Volatility Skew and the Valuation of Mortgages

Abstract

Mortgage-backed securities contain embedded options and are thus exposed to the uncertainty of interest rates. The Black formula, used by practitioners to specify the volatility of rates, assumes the same yield volatility for all option strikes. But swaptions struck at rates below the at-the-money rate consistently trade at volatilities higher than those struck at rates above the at-the-money rate. This feature is called off-the-money (OTM) volatility skew. It is different from the at-the-money (ATM) volatility skew, which is evidenced by the fact that at-the-money swaptions trade at higher volatilities in a low-rate environment than in a high-rate environment. Volatility skew arises from assumptions regarding the distributions of interest rates. We discuss various term-structure models, their apprehension of volatility skew and the way they impact pricing, risk analysis and hedging of MBS.