Use Expected Volatility for Greeks, Not Realized Volatility
Summary
The discussion distinguishes expected, implied, and realized volatility in option risk calculations. It clarifies that the recommendation to use expected volatility does not mean using realized volatility: realized volatility describes past price variation, while expected volatility refers to a forecast of future variation. Implied volatility is commonly used in practice as an estimate of future volatility when calculating Greeks, including delta for hedging.
The answers caution that expected volatility is rarely known in advance. An example that calculates a hedge using volatility known after the fact illustrates a model’s possible limitations, but cannot provide a feasible real-time procedure. Implied-volatility-based Greeks are model-dependent risk measures rather than truth, and the assumed price process matters. Different models or parameters may serve trading analysis, while risk-control calculations generally need consistent assumptions. The discussion is conceptual and offers no empirical comparison establishing which volatility input performs best across options, assets, or market conditions.
Key ideas
- Expected volatility is a forecast of future variation, not the same quantity as realized volatility.
- Implied volatility is commonly used as a practical estimate of future volatility when calculating option Greeks.
- Using volatility observed only after the fact cannot guide a real-time hedge.
- Greeks depend on the pricing model and its assumed underlying price process.
- Treat model-based Greeks as risk-management estimates rather than exact descriptions of market risk.
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Full text
# Should you compute the greeks on realized or implied volatility? # Should you compute the greeks on realized or implied volatility? I am reading Trading Volatility by Collin Bennett and he says that you should compute the Greeks using realized volatility rather than implied volatility? Is this actually true? As far as I know the greeks are usually computed using implied volatility ## Answer by AKdemy (score 4, accepted) https://quant.stackexchange.com/a/69898 He writes on P. 97 that > Investors should use expected vol, not implied vol, to calculate Greeks. Expected VOL is NOT realized vol. He also writes on P.96 that > (using implied volatility as an estimate of future volatility is standard market practice for calculating Greeks) He mention this in an example demonstrating where discrete delta hedging is causing losses (Lehman collapse) and as he puts it > because using implied volatility as an incorrect future volatility assumption to calculate the delta led to a significant loss The problem is that in reality, you seldom (if ever) will be able to compute expected vol. It may serve as an example illustrating shortcomings, but computing a delta hedge, as he does, after knowing the volatility (ex-post) is simply infeasible in real world settings. Or putting his example differently, if you would have known Lehman would collapse (or that Bitcoin reached close to 70K), I doubt you would still write in this forum. ## Answer by user2559936 (score 1) https://quant.stackexchange.com/a/69895 you find implied volatility using root finding methods, and with this value you get the greeks, obviously it's a model, not the truth, but something usefull to control risks you should know that underling stochastic process should be considered when creating the model (most time it doesn't reflect, like black and sholes and geometric brownian motion for stocks), that's why sometimes traders use others methods to calculate greeks, they use others models that 'make sense' to trade or, in this case, others parameters. you will see different parameters to trade intraday or 'interdays', it's a trader model, not related to risk controls
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