Comparing Empirical Minimum Variance Hedging with Delta-Vega Hedging and Model-Based Delta hedging (Black-Scholes, GARCH, and SABR) Under Normal and Extreme Market Conditions

Abstract

Options are one of the most used instruments in risk management and are used by corporations and investors manage their risk exposure. For the issuer of an option, there is an exposure to the underlying asset. This is usually managed through whats called hedging. The most well-known hedging method is the delta hedge, from the Black-Scholes framework. In the Black-Scholes framework, the position in the underlying asset is continuously adjusted to counter changes in the option value, while assuming constant volatility. In practice, however, the assumption of constant volatility doesn’t hold. The relationship between the underlying price and its implied volatility leads to hedging errors that become more pronounced during periods of market stress. The approaches proposed to handle these limitations include, stochastic volatility models such as SABR, time-varying volatility models such as GARCH, the empirical minimum variance hedge developed by Hull and White, and combined delta vega strategies that aim to neutralise both price and volatility exposure at the same time. Each approach captures a different part of the relationship between price and volatility, and each has its own strengths and weaknesses. This thesis aims to evaluate and compare these hedging strategies under both normal and more stressed market conditions. The goal is to provide insight into which strategies remain robust during both normal and extreme market regimes. The thesis is conducted as a quantitative replication and extension of the work by Hull and White from 2017. The dataset is sourced from OptionMetrics and covers the period 2015 to 2025. The dataset includes index options, equity options, and ETF options, and each trading day is classified into a normal, elevated, or extreme regime based on the VIX index level. Each methods performance is measured through the sum of squared hedging errors relative to the Black-Scholes benchmark, with Newey-West corrections applied to account for autocorrelation in the daily loss differentials. The theoretical literature is reviewed in order to motivate the construction of each hedge and to interpret the difference in hedging performance. The hedging strategies discussed are the standard Black-Scholes delta hedge, the GARCH plug-in delta hedge, the GJR-GARCH minimum variance correction, the SABR model-based delta hedge, the empirical minimum variance hedge, the model-free delta-vega hedge, and the GARCH-scaled delta-vega overlay. The thesis shows that it is highly uncertain whether any hedging method dominates across market conditions. The investigated approaches share strengths and weaknesses, and their relative performance depends on the option type, the moneyness, and the volatility regime. The model-free delta-vega hedge delivers the largest and most consistent improvement over Black-Scholes, while the empirical minimum variance hedge also improves on the benchmark, although by a smaller margin than originally reported. The SABR approach yields modest gains and exhibits a clear difference between calls and puts. The GARCH based delta hedges perform poorly because they discard the smile information embedded in implied volatility. The broader analysis is that effective hedging depends less on forecasting volatility itself and more on capturing the relationship between the underlying price and its implied volatility. Practitioners should therefore prioritise hedging strategies that target volatility exposure directly rather than those that rely on historical return-based forecasts.