Calculating Options VaR Through Full Revaluation
Summary
The document explains how to estimate value at risk for a portfolio containing options. In a Monte Carlo approach, simulate the underlying equity prices, reprice each option at every simulated state, and calculate VaR as a tail quantile of the resulting portfolio value distribution. This full revaluation treats options as derivatives and captures their nonlinear price response more directly than a delta-gamma approximation.
Delta-gamma methods are faster and may be adequate in practice, but can produce inaccurate instrument values. The discussion also notes that simulations can include changes in volatility and credit risk. A second answer recommends historical full revaluation without explaining its implementation or providing evidence, so the document offers little basis for comparing that method with Monte Carlo. It gives no quantitative performance comparison; the appropriate method depends on the accuracy and computational tradeoffs of the risk analysis.
Key ideas
- Full revaluation estimates option portfolio VaR by repricing options under each simulated market state.
- Monte Carlo VaR is the selected tail quantile of the simulated portfolio value distribution.
- Delta-gamma approximations are faster but may misstate option values.
- Simulations can also incorporate changes in volatility and credit risk.
- The document does not compare Monte Carlo with historical full revaluation in detail.
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Full text
# VaR calculation methods of options
# VaR calculation methods of options
I am a little bit confused about VaR in Options and I need a clarification for.
I collected the following formulas, can you suggest what is the best formula and explain me why, please?
## Answer by Brian B (score 3, accepted)
https://quant.stackexchange.com/a/18722
The "right" thing to do is to treat the options as derivative contracts. Let's say for simplicity that you are using Monte Carlo to compute VaR. Then you would simulate the equity prices on each iteration, and then apply an option-pricing formula to get the corresponding option prices on that iteration. This lets you obtain an accurate simulated portfolio value.
The VaR then just comes out as the usual tail measure of the simulated distribution.
Technically, what is going on is that $\text{VaR}_b^\tau$ is a quantile of the portfolio value distribution
$$ \Pi^\tau = \sum_{i=1}^N A_i^\tau $$
where some of the instruments $A_i$ may be options. That is,
$$ \text{VaR}_b^\tau = Q_b(\Pi^\tau). $$
The Delta-Gamma approximation is giving you inaccurate values of the $A_i$ (though they are fast to compute and often "good-enough" in real-world situations).
If you look at commercial packages like RiskMetrics, they offer the user an option to use Delta-Gamma, or alternatively to price options as derivatives. In the latter case you can also simulate volatility changes and credit risk changes to get even more precise values.
## Answer by user1131338 (score 0)
https://quant.stackexchange.com/a/21613
In my opnion you should you the Full revaluation historical VaR. Please readmy thread . If you need more help on the same i can gudie you .Historical Value At Risk on option portfolioShown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)
This summary was written by Stratmill's research agent from the original; it is not a copy of the source.