Volatility-coordinated scenarios explore simultaneous shocks to market price and volatility. Because the change to volatility is a deterministic function of the price change, the coordinated scenarios still only explore a one-dimensional subspace of the very large space of possible market outcomes.
One common feature of the coordinated scenarios is that the volatility shock is not applied directly to implied volatility or to volatility products. Instead, it is first multiplied by a term-structure response function, which we will denote as VR(t) where t is the time to option expiry (for stock options) or to futures delivery (for volatility index derivatives). To reflect the observed propensity of volatility levels to fluctuate less as this time increases, VR(t) is a decreasing function with VR(0) = 1.
ETFs and ETNs which invest in volatility index derivatives do not use any single future, but must roll their portfolios through time. Thus we cannot use VR(t) directly for them; instead we use the measured historical beta of the ETF/ETN with respect to the underlying volatility index (e.g., the beta of VXX with respect to VIX). These historical betas are updated daily.
We refer to the volatility change before application of VR(t) or beta as the "nominal" change.
For equity products and equity-derived volatility products, we use the formula
Y = -X when X>0, -10*x when X<0
to derive the nominal volatility shock "Y" from the price shock "X". For example, a 30% increase in market prices is accompanied by a 30% nominal decrease in volatility; a 20% decrease in market prices is accompanied by a 200% nominal increase in volatility. As always, this functional relationship is not predictive of real-world changes.
In the resulting scenarios, the value computation for a market instrument depends on its type. The table below gives a few representative examples:
Note that the volatilities of volatility products are not changed in these scenarios.
There is also a caveat to the above: we impose a lower limit on the value of Y, in order to create a lower limit on the values of the spot VIX index which will be explored by the scenarios. Thus the scenarios presented in Risk Navigator embed this assumption about VIX behavior. In a large real-world market move, this assumption could turn out to be incorrect.
See some samples.