A Forward Equation for Barrier Options under the Brunick&Shreve Markovian Projection

Ben Hambly, Matthieu Mariapragassam and Christoph Reisinger

Papers from arXiv.org

Abstract: We derive a forward equation for arbitrage-free barrier option prices, in terms of Markovian projections of the stochastic volatility process, in continuous semi-martingale models. This provides 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 (PIDE) is introduced which provides up-and-out call prices, under a Brunick-Shreve model, for the complete set of strikes, barriers and maturities in one solution step. Similar to the vanilla forward PDE, the above-named forward PIDE can serve as a building block for an efficient calibration routine including barrier option quotes. We provide a discretisation scheme for the PIDE as well as a numerical validation.

Date: 2014-11, Revised 2016-09
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Citations: View citations in EconPapers (6)

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