Full Revaluation VaR with Implied Volatility Surfaces

Summary

The document outlines a full revaluation approach to historical value-at-risk for derivative portfolios when both spot prices and implied volatility are risk factors. The first step is to identify how the volatility surface will be represented, such as through an at-the-money point, skew, a full surface, or a parameterized model. The scenario then applies returns to the selected surface factors before repricing the portfolio.

A central implementation issue is ensuring that the resulting implied volatility surface remains free of arbitrage. The response does not specify a method for conditioning volatility changes on spot moves, estimating the joint historical scenarios, or enforcing arbitrage constraints. It gives no empirical comparison or VaR results, so it is a high-level outline rather than a complete modeling recipe. The suitability of the approach depends on risk-factor choice, scenario construction, and the ability to produce valid surfaces for full repricing.

Key ideas

• Full revaluation VaR begins by choosing which implied volatility risk factors to simulate.
• A model may represent volatility with a single point, skew, a full surface, or a parameterized specification.
• After applying surface changes, check that the resulting implied volatility surface is arbitrage-free before repricing.
• The outline leaves the joint modeling of spot and volatility changes and the arbitrage-control procedure unspecified.

Tags

# Resources on VaR modelling for derivative portfolios?


# Resources on VaR modelling for derivative portfolios?












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?

## Answer by Kermittfrog (score 1)

https://quant.stackexchange.com/a/53767

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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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.