Hi All, suppose we have two delta hedging strategy for a call, say, usual black scholes and another one. We want to compare the two strategies in terms of their daily rehedging PnL, i.e., (nextday_OptionPrice-today_OptionPrice)-delta*(nextday_stockPrice-today_StockPrice). We have a distribution for each of the two stratigies. We compare them in terms of difference of mean of daily PnL and standard deviation. The problem is that mean is usually zero while standard deviation is 10 times higher, which makes the comparison of mean meaningless. Do we know of a better way to compare them? thanks.

That's not really a problem, it's good that the mean is small compared to the standard deviation. It's how it's supposed to be. If for one strategy the mean is negative, you have "bleeding", so that strategy is clearly wrong. And if you have a positive mean, it's a bit of a question mark: what will stop this from turning negative at some point in the future? A hedged portfolio can produce a steady is independent of strategy. If, on the other hand you have one strategy that has approx. zero P&L and another one that has positive P&L, then the second one is "punting". the trader took a view on how the underlying will evolve, and underhedged, or overhedged accordingly. It's just a bet, and you can lose as easily as you can win. So basically you have two things to look at: - are the means approximately zero for both strategies? if one has non-zero mean, discard it- if both have mean zero, the strategy with lower stdev is better.

Hi Costeanu, these are very wise comments. One technical issue, both strategies has non-zero mean hedge PnL, as it is not possible to achieve zero with discrete hedging. Then what can I do?

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