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.