I'm trying to do some risk analysis on a portfolio of bonds, currency, stocks and short calls. The short calls expire in approximately 15-30 days and I've only got around 20 days of pricing data on them. Can I extrapolate the call positions into the past on a rolling maturity basis so that I can look at how a portfolio containing calls would've performed in the past? How are extreme risks generally measured with limited data e.g. 30 day options?
It doesn't make sense to use option price series data for computing option risk anyway. Since they are derivatives (i.e. their value is derived from other securities) it is more basic and reasonable to handle the underlying risks.
As hinted by John, the risks to an option portfolio are generally considered in the context of inputs to a pricing model (which may be as simple as the Black-Scholes formula). The most important of these is underlying price, and the second most important is volatility.
When options are short-dated like yours, there is not usually much volatility value left in them. Therefore the risk could reasonably be captured simply by making sure your risk model considers changes in the option underlying, and repricing options accordingly.
If you had longer-dated options, you would certainly want some model of volatility surface dynamics linked to stock prices. That is a far more complex undertaking.