ExIRExIR 16711 bronze badge $endgroup$ one $begingroup$ Many thanks for serving to, but does that necessarily mean theta pnl only partly offsets Gamma pnl rather than completely although implied vol = understood vol? Simply because assuming interest rates are zero, there is no other source of producing income. $endgroup$
the identified possibility elements are without a doubt enough to materially demonstrate the expected value modify on the position and, if (2) the designs accustomed to compute sensitivities to those possibility factors are proper.
The above mentioned variance I alternatively see as follows: after we re-make investments/re-borrow at $t_1$ to produce both of those techniques agree we make the "operate scenario" self-funding. In contrast, your organization opts to Permit intermediate gains/losses fall out. There can be explanations for this. Perhaps it is a method to work out taxes? I do not know. $endgroup$
But you will need to consider the dilemma in a bigger image feeling. How would hedging frequency have an affect on the outcomes in excess of thousands of simulations?
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It is necessary to match P&L statements from diverse accounting durations, as any modifications after some time become far more significant compared to the figures them selves.
$begingroup$ Rather Normally The 2 PnLs usually do not necessarily coincide. From the "school scenario" you don't contact the portfolio at $t_1=t+delta t$ and liquidate it only at $t_2=t+2delta t,.
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$begingroup$ The information I have discovered about delta hedging frequency and (gamma) PnL on This page and diverse Other people all reiterate the exact same issue: the frequency at which you delta-hedge only has an effect on the smoothness and variance within your PnL.
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To generate the two strategies comparable you should imagine investing/borrowing $PnL_1$ at amount $r$ to ensure that it stays inside the process until eventually $t_2,.$ At the moment your
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Now, in the above mentioned clarification, we assumed the inventory was carrying out on some consistent vol at all moments in time. Imagine if the intraday vol diverges significantly through the day by day vol? Ie: As an EXAGGERATION, say you evaluate some stock so you calculate from your earlier 10 day closing selling prices which the stock is doing with a 1 vol. Virtually closes where by it opened every day. You then commit to look closer and measure vol in thirty moment increments instead of by day-to-day closing price ranges. Whenever you seem intraday/thirty min increments, the thing is the stock moves a whole lot, but based upon closing price ranges performs nonetheless over a one vol.