TaiHo Wang, Barach College, City University of
New York
Target Volatility Option Pricing in Lognormal
Fractional SABR Model
Abstract
We examine the pricing of target
volatility options in the lognormal fractional SABR model.
A decomposition formula by Ito's calculus yields a theoretical replicating
strategy for the target volatility option, assuming the accessibility of all
variance swaps and swaptions. The same formula also suggests an approximation
formula for the price of target volatility option in small time by the
technique of freezing the coefficient.
Alternatively, we also derive closed formed expressions for a small
volatility of volatility expansion of the price of target volatility option.
Numerical experiments show accuracy of the approximations in a reasonably
wide range of parameters.
