I am trying to build a "What-If" Portfolio, consisting of a total of 20 options, across different tenors, strikes (delta), but on the same security.
Simply put, the objective is for me to test the damage to the total portfolio value in different scenarios, for e.g. 3% lower in underlying price, 10% move higher in volatility(guesstimate). This is simple to test in my model, i.e. applying the "shock" in underlying price, IV and time(according to no. of forward days in the simulation) and plugging it into a black scholes model.
However, I am trying to achieve a more realistic "shock" parameter in volatility input. Rather than applying a parallel shock in volatility across all the options in my portfolio(e.g. a flat 10% increase for all the options, regardless of delta, term structure rolldown), I want to be able to account for it even if i have to make some assumptions. i.e. an out of the money put should see a lower increase in vol than something ATM.
What is the best way to go about quantifying these or making some sort of approximations to the volatility movement/Delta change when underlying price moves?
TLDR: How do i extrapolate the local volatility of a option at (5, 10,25 etc delta), at (T+1, +2, +3 day), assuming i know the volatility of a 50delta option today T+0.