Multidimensional Shannon Wavelet Inverse Fourier Technique for Pricing Financial European Options

Colldeforns-Papiol, Gemma; Ortiz-Gracia, Luis; Oosterlee, Cornelis W.

doi:10.2139/ssrn.2786974

Cited by 2 publications

(2 citation statements)

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“…Following wavelets theory, a function f ∈ L 2 (R) can be approximated at the level of resolution m by, (8) f…”

Section: Shannon Wavelets and Swift Methodsmentioning

confidence: 99%

“…For this reason, there is an increasing interest in looking for alternative and more efficient methods. Here we propose the SWIFT method, which was originally developed for European options pricing in [21] and further extended to price Bermuda options ( [15]), European options under high dimensional stochastic models ( [10]) and two-dimensional options ( [8]). The SWIFT method gives us an accurate and extremely fast recovery of the density function and we give a prescription on how to select the parameters appearing in the numerical method.…”

Section: Introductionmentioning

confidence: 99%

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Computation of market risk measures with stochastic liquidity horizon

Colldeforns-Papiol

Ortiz-Gracia

2018

Journal of Computational and Applied Mathematics

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The Basel Committee of Banking Supervision has recently set out the revised standards for minimum capital requirements for market risk. The Committee has focused, among other things, on the two key areas of moving from Value-at-Risk (VaR) to Expected Shortfall (ES) and considering a comprehensive incorporation of the risk of market illiquidity by extending the risk measurement horizon. The estimation of the ES for several trading desks and taking into account different liquidity horizons is computationally very involved. We present a novel numerical method to compute the VaR and ES of a given portfolio within the stochastic holding period framework. Two approaches are considered, the delta-gamma approximation, for modelling the change in value of the portfolio as a quadratic approximation of the change in value of the risk factors, and some of the state-ofthe-art stochastic processes for driving the dynamics of the log-value change of the portfolio like the Merton jump-diffusion model and the Kou model. Central to this procedure is the application of the SWIFT method developed for option pricing, that appears to be a very efficient and robust Fourier inversion method for risk management purposes.

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“…Following wavelets theory, a function f ∈ L 2 (R) can be approximated at the level of resolution m by, (8) f…”

Section: Shannon Wavelets and Swift Methodsmentioning

confidence: 99%