Historical and Risk-Factor VaR Methods for Call Options
Summary
The document compares ways to estimate value at risk for a call option. If historical prices for the option are available, an analyst can calculate returns over the chosen horizon and estimate VaR from a tail percentile. For a current option without a usable price history, the discussion describes repricing under historical changes in the underlying and other relevant risk factors, including implied volatility, dividends, and interest rates.
The key limitation is that underlying-price history alone does not capture all the drivers of an option’s value. A fuller simulation needs historical risk-factor data and a defined option, horizon, and confidence level. The response also describes the buyer’s maximum loss as the premium in a worst-outcome framing, but this is not a general VaR procedure: the result depends on the chosen horizon, probability threshold, and whether the option expires unexercised. The question’s strike and expiry dates are not enough to determine VaR by themselves.
Key ideas
- Option VaR can be estimated from historical option returns when the option’s own price history is available.
- Repricing a current option requires historical changes in the underlying and relevant pricing factors.
- Implied volatility, dividends, and interest rates can materially affect option values.
- The VaR estimate depends on the horizon, confidence level, and available risk-factor data.
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# Calcul du VaR sur une option call # Calcul du VaR sur une option call Bonsoir. J'aimerais solliciter de l'aide à travers ce premier message. J'ai besoin de savoir comment calculer la VaR d'une option call dont le strike = 3200, date d'expiration est le 20/12/2024 et dont j'ai les données du sous jacent notamment la cotation du 01-01-2020 au 05-08-2022. C'est un peu urgent. Merci beaucoup pour toute éventuelle aide. ## Answer by TickaJules (score 1) https://quant.stackexchange.com/a/71978 It depends what you are looking for: #1: You have a portfolio of one option and you want to know VaR at 95% say over the next week. You have historical data on the underlying, but would need information on vol surfaces to fully reprice the option. #2: You have historical prices of the option itself, so VaR is straightforward (just determine how to calculate the weekly returns and the percentile of the distribution). #3: You have a portfolio of one option and you ask generically for the 95% worst end-outcome from the option owner's perspective (which, if you've bought a call option, is the event that you do not exercise it, hence just lose the premium). That assumes the option isn't too far out of the money (so probability of exercise is > 5%). ## Answer by boonga (score 1) https://quant.stackexchange.com/a/71979 VaR on options / bonds where there is a maturity component is not as straight forward as one might think. - work out what option you would like to simulate i.e. your delta strike (not absolute), your relative (not absolute) time to maturity T (in years) - Now you need historical data on all your risk factors (vol, div yield, risk free rate, underlying price) Let's say you are looking at daily return horizon (daily VaR) over 1 year lookback. Then you will need history daily for the past 1 year. Work out each daily returns (log returns for vol and underlying, differential returns for yields). - Then for each of these returns you will simulate your delta option price from your current base levels (current underlying price, current rate, current div yield, current implied vol) and come up with 250+ (1 year) simulated prices less current price to work out the 95%, 97.5%, 99% VaR. In summary, you can't work out the VaR with use the history of option prices on 3200 strike, 12/20/2024 expiry options. you need history of implied vol surface, implied divs, stock prices (easy), risk free rate at T (which will come from history of your term structure)
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