Discrete-Time Approximation of Functionals in Models of Ornstein–Uhlenbeck Type, with Applications to Finance

Michael Schröder ()

Methodology and Computing in Applied Probability, 2015, vol. 17, issue 2, 285-313

Abstract: Abstract The paper provides benchmark approximation techniques for handling in models in continuous-time functional relationships in variables that are sampled discretely over time. The methods are demonstrated for value-functional-type of expectations in models of Ornstein–Uhlenbeck type. Based on Laguerre reduction series, a three-step program for these functionals is shown to result in both a continuous and a discrete time setting. The program is illustrated in the options case and in models based on GIG-distributions, yielding novel series representations for calibration when variance is discretely-sampled in particular. By numerical examples it is shown how the series enable computation accuracies of some 3 decimal places, for example, with just a single digit number of terms; for this the paper considers discretely-sampled situations with dimensions of up to 4 digits, and even in these dimensions significant discrepancies with the continuously-sampled values are found to persist.

Keywords: Lévy processes; Generalized OU processes; Orthogonal polynomials; Laguerre reduction series; Numerical methods for functionals of Lévy processes; Stochastic volatility models; Explicit methods for contingent claim valuation; Primary 60G51; 33C45; 91G20; Secondary 60G10; 33F05; 91G60 (search for similar items in EconPapers)
Date: 2015
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DOI: 10.1007/s11009-013-9351-x

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