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
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.
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