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Semi-static variance-optimal hedging in stochastic volatility models with Fourier representation

Part of: Mathematical finance Stochastic analysis Stochastic processes

Published online by Cambridge University Press:  01 October 2019

Paolo Di Tella ,
Martin Haubold  and
Martin Keller-Ressel
Paolo Di Tella*
Affiliation:
Technische Universität Dresden
Martin Haubold*
Affiliation:
Technische Universität Dresden
Martin Keller-Ressel*
Affiliation:
Technische Universität Dresden
*
* Postal address: Institut für Mathematische Stochastik, Technische Universität Dresden, 01062 Dresden, Germany.
* Postal address: Institut für Mathematische Stochastik, Technische Universität Dresden, 01062 Dresden, Germany.
* Postal address: Institut für Mathematische Stochastik, Technische Universität Dresden, 01062 Dresden, Germany.
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Abstract

We introduce variance-optimal semi-static hedging strategies for a given contingent claim. To obtain a tractable formula for the expected squared hedging error and the optimal hedging strategy we use a Fourier approach in a multidimensional factor model. We apply the theory to set up a variance-optimal semi-static hedging strategy for a variance swap in the Heston model, which is affine, in the 3/2 model, which is not, and in a market model including jumps.

Keywords

Variance-optimal and semi-static hedgingvolatility modelFourier representationsquare-integrable martingale

MSC classification

Primary: 60H05: Stochastic integrals 60H30: Applications of stochastic analysis (to PDE, etc.) 60G46: Martingales and classical analysis
Secondary: 91G20: Derivative securities 91G80: Financial applications of other theories (stochastic control, calculus of variations, PDE, SPDE, dynamical systems)
Type
Research Papers
Information
Journal of Applied Probability , Volume 56 , Issue 3 , September 2019 , pp. 787 - 809
Copyright
© Applied Probability Trust 2019 

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