I want to develop a tool for risk management of options portfolio, as have seen several posts here and other forums about this. Just say the simple case as first step, to use the greeks approximation of pnl calculation for different scenarios. pnl = delta * dS + 0.5 * gamma * dS^2 + vega * dIV + theta * dT (copy from a sle's reply The different scenarios could be produced by historical or monte carlo simulation. The problem I encountered is the dIV more complicated due to the volatility surceface dynamic risk. Take historical simulation as example, we could get the dS 0.05 as a scenario from the historical data of 02/Jan/14, bu we could not get the dIV 0.15 directly. Because when the underlying price changes to S*1.05 (S is today's price), the IV probably not euqal to IV*1.15, as it should be related to the underlying price changes. Historical data: 2014-01-02 dS=0.05, dIV=0.15 (the number is just for example) Not sure if there is misunderstanding of volatility dynamics. So my questions are, 1). does it make sense to ignore the volatility dynamic risk and use IV*1.15, to make it simple as first step. (At least make sence for some specific option market?) 2). If not, we have to take volatility dynammics into account, what models are usually used in market practice (Heston, SABR, Dupire local volatility or something else)? Is there any approximation calculation of these models to reduce the computing time, just likt the pnl approximation above? 3). There is another alternative approach, use today's volatility surface to interpolate the IV for scenario S(t)=S*1.05. This is to use static vol surface not dynamic. Does it make sense compared to get IV scenario from historical data? Much appreciate for any suggestions.
Here is an interesting article from a MIT Finance Professor that may address some of your questions: http://www.mit.edu/~junpan/ddjpb.pdf "This section is a brief review of delta and gamma based VaR calculation methods for options. As we shall see, as a last resort, one can estimate VaR accurately, given enough computing resources by Monte Carlo simulation, assuming of course that one knows the correct behavior of the underlying prices and has accurate derivative pricing models. In practice, however, brute force Monte Carlo simulation is not efficient for large portfolios and we will therefore take the delta gamma approach... with an examination of the accuracy of delta gamma based methods with stochastic volatility and skewed return shocks of various sorts..." -- Best Option Analysis Software
if you choose historical simulation, then it makes sense to use historical IV surfaces to generate IV scenarios Alternatively if you want to use an analytical method, look up Crouhy & Galai (if memory serves). They developed some analytical approaches for calculating VaR of non-linear portfolios.