I have started Chapter 1 of Dynamic Hedging by Taleb and it starts by saying

"Even if traders knew the exact future volatility but hedged themselves (rebalanced the gamma) at discretely spaced increments, they would have difficultly predicting the final P/L".

"If they traded every millionth of a second they would get a P/L with certainty. Increasing the frequency of adjustments would compress the results as shown"

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"The mean is the Black Scholes Merton value of the security"

I find this very much starts at the deep end and is fairly poorly explained sentence. Could someone please help me make sense of this.

  • $\begingroup$ Isn't it just the familiar point that the BSM proof requires continuous time hedging, which is not possible in practice? Best you can do is hedge "frequently" which is not really the same as "continuously"... $\endgroup$ – noob2 Mar 15 '16 at 18:33
  • $\begingroup$ I've got to read this book. If you want perhaps an easier approach to options, try Sheldon Natenburg's book "option volatility and pricing". Anyway, my guess at this one is Taleb is basically saying the gamma and delta changes all the time with the underlying, and you can't predict the future. Therefore you can't 100% predict PnL until the hedge is in place and all the cash flows are known... $\endgroup$ – rupweb Mar 16 '16 at 11:25

He's saying that if you know the volatility, and you hedge continuously, you can lock in the exact Black-Scholes price. Any deviation from that delta hedging scheme must result in noise. ie the replicated price must have a distribution with some width around the theoretical value. This noise does not create systematic profit or loss, because it's just doing market transactions in the underlying stock. Hence the distribution of the replicated price is still centered around the theoretical value. The greater the deviation from continuous hedging, the wider the distribution of the replicated price. Nothing earth shattering.

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