LIBOR N‐dimensional Wishart (“LNW” for short) market model and derive a closed‐form, accurate, efficient caplet pricing formula. The capacity of the LNW model to capture stochastic skews is examined and compared with that of LIBOR multi‐Heston (“LMH” for short) market model with two and three stochastic volatilities. We find that the LNW model outperforms its LMH counterparts in terms of both in‐sample and out‐of‐sample pricing errors. © 2013 Wiley Periodicals, Inc. Jrl Fut Mark 34:1146–1169, 2014