Trading Volatility: The Importance of Hedging with the Right Volatility in the Right Environment: A Theoretical and Empirical Assessment of the P&L Effects when Trading Volatility with Black-scholes

Abstract

Volatility as an asset class provides investors with unique opportunities to reap the volatility risk premium. A popular way to trade this premium is to sell options and delta-hedge them, which is a bet on the implied volatility being higher than the realised volatility. A way to price options is through the Black-Scholes model, which most market practitioners still use to calculate the delta of the option and hedge it to be exposed to volatility. This thesis seeks to address the effectiveness of trading volatility with the Black-Scholes model through a relaxation of the assumptions pertaining to continuous hedging and constant volatility. To do this, this thesis seeks to first simulate several volatility scenarios to develop expectations on how empirical data should perform before conducting a backtest on delta-hedged options over a 13-year period. This thesis illustrates the inherent path-dependency in trading volatility arising from dollar gamma exposure and imperfect delta-hedging. Further, this thesis addresses the notion that the delta-hedge can be under- or over-hedged relative to the RV, resulting in hedging errors with large implications for the return of the short volatility trade. This thesis further observes that the performance of delta-hedging strategies depends on the stability of the volatility environment. Lastly, this thesis confirms the notion of left-tail risk inherent in selling options and that volatility can be beneficial to time rather than to be continuously exposed to. In sum, this thesis acts as a comprehensive guide to understanding the mechanics of trading volatility with delta-hedged options and the mechanics that the drive the profitability of these trades.