Target volatility option pricing in the lognormal fractional SABR model

We examine in this article the pricing of target volatility options in the lognormal fractional SABR model. A decomposition formula of Itô's calculus yields an approximation formula for the price of a target volatility option in small time by the technique of freezing the coefficient. A decompo...

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Bibliographic Details
Published in:Quantitative finance 2019-08, Vol.19 (8), p.1339-1356
Main Authors: Alòs, Elisa, Chatterjee, Rupak, Tudor, Sebastian F., Wang, Tai-Ho
Format: Article
Language:English
Subjects:
Decomposition formula
Lognormal fractional SABR model
Small volatility of volatility approximation
Target volatility option
Volatility
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Summary:We examine in this article the pricing of target volatility options in the lognormal fractional SABR model. A decomposition formula of Itô's calculus yields an approximation formula for the price of a target volatility option in small time by the technique of freezing the coefficient. A decomposition formula in terms of Malliavin derivatives is also provided. Alternatively, we also derive closed form expressions for a small volatility of volatility expansion of the price of a target volatility option. Numerical experiments show the accuracy of the approximations over a reasonably wide range of parameters.
ISSN:1469-7688
1469-7696
DOI:10.1080/14697688.2019.1574021