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Joined: July 10th, 2013, 6:42 am

Delta Hedging using actual volatility

June 13th, 2014, 8:12 pm

Bear with me folks, but I dont quite understand the mark-to-market profit formula on page 200 & 201 (especially). Correct me if I am wrong in my logic:First, at the beginning of day 0 you buy the option for [$]V^i[$] and use "actual" (the true underlying) volatility to determine the magnitude of the [$]\Delta^a[$] for the stock position. At the end of day 0 we must "Mark-to-Market" (= if we had liquidated our position at the end of day 0) so we look at the value portfolio and observe that the option has now value of [$]V^i + dV^i[$], stock pos is -[$]\Delta^a(S+dS)[$] and we ignore cash just for simplicity. So we made Mark-to-Market profit of:[$]\Pi_1-\Pi_0=(V^i + dV^i)-\Delta^a(S+dS) - (V^i- \Delta^aS)[$]=[$]dV^i-\Delta^adS[$]Now comes the part that I dont quite understand: The book continues and says "Since the option would be correctly valued at [$]V^a[$], we have:[$]dV^a-\Delta^adS=0[$]So we can write the mark-to-market profit over one time step as:[$]dV^i-dV^a[$]"This expression clearly is the difference in the change of the value of the portfolio with different [$]dV[$] values. But what is the economic reasoning behind taking this difference? The rest of the derivation seems to be logical.Thanks
Last edited by JSHellen on June 12th, 2014, 10:00 pm, edited 1 time in total.
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Joined: December 7th, 2014, 6:04 pm

Delta Hedging using actual volatility

December 8th, 2014, 12:34 pm

please, how can profit be made using from a accurate forecast volatility than that quoted by the market.
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Delta Hedging using actual volatility

December 8th, 2014, 12:54 pm

the most direct trades are probably to go long/short VIX futures if you think you have some edge with SPX volatility beyond that alreadyreflected in the current futures prices. I strongly urge comprehensive backtesting and a close study of VIX settlement behaviors inthe stressed out markets of the financial crisis. Good luck!

PW by JB has been "Serving the Quantitative Finance Community" since 2001. Continued...

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