March 15th, 2010, 7:36 pm
QuoteOriginally posted by: pankajchitlangiaam clear on "b" ... but still not able to convince myself on "a" though i know intuitively it should be 1% per day movement on stock but not able to explain logicallyIf the process is a GBM then, so long as you hedge/observe often enough (a.k.a. infinitely often), the realized volatility is guaranteed to be sigma with probability 1 over any finite subinterval, so you always realize exactly your premium.If you are only hedging every day then it matters not just what the realized volatility is but also where the price is relative to your strike when the realization happens.Try experimenting with an Excel MC framework and you can convince your self of this quite quickly. Rebonato's very thick book "Volatility and Correlation" also has some pretty good discussion of option replication and hedging that you might find useful.