Deep Hedging with Options Using the Implied Volatility Surface

Pascal Fran\c{c}ois, Genevi\`eve Gauthier, Fr\'ed\'eric Godin and Carlos O. P\'erez-Mendoza

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Abstract: We propose an enhanced deep hedging framework for index option portfolios, grounded in a realistic market simulator that captures the joint dynamics of S&P 500 returns and the full implied volatility surface. Our approach integrates surface-informed decisions with multiple hedging instruments and explicitly accounts for transaction costs. The hedging strategy also considers the variance risk premium embedded in the hedging instruments, enabling more informed and adaptive risk management. In this setting, state-dependent no-trade regions emerge naturally, improving rebalancing efficiency and hedging performance. Tested across simulated and historical data from 1996 to 2020, our method consistently outperforms traditional delta and delta-gamma hedging, demonstrating superior adaptability and risk reduction.

Date: 2025-04, Revised 2025-04
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