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Low-Dimensional Partial Integro-differential Equations for High-Dimensional Asian Options

In: Inspired by Finance

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  • Peter Hepperger

    (Technische Universität München, Mathematische Statistik M4)

Abstract

Asian options on a single asset under a jump-diffusion model can be priced by solving a partial integro-differential equation (PIDE). We consider the more challenging case of an option whose payoff depends on a large number (or even a continuum) of assets. Possible applications include options on a stock basket index and electricity contracts with a delivery period. Both of these can be modeled with an exponential, time-inhomogeneous, Hilbert space valued jump-diffusion process. We derive the corresponding high- or even infinite-dimensional PIDE for Asian option prices in this setting and show how to approximate it with a low-dimensional PIDE. To this end, we employ proper orthogonal decomposition (POD) to reduce the dimension. We generalize the convergence results known for European options to the case of Asian options and give an estimate for the approximation error.

Suggested Citation

  • Peter Hepperger, 2014. "Low-Dimensional Partial Integro-differential Equations for High-Dimensional Asian Options," Springer Books, in: Yuri Kabanov & Marek Rutkowski & Thaleia Zariphopoulou (ed.), Inspired by Finance, edition 127, pages 331-348, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-02069-3_15
    DOI: 10.1007/978-3-319-02069-3_15
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