Using PCA to Stress Test Volatility Surfaces Beyond Historical Data

Summary

The document describes an approach to historical and hypothetical stress testing of equity volatility surfaces when the available surface history is short and lacks the crisis period of interest. The author fits an arbitrage-free SVI parameterization to daily surfaces, applies principal component analysis to changes in those parameters, and attempts to steer the resulting surfaces toward target short-term at-the-money volatility estimates informed by the VIX. The intended application is constructing a COVID-era scenario despite having only VIX observations for that period.

The author reports two practical limitations: a regression linking VIX to single-stock implied volatility does not predict stressed levels well, and optimization produces surfaces below the volatility levels observed during COVID. The proposed workflow is a problem statement rather than a validated stress method. Its results may be constrained by the lack of crisis observations in the PCA sample, and the document gives no final remedy or evidence that the generated surfaces capture realistic joint market stresses.

Key ideas

• Fit an arbitrage-free SVI surface to each day’s option data before analyzing surface changes.
• PCA of SVI parameter evolution can provide directions for hypothetical surface shocks.
• VIX-based estimates of single-stock implied volatility may fail in extreme stress conditions.
• A PCA sample without crisis observations may limit the severity of generated stress surfaces.
• The document identifies challenges but does not present a tested solution.

Tags

# Volatility Surface Stress Testing - PCA


# Volatility Surface Stress Testing - PCA












I’m currently working on creating historical and hypothetical stress tests, but I’m facing challenges in implementing a method to realistically stress volatility surfaces.

In terms of data, I have daily volatility surfaces from the past two months, as well as 10 years of historical data on the VIX, closing prices, yield curves, etc.

For the historical stress tests, I specifically want to create a COVID scenario, but I don’t have volatility data covering that period (except for the VIX...).

Here’s what I’ve done so far:

- I calibrate an SVI model daily on the volatility surfaces (Raw SVI - Arbitrage Free).

- I apply PCA on the evolution of the parameters of my SVI models.

The part where I’m currently stuck:

- I estimate certain volatility points (ATM short term) by interpolating with the VIX.

- I shock the PCA scores to obtain volatility surfaces where the points converge towards the target points through an optimization method.

Unfortunately, I’m encountering two problems:

- The regression method between the VIX and IV is not relevant for predicting IV levels in stress situations.

- The optimizer converges to surfaces with IV levels significantly lower than those observed during the COVID period. I interpret this as the result of the initial PCA dataset not including any stress periods for single stock volatility.

My question is: What do you think of the method used, and do you have any ideas on how to achieve my goal?

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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