Choosing Implied Volatility Shifts for Option Stress Scenarios

Summary

The document asks how to pair a large underlying price shock with plausible implied volatility changes when stress testing an options portfolio. It compares three approaches: applying a uniform volatility increase, using a high historical volatility level, or shifting the at-the-money point along a calibrated SABR smile and recalculating the curve.

The response offers an empirical observation: changes in skew convexity over time may be small relative to parallel upward shifts in volatility measured in percentage points. On that basis, it suggests that using a fixed historical volatility level may be less problematic than the questioner expects. This is a brief, experience-based comment rather than a documented study or calibrated stress methodology; it gives no data, market details, or validation procedure. The note therefore raises a practical modeling consideration but does not establish how to select a suitable volatility shock for a particular asset, market regime, or portfolio.

Key ideas

• Stress testing options requires assumptions about volatility alongside the underlying price move.
• A uniform volatility shift, a historical volatility level, and a recalibrated smile shift are possible approaches.
• The response suggests that parallel volatility changes may outweigh changes in skew convexity over time.
• The empirical claim is not supported with data or a market-specific calibration method.

Tags

# Selecting volatility for stress scenario


# Selecting volatility for stress scenario












I would like to stress my position in options, changing underlying price $S$ and volatility $\sigma$ at the same time.

Let's assume that after some analysis of the price history I concluded that my scenario has to be a $30\%$ decrease in the underlying's price. How do I select appropriate implied volatility changes for options in my portfolio, which go along with $-30\%$ price in the scenario?

In order of complexity, I can think of the following:

- Add $+N$ bps to implied volatilities of all options in the portfolio (no justification, just do it).

- Use some high historical volatility. At first, it looks better than the first approach, but implied volatility varies between strikes, so any fixed value or percentage increase might unrealistically distort the scenario across the portfolio.

- Calibrate SABR and apply the backbone shift of $ATM$ to $ATM\times0.7$, recalculating the entire smile, then sample new implied volatilities from that new smile.

How do market participants source $\sigma$ changes for a given stressed shift in $S$?

## Answer by KaiSqDist (score 1)

https://quant.stackexchange.com/a/80379

Not a stress testing expert, but from my own (empirical) research about how the volatility skew changes across time - you'd be surprised how insignificant the change in convexity of the volatility skew is as compared to parallel upwards shift in the volatility skew in (%) points (across time).

Therefore, I would say that (2.) is not that big of a concern.

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