A New Simple Approach for Constructing Implied Volatility Surfaces

Abstract:     
Standard option pricing models specify the dynamics of the security price and the instantaneous variance rate, and derives its no-arbitrage implication for the option implied volatility surface. Market models start with an initial implied volatility surface and a diffusion specification for the implied volatility dynamics, and derive the no-arbitrage constraints on the risk-neutral drift of the dynamics. This paper proposes a new approach, which specifies the security price and the implied volatility dynamics while leaving the instantaneous variance rate dynamics unspecified. The allowable shape for the initial implied volatility surface is then derived based on dynamic no-arbitrage arguments. Two parametric specifications for the implied volatility dynamics lead to extreme tractability, as the whole implied volatility surface is determined by a quadratic equation. The paper also proposes a dynamic calibration methodology and calibrates the two models to over-the-counter currency option and equity index option implied volatility surfaces over an 11-year period. The model with lognormal implied variance dynamics generates superior performance over standard option pricing models of similar complexities. Furthermore, constructing implied volatility surfaces using our two models is 100 times faster than using traditional option pricing models.

Number of Pages in PDF File: 58

Keywords: Implied volatility surface, vega-gamma-vanna-volga, square-root variance model, lognormal variance model, dynamic calibration, unscented Kalman filter

JEL Classification: C13, C51, G12, G13

working papers series