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A forward equation for barrier options for efficient model calibration

7. December 2017
Kategorie: 
Research Seminars
Rudower Chaussee 25, Room 1.115, 5 p.m.
Christoph Reisinger (University of Oxford)

In this talk, we present a novel and generic calibration framework for barrier options in a large class of continuous semi-martingale models. We derive a forward equation for arbitrage-free barrier option prices in terms of Markovian projections of the instantaneous variance. This gives a Dupire-type formula for the coefficient derived by Brunick and Shreve for their mimicking diffusion and can be interpreted as the canonical extension of local volatility for barrier options. Alternatively, a forward partial-integro differential equation is deduced which yields up-and-out call prices for the complete set of strikes, barriers and maturities in one solution step. We apply this methodology to the calibration of a path-dependent volatility model (PDV) and a new Heston-type local stochastic volatility model with local vol-of-vol (LSV-LVV), using a two-dimensional particle method, for a set of EURUSD market data of vanilla and no-touch options. Finally, we conclude by extending the main Markovian projection formula to handle stochastic rates and discuss how the algorithms can be adapted at little extra computational cost. (Joint work with Matthieu Mariapragassam.)

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