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I'm interested in finding resources related to historical VaR calculation for derivative portfolios where both spot and implied volatility changes are accounted for.

The resources I've been able to find so far haven't conditionally estimated the IV Surface changes based on the spot changes, or they've estimated only a single point on the surface.

What's the normal approach to this problem?

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  • $\begingroup$ Good question, and sure there will be many great answers, but here is one suggestion. Taleb's dynamic hedging, though named hedging, is essentially about risk, and the methods discussed can be easily adapted for VaR calculation. $\endgroup$ May 1, 2020 at 19:37

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In a Full reval scenario, you would 1) identify your risk factors (ATM point? Skew? Surface? SABR?)

Say you want to simulate all surface points. Then, after you have applied your surface returns you need to first make sure that your new IV surface is free of arbitrage. That is an art in itself, though. Then you do the valuation as is usual.

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  • $\begingroup$ It's the "simulate all surface points" that I'm specifically interested in. Is standard practice to simulate them independently? I would have expected not. Assuming my portfolio has risk across the smile, the risk factors are many. $\endgroup$
    – TCopple
    May 1, 2020 at 21:23
  • $\begingroup$ Re independence of simulation point, you are using historical simulation, so would have thought any dependencies between the points would already be built in the historical scenarios. $\endgroup$ May 2, 2020 at 12:05
  • $\begingroup$ @Magicisinthechain that sort of what I'm asking about. How do I produce such dependent sampling? I could draw spot changes from T AND vol surface changes from T, but I suspected there was a better, more stochastic, way to model the dependence between the two, without relying on observed measrues. $\endgroup$
    – TCopple
    May 2, 2020 at 23:18
  • $\begingroup$ thanks! For historical VaR, the standard would be to source the historical data, then translate the data into shifts, e.g., S_2-S_1, or (S_2-S_1)/S_1, and then apply these shifts to the current values, so you get the distribution. You can do this for each individual point of the surface, and hence any dependencies will flow through, though one has to check for arbitrage etc. Parametric approaches are possible, but these are usually for other simulation approaches- e.g., Monte Carlo. $\endgroup$ May 3, 2020 at 12:50

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