You can also analyse the skewness and kurtosis of the period of time PnL by taking 3rd and 4th times of $Y_t$ respectively. Presumably you will conclude that for two sequence with identical expectation and variance, you are going to want the one with constructive skew or decreased kurtosis, but perhaps not depending upon the self confidence of the market check out, etcetera..

$begingroup$ The pnl calculation is completed in 2 methods. By definition, you value your portfolio as of now, you worth your portfolio as of yesterday, and the difference will likely be your pnl.

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so Everything you get rid of on high quality payment you attain with your gamma trading account and you simply split whilst you expect!

$begingroup$ The theta PnL here is the choice rate paid (for some time-price of the choice); it is just a greek word for it with an extra feature showing how the choice top quality continously declines With all the passage of time.

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Therefore if I buy a choice and delta hedge then I generate profits on gamma but eliminate on theta and both of these offset one another. Then how can I Get better choice cost from delta hedging i.e. shouldn't my pnl be equivalent to the choice price compensated?

Vega p/l is by definition the p/l on account of moves in implied volatility. The second part of the concern you've got answered your self. Small dated alternatives have more gamma publicity, lengthy dated solutions have a lot more vega publicity.

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– equanimity Commented Oct seven, 2021 at one:07 $begingroup$ The purchase matters only for the cumulatuve brute-drive P&L. The get won't subject for impartial brute-power P&L or for risk-theoretical P&L (Taylor sereis approximation of the P&L applying deltas - to start with buy and gammas and cross-gammas - 2nd order risk actions). I believe you are inquiring about RTPL? $endgroup$

$begingroup$ Quite In a natural way The 2 PnLs usually do not essentially coincide. Within the "college case" you don't touch the portfolio at $t_1=t+delta t$ and liquidate it only at $t_2=t+2delta t,.

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