SERVING THE QUANTITATIVE FINANCE COMMUNITY

JSHellen
Topic Author
Posts: 13
Joined: July 10th, 2013, 6:42 am

### Delta Hedging using actual volatility

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.

nibekudos
Posts: 2
Joined: December 7th, 2014, 6:04 pm

### Delta Hedging using actual volatility

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

Alan
Posts: 10271
Joined: December 19th, 2001, 4:01 am
Location: California
Contact:

### Delta Hedging using actual volatility

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!