Volatility Adjustments
VIX Level and S&P 500 (SPX) Return
Many of the Predictive Stress Tests specify a VIX level. For these stress tests, the change in volatility for options and other volatility-sensitive derivatives is determined in two steps,
The increase in the VIX is used to shift in the one-month SPX volatility smile, by decomposing the increase in the VIX into movement in and along the SPX volatility smile (see, Derman and Miller, The Volatility Smile, 2016, Chapter 8).
The shift in the SPX volatility smile is use to calculate a change in the implied volatility of the derivative. If the magnitude of the underlying return is less, or the time to expiry is greater, the implied volatility of the derivative will increase less.
VIX Return and SPX Return
Similar to “VIX Level and S&P 500 (SPX) Return”, only we start by specifying a return on the VIX, and use that to calculate the VIX level in the stress scenario. All other steps are identical.
Underlying Return and Volatility Shock
Implied volatility is shifted for movement along the smile, based on the underlying return. After that, a specified volatility shock is then added. In this way, the shock represents a shift in the smile. No adjustment is made for time to maturity.