Regime-Dependent Smile-Adjusted Delta Hedging

Abstract

Most research on option hedging has compared the performance of delta hedges derived from different stochastic volatility models with Black-Scholes-Merton (BSM) deltas, and in particular with the 'implied BSM' model in which an option's delta is based on its own market implied volatility. Various empirical studies of vanilla options on different equity indices have provided substantial evidence that minimum variance deltas outperform the partial derivative delta, but no clear evidence that they can consistently outperform the implied BSM delta, or other simple smile-adjusted deltas that are popular with option traders. This paper focuses exclusively on smile adjustments to BSM deltas with an emphasis on those which depend on the market regime. Using 16.5 years of daily closing prices for FTSE 100 vanilla options, out-of-sample tests of their hedging performance clearly demonstrate that even the simplest of the regime-dependent smile adjustments will consistently and significantly improve on implied BSM delta hedging, for options of all moneyness and maturities and whether rebalancing is daily, weekly or fortnightly. For most options and over all hedging horizons the regime-dependent smile-adjusted delta-hedging errors are only 50%-60% as large as the implied BSM hedging errors, on average. During volatile market periods the risk reduction is much greater than it is during tranquil periods.