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I was wondering if any quant guru can help . How to calculate the PnL explained using full reval aka scenario based = > t - (t-1) approach for linear instrument. I am finding difficulty to understand the order for the input and how to move them. My portfolio contains Physical forward and future.

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  • $\begingroup$ It's difficult to answer without more information. Sometimes what is locally linear , isn't over a large move. $\endgroup$
    – dm63
    Commented Apr 20, 2016 at 0:19

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Don't assume that everything is linear and has no cross gammas. Test this assumption. It's likely to turn out be wrong, especially when the markets move a lot.

There are two methodologies for brute-force. Ideally, you should do both every day.

"Cumulative" or "waterfall" or "progressive": start at the T-1 model price. Sequentially reprice, cumulatively changing the significant model inputs one at a time from the T-1 value to th T+0 value. The order in which you change the inputs matters somewhat. Usually Calendar01 comes first (the P&L from the changes in the holiday calendars, which happens very rarely), then the time (the P&L due to passage of time - theta, time decay, carry, rolldown..), then the other inputs (interest rates, various spreads) in the order of their significance. Be careful when you're bumping the time, and some of your inputs are futures contracts that are close to expiry. The change in the model price on each step is the P&L contribution of this input change (both linear and non-linear - they cannot be identified separately). When two model inputs (note that this includes time) have non-zero cross gamma, them the cross gamma contribution is part of the contribution of the input that is changed second, is not included in the contribution of the input that is changed first, and can't be identified separately. Since at the end you use all T+0 inputs, the pricer should output the T+0 model price at the end, with no unexplained P&L.

"Independent" or "Restore" or "Component Slide": start with T-1 inputs. Independently change each significant model input to its T+0 value, but restore it to T-1 value afterwards. Once again, the change in the model price on each step is the P&L contribution of this input change (both linear and non-linear - they cannot be identified separately). If you know that two inputs have material cross gamma, then change both of them together - then the P&L contribution of the cross gamma is the difference betwen the P&L contribution of the two inputs changed simultaneously less the P&L contributions of the two inputs changed separately. The order does not matter. There is likely to be some unexplained P&L.

Note that neither methodology breaks out the contribution of first-order (delta) from second-order (gamma etc) risks. You should also run "risk-theoretical P&L" (Taylor sereis approximation of the P&L - multiply the T-1 sensitivities by the changes in the inputs) to see that, and to confirm that your risk measures are comprehensive and accurate.

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