Libor Local Volatility Model: A New Interest Rate Smile Model

Abstract

Interest rate smile models are relatively complex, and even basic smile calibration processes are numerically intensive and inefficient. This paper presents a much simpler and more practical model that handles the interest rate smile in a fundamentally different way. The model postulates a spot process of the rolling Libor, which permits Dupire-type local volatility stripping in the asset class of interest rates. Direct local volatility stripping will make interest rate smile calibration a magnitude more efficient. The model also formulates a backward-pricing partial differential equation using a numeraire deflated value, which can be used to price suitable path-dependent interest rate derivatives with a smile. This self-contained smile model possesses all the good features of a Dupire-type local volatility model, including numerical simplicity and efficiency. The new modeling approach can potentially make interest rate smile modeling as efficient as equivalent smile modeling in equity or foreign exchange.