Modeling Option Portfolio Scenarios with Spot Shocks and Volatility Skew

Summary

The document frames a scenario-analysis problem for a portfolio of equity options on one underlying, spanning different strikes and expiries. A basic approach shocks the underlying price, implied volatility, and time, then reprices each option with Black–Scholes. The question focuses on improving the volatility assumption: a parallel implied-volatility shift ignores differences across the volatility surface, including strike skew and term structure changes as options roll forward.

The author asks how to estimate local volatility changes across deltas and future dates, including how volatility may respond when spot moves. The example suggests that an out-of-the-money put might not experience the same volatility increase as an at-the-money option, but the document provides no method, calibration data, or empirical evidence to quantify that relationship. It is therefore a useful statement of the scenario-modeling challenge, not a worked solution; any assumptions would need to be specified and validated for the underlying and horizon.

Key ideas

• A portfolio scenario can be evaluated by shocking spot, implied volatility, and time, then repricing the options.
• A parallel implied-volatility shock does not represent changes across strike skew or expiry structure.
• Spot moves can coincide with different implied-volatility responses at different strikes or deltas.
• Estimating future volatility-surface changes requires assumptions about both strike and time evolution.
• The document poses the modeling problem but offers no calibration method or evidence for a particular shock rule.

Tags

# Equity Options - "How do I build a forward simulation model with regards to shocks in spot pricing and IV?"


# Equity Options - "How do I build a forward simulation model with regards to shocks in spot pricing and IV?"












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.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.