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I simulated a return series so that the realised vol is exactly equal to the implied vol being priced in. I then compared the profit made from holding a put position throughout the period against replicating strategy and realised that holding a put option still made more money than replicating strategy despite the realised vol is exactly the same as the implied vol. Why is this the case?

Many thanks.

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    $\begingroup$ The replication error is zero on average (and not for a single realisation) assuming you dynamically rebalance your replicating portfolio continuously (over each infinitesimal period of time). Furthermore, this might be due to a discrete sampling effect (implied volatility is a "continuous" variance vs. you measure the variance of the discrete log-returns). $\endgroup$ – Quantuple Jan 23 '17 at 13:12
  • $\begingroup$ @Quantuple: Your statement that the replication error is not path-wise zero in the limit of continuous delta hedging surprises me. My understanding is that its variance goes to zero in the limit. Assuming complete, frictionless markets with known dynamics, ... $\endgroup$ – LocalVolatility Jan 27 '17 at 11:25
  • $\begingroup$ @LocalVolatility you are of course right I mixed up 2 ideas in my sentence and nevery re-read it. Thank you for clarifying and keeping an eye open! $\endgroup$ – Quantuple Jan 27 '17 at 14:12

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