Simulation of Arbitrage-Free Implied Volatility Surfaces

Abstract

We present a computationally tractable method for simulating arbitrage-free implied volatility surfaces. We illustrate how our method may be combined with a data-driven model based on historical SPX implied volatility data to generate dynamic scenarios for arbitrage-free implied volatility surfaces. Our approach conciliates static arbitrage constraints with a realistic representation of statistical properties of implied volatility co-movements.

Keywords: Implied volatility, scenario simulation, volatility modeling, risk management, factor models, arbitrage

JEL Classification: G13, G17, C15, C22, C45, C53, C63