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

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  • Michael Schröder

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.

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  • Michael Schröder, 2015. "Discrete-Time Approximation of Functionals in Models of Ornstein–Uhlenbeck Type, with Applications to Finance," Methodology and Computing in Applied Probability, Springer, vol. 17(2), pages 285-313, June.
    • Handle: RePEc:spr:metcap:v:17:y:2015:i:2:d:10.1007_s11009-013-9351-x
    DOI: 10.1007/s11009-013-9351-x
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    References listed on IDEAS

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