A Panel Cointegration Analysis of the Dynamics of FX Option Implied Volatility Surface

Abstract

Implied volatility surface has been studied extensively for various option markets including equities, foreign currencies, and commodities. Previous studies report that option implied volatility varies across moneyness, maturity, and time, yet, once the level is controlled for, the shape of the volatility surface relative to the volatility implied for at-the-money (ATM) option is stable even over the period of the 1987 stock market crash. This study examines the dynamics of the implied volatility surface for euro-US dollar options, using a recently developed panel cointegration test that allows multiple structural breaks while accounting for cross-sectional dependence. In the model, the option implied volatility Is specified as a quadratic function of ATM volatility, spot and forward rates. The three factors together account for 98 percent of variations in the option implied volatilities across five moneyness, five maturities and over eight years of daily observations from Jan. 2006 to Dec. 2014. The estimated volatility surface however is not stable over time. Rather, its relationship with the three underlying factors exhibits substantial changes around the periods of the Global Financial Crisis and subsequent Euro-zone crisis. This finding is in a stark contrast to previous studies which report the shape of volatility surface is stable over time.