For realistic levels of spreads and interest rates, we can approximate the CS01 with the time to maturity. This could permit you to work out A fast approximation on the PnL using the data you have got.

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Once you then build the portfolio once more by borrowing $S_ t_1 $ at fee $r$ you could realise a PnL at $t_2$ of

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Meaning if $sigma$ alterations as the fundamental adjustments you could potentially account for that second-buy effect with further sensitivities (vanna specifically), but those results are frequently A lot more compact and might be insignificant according to your goal.

Let's also take into account regular interest price r and continual hazard amount $lambda$ around the life of the contract. $$

This process calculates the worth of the trade according to The present plus the prior day's rates. The method for rate influence using the revaluation system is

Cash is how much you're investing (inclusive of margin). Your funding charges is forty nine * Cash as that is simply how much you happen to be borrowing for getting to 50x leverage.

$begingroup$ Assuming that you'll be Functioning for a lender, you'll find a few diverse P&Ls based on the purpose/ usage:

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$begingroup$ In Black Scholes framework, assuming zero fascination costs and realized volatility to generally be similar as implied volatility, gamma pnl is exactly same and reverse of theta pnl.