On the application of spectral filters in a Fourier option pricing technique

Ruijter, Marjon; Versteegh, M.; Oosterlee, Cornelis W.

doi:10.21314/jcf.2015.306

Cited by 46 publications

(31 citation statements)

References 14 publications

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“…For the WA method, we present a second variant called the WA R method [15], avoiding the a priori choice of an interval for the approximation. Regarding the COS method we also present another variant called filtered-COS [17]. This alternative method may be helpful when dealing with the so called Gibbs phenomenon.…”

Section: Numerical Inversion Methodsmentioning

confidence: 99%

Efficient VaR and Expected Shortfall computations for nonlinear portfolios within the delta-gamma approach

Ortiz-Gracia

Oosterlee

2014

Applied Mathematics and Computation

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a b s t r a c tWe present four numerical methods to compute the Value-at-Risk and Expected Shortfall risk measure values of portfolios with financial options. The numerical methods are based on either wavelets or Fourier cosine approximations and belong to the class of Fourier inversion methods. We show that the risk measures can be efficiently calculated in terms of accuracy and CPU time. Besides, we provide a theoretical result about the shape of the resulting probability density. This a priori knowledge, allows us to enhance the efficiency and effectiveness of the proposed methods. Finally, we assess the accuracy of the approach in the presence of convexity or concavity properties of the financial portfolios.

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Section: Numerical Inversion Methodsmentioning

confidence: 99%

Efficient VaR and Expected Shortfall computations for nonlinear portfolios within the delta-gamma approach

Ortiz-Gracia

Oosterlee

2014

Applied Mathematics and Computation

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“…We analyze the use of p = 1 . Filtering was already successfully applied in the context of the Delta-Gamma approximation in [28] , based on the work by Ruijter et al [39] , and we refer to the references for the filter details. Adding the filter is almost trivial as it merely implies a multiplication with a specific filter term.…”

Section: Var Es and The Delta-gamma Approachmentioning

confidence: 99%

On the data-driven COS method

Leitao

Oosterlee

Ortiz-Gracia

et al. 2018

Applied Mathematics and Computation

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a b s t r a c tIn this paper, we present the data-driven COS method, ddCOS. It is a Fourier-based financial option valuation method which assumes the availability of asset data samples: a characteristic function of the underlying asset probability density function is not required. As such, the presented technique represents a generalization of the well-known COS method [1]. The convergence of the proposed method is O(1 / √ n ) , in line with Monte Carlo methods for pricing financial derivatives. The ddCOS method is then particularly interesting for density recovery and also for the efficient computation of the option's sensitivities Delta and Gamma. These are often used in risk management, and can be obtained at a higher accuracy with ddCOS than with plain Monte Carlo methods.

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“…To improve the error of the decomposition in the continuously monitored case we can improve the slope of the function on the input to the Hilbert transform by using a spectral filter. We use an exponential filter which has previously achieved good results in option pricing applications (Ruijter et al, 2015;Phelan et al, 2017). The filter is described by Eq.…”

Section: Decomposition Errormentioning

confidence: 99%

Fluctuation Identities with Continuous Monitoring and Their Application to Price Barrier Options

et al. 2017

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We present a numerical scheme to calculate fluctuation identities for exponential Lévy processes in the continuous monitoring case. This includes the Spitzer identities for touching a single upper or lower barrier, and the more difficult case of the two-barriers exit problem. These identities are given in the Fourier-Laplace domain and require numerical inverse transforms. Thus we cover a gap in the literature that has mainly studied the discrete monitoring case; indeed, there are no existing numerical methods that deal with the continuous case. As a motivating application we price continuously monitored barrier options with the underlying asset modelled by an exponential Lévy process. We perform a detailed error analysis of the method and develop error bounds to show how the performance is limited by the truncation error of the sinc-based fast Hilbert transform used for the Wiener-Hopf factorisation. By comparing the results for our new technique with those for the discretely monitored case (which is in the Fourier-z domain) as the monitoring time step approaches 1 arXiv:1712.00077v1 [q-fin.CP] 30 Nov 2017 zero, we show that the error convergence with continuous monitoring represents a limit for the discretely monitored scheme.

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On the application of spectral filters in a Fourier option pricing technique

Cited by 46 publications

References 14 publications

Efficient VaR and Expected Shortfall computations for nonlinear portfolios within the delta-gamma approach

Efficient VaR and Expected Shortfall computations for nonlinear portfolios within the delta-gamma approach

On the data-driven COS method

Fluctuation Identities with Continuous Monitoring and Their Application to Price Barrier Options

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