Chebyshev interpolation for parametric option pricing

Maximilian Gaß, Kathrin Glau (), Mirco Mahlstedt and Maximilian Mair
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Maximilian Gaß: Technical University of Munich
Kathrin Glau: Technical University of Munich
Mirco Mahlstedt: Technical University of Munich
Maximilian Mair: Technical University of Munich

Finance and Stochastics, 2018, vol. 22, issue 3, No 7, 731 pages

Abstract: Abstract Recurrent tasks such as pricing, calibration and risk assessment need to be executed accurately and in real time. We concentrate on parametric option pricing (POP) as a generic instance of parametric conditional expectations and show that polynomial interpolation in the parameter space promises to considerably reduce run-times while maintaining accuracy. The attractive properties of Chebyshev interpolation and its tensorized extension enable us to identify broadly applicable criteria for (sub)exponential convergence and explicit error bounds. The method is most promising when the computation of the prices is most challenging. We therefore investigate its combination with Monte Carlo simulation and analyze the effect of (stochastic) approximations of the interpolation. For a wide and important range of problems, the Chebyshev method turns out to be more efficient than parametric multilevel Monte Carlo. We conclude with a numerical efficiency study.

Keywords: Multivariate option pricing; Complexity reduction; (Tensorized) Chebyshev polynomials; Polynomial interpolation; Fourier transform methods; Monte Carlo; Parametric Monte Carlo; Online–offline decomposition; 91G60; 41A10 (search for similar items in EconPapers)
JEL-codes: C63 D52 G12 (search for similar items in EconPapers)
Date: 2018
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Citations: View citations in EconPapers (18)

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DOI: 10.1007/s00780-018-0361-y

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