|
|||||
|
|
Target volatility option pricing in the lognormal fractional SABR model |
|
| Authors: | Elisa Alòs Rupak Chatterjee Tai-Ho Wang |
| Institution: | 1. Departament d'Economia i Empresa and Barcelona Graduate School of Economics, Universitat Pompeu Fabra, c/Ramon Trias Fargas, 25–27, 08005 Barcelona, Spain;2. Department of Physics, Center for Quantum Science and Engineering, Stevens Institute of Technology, Castle Point on Hudson, Hoboken, NJ 07030, USA;3. Department of Mathematics, Baruch College, The City University of New York, 1 Bernard Baruch Way, New York, NY 10010, USA;4. Department of Mathematical Sciences, Ritsumeikan University, Noji-higashi 1-1-1, Kusatsu, Shiga 525-8577, Japan |
| Abstract: | 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. |
| Keywords: | Lognormal fractional SABR model Decomposition formula Target volatility option Small volatility of volatility approximation |