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On the Efficacy of Fourier Series Approximations for Pricing European Options

Applied Mathematics 2014年第17期5卷 2786-2807页

作者： A. S. Hurn K. A. Lindsay A. J. McClelland School of Economics and Finance Queensland University of Technology Brisbane Australia numerix Pty Ltd Sydney Australia

This paper investigates several competing procedures for computing the prices of vanilla European options, such as puts, calls and binaries, in which the underlying model has a characteristic function that is known in semi-closed form. The algorithms investigated here are the half-range Fourier cosine series, the half-range Fourier sine series and the full-range Fourier series. Their performance is assessed in simulation experiments in which an analytical solution is available and also for a simple affine model of stochastic volatility in which there is no closed-form solution. The results suggest that the half-range sine series approximation is the least effective of the three proposed algorithms. It is rather more difficult to distinguish between the performance of the half-range cosine series and the full-range Fourier series. However there are two clear differences. First, when the interval over which the density is approximated is relatively large, the full-range Fourier series is at least as good as the half-range Fourier cosine series, and outperforms the latter in pricing out-of-the-money call options, in particular with maturities of three months or less. Second, the computational time required by the half-range Fourier cosine series is uniformly longer than that required by the full-range Fourier series for an interval of fixed length. Taken together, these two conclusions make a case for pricing options using a full-range range Fourier series as opposed to a half-range Fourier cosine series if a large number of options are to be priced in as short a time as possible.

关键词： Fourier Transform Fourier Series Characteristic Function Option Price

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On the compensator of the default process in an information-based model

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Probability, Uncertainty and Quantitative Risk 2017年第1期2卷 230-250页

作者： Matteo Ludovico Bedini Rainer Buckdahn Hans-Jurgen Engelbert numerix MilanoItaly Universite de Bretagne Occidentale BrestFrance´School of MathematicsShandong UniversityJinanShandong ProvincePeople’s Republic of China Friedrich-Schiller-Universitat Fakult¨at f¨ur Mathematik und InformatikInstitut f¨ur StochastikJena¨Germany

This paper provides sufficient conditions for the time of bankruptcy(of a company or a state)for being a totally inaccessible stopping time and provides the explicit computation of its compensator in a framework where the flow of market information on the default is modelled explicitly with a Brownian bridge between 0 and 0 on a random time interval.

关键词： Default time Totally inaccessible stopping time Brownian bridge on random intervals Local time Credit risk Compensator process

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