Article by: Peter Carr and Roger Lee
Published by: University of Chicago
Date: 26 Oct 2007
“In this paper we develop strategies for pricing and hedging options on realized variance and
volatility. Our strategies have the following features.
- Readily available inputs: We can use vanilla options as pricing benchmarks and as hedging
instruments. If variance or volatility swaps are available, then we use them as well. We do
not need other inputs (such as parameters of the instantaneous volatility dynamics). - Comprehensive and readily computable outputs: We derive explicit and readily computable
formulas for prices and hedge ratios for variance and volatility options, applicable at all times
in the term of the option (not just inception). - Accuracy and robustness: We test our pricing and hedging strategies under skew-generating
volatility dynamics. Our discrete hedging simulations at a one-year horizon show mean absolute
hedging errors under 10%, and in some cases under 5%. - Easy modification to price and hedge options on implied volatility (VIX).
“Specifically, we price and hedge realized variance and volatility options using variance and volatility
swaps. When necessary, we in turn synthesize volatility swaps from vanilla options by the Carr-Lee
methodology; and variance swaps from vanilla options by the standard log-contract methodology.”
Full article (PDF): Link