$ From the "get the job done circumstance" you liquidate the portfolio at $t_1$ realising its PnL (allow me to simplify the notation a tad)
Vega and Theta are sensetivities to volatility and time, respectively, so their contribution will be:
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When there is autocorrelation while in the intraday return procedure that you end up picking to hedge at (that can in turn have an affect on everyday annualised volatility), then your P/L is definitely influenced by your option of hedging interval.
A PnL explained report will usually incorporate one row for every trade or group of trades and can have in a minimum these columns:
So, could it be proper to state then delta-hedging rebalancing frequency right influences the quantity of P&L then? $endgroup$
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Vega p/l is by definition the p/l on account of moves in implied volatility. The second Element of the concern you've got answered yourself. Small dated choices have extra gamma exposure, long dated selections have a lot more vega exposure.
$begingroup$ The data I have found about delta hedging frequency and (gamma) PnL on This web site and diverse Other folks all reiterate the identical issue: which the frequency at which you delta-hedge only has an impact on the smoothness and variance of your PnL.
As it is the pnl in the hedge that offsets the option top quality. Remember to disregard variances on account of periodic vs ongoing for this question. $endgroup$
I'm considering understanding the PnL among $t_0$ and $t_2$ of becoming very long one particular more info device of risky asset. Having said that I have two contradictory reasonings:
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On the other hand, the gamma PnL is compensated for you around the facet, not on the choice premium, but from the investing routines within the fundamental you execute your hedging account.
$begingroup$ In Black Scholes framework, assuming zero fascination charges and recognized volatility for being very same as implied volatility, gamma pnl is precisely identical and opposite of theta pnl.