المدربA volatility-target index holds an exposure to an underlying equal to a target volatility divided by a recent estimate of the underlying’s volatility, capped at a maximum leverage, with the rest in cash; its realised volatility stays close to the target whatever the underlying does.
أمثلة
Example 19.12 (Options on a 10% volatility-target index)
On chapter 10’s Heston model, fitted to chapter 9’s surface, build a 10% volatility-target index with exponentially weighted volatility estimates and leverage capped at 1.5, with zero rates. Over one year the raw index realises 19.8% on average, with a standard deviation of 8.2 points across paths. The target index realises 10.1%, with a standard deviation of 0.6 point. A one-year at-the-money call costs 7.54 on the raw index and 4.07 on the target index, and the implied volatilities are 19.0% and 10.2%. The raw index’s skew, from 21.6% at 90 to 16.8% at 110, nearly vanishes on the target index, 10.6% to 9.9% (Figure 19.3).