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Delta hedging is a fundamental topic in portfolio and risk management. In this post, we discuss which volatility measure should be used in the delta hedging process, while a future edition will examine the appropriate hedging frequency and time horizon.
 

Which Free Lunch Would You Like Today Sir?

Reference [1] is a classic article on delta hedging that addresses the following question: if an investor has an accurate estimate of future realized volatility that differs from current implied volatility, a position can be initiated to exploit this discrepancy and then dynamically hedged—but which volatility should be used as the input in the hedging process?
 

Hedging with Actual Volatility

Pros

-Hedging with actual volatility guarantees the final profit at expiration, equal to the difference between theoretical option values under actual and implied volatility.

-The final profit has zero variance, making it attractive from a long-term, global risk–reward perspective.

-Expected profit is often insensitive to small errors in the volatility used for hedging, providing some robustness to estimation error.

Cons

-Mark-to-market P&L during the life of the option can fluctuate significantly, which is problematic for short-term risk management.

-Interim P&L depends on the true drift of the underlying asset, introducing uncertainty before expiration.

-In practice, traders are rarely confident in their estimate of actual volatility, weakening the appeal of this approach.
 

Hedging with Implied Volatility

Pros

-Mark-to-market P&L evolves smoothly with no random fluctuations, which is advantageous for daily risk monitoring.

-The trader only needs to be directionally correct about volatility (i.e., actual > implied or vice versa), not to estimate actual volatility precisely.

-Implied volatility is directly observable from the market, simplifying implementation.

Cons

-The final profit is path-dependent and therefore uncertain at inception.

-While profits are always positive in expectation, their magnitude cannot be known in advance.

-Profitability depends on the realized price path, particularly whether the underlying remains near regions of high gamma.

Reference

[1] R Ahmad, P Wilmott, Which Free Lunch Would You Like Today Sir?, Wilmott, 2005
 

Delta Hedging with Implied vs. Historical Volatility

Similar to the previous paper, Reference [2] examines the effectiveness of hedging using implied versus realized volatility. The study is based on empirical analysis using index ETF options, specifically the Nasdaq-100 ETF (QQQ).
 

Findings

-The study examines the role of volatility estimation in delta-neutral hedging, with a focus on short-term options trading and risk management.

-It empirically compares implied volatility (IV) and historical volatility (HV) using Nasdaq-100 ETF (QQQ) options over several months of daily data.

-The analysis evaluates hedging performance, return stability, transaction costs, hedging errors, and sensitivity under varying market volatility conditions.

-Results show that IV-based hedging delivers more stable returns, lower return volatility, and better risk mitigation, making it more suitable for conservative and risk-averse investors.

– IV-based strategies benefit from forward-looking, market-implied inputs, which improve delta accuracy, reduce rebalancing frequency, and lower transaction costs.

-HV-based hedging can generate higher potential returns but exhibits greater variability, larger hedging errors, and higher portfolio risk, particularly during volatile markets.

-Sensitivity tests confirm that IV adapts more effectively to changing market conditions than HV.

-The study highlights a clear trade-off between stability and return potential, emphasizing that volatility measure selection should depend on market conditions and risk preferences.

The findings provide practical guidance for traders and risk managers and contribute to the literature on optimal volatility modeling under real-world constraints. Though the paper has some limitations, notably the small sample size, this research direction is worth pursuing, particularly in establishing a delta band and determining the optimal hedging frequency.

Reference

[2] Yimao Zhao, Implied Volatility vs. Historical Volatility: Evaluating the Effectiveness of Delta-Neutral Hedging Strategies, Proceedings of the 2025 5th International Conference on Enterprise Management and Economic Development (ICEMED 2025)
 

Closing Thoughts

Taken together, these two studies highlight that the choice of volatility input is an important decision in delta hedging, rather than a technical detail. Both papers show that implied volatility, with its forward-looking and market-based nature, generally delivers more stable hedging performance, lower tracking errors, and better risk control, particularly in short-term and actively rebalanced strategies.

Historical or realized volatility, while simpler and sometimes effective in calmer market regimes, tends to lag during volatility shifts and leads to larger hedging errors. The broader implication for practitioners is that effective delta hedging requires aligning the volatility measure with market conditions, risk tolerance, and trading horizon, rather than relying on a one-size-fits-all approach.

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