Numerical Pricing of European Options with Arbitrary Payoffs

Pachon, Ricardo

doi:10.2139/ssrn.2712402

Cited by 3 publications

(3 citation statements)

References 4 publications

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“…where (1) , (2) , and (3) are, respectively, the spot prices of gasoline, heating oil, and crude oil. Exchange options are spread options with = 0; see [15].…”

Section: Basket Derivatives and Taylor Expansionsmentioning

confidence: 99%

“…While a Taylor expansion of the second order for spread pricing has been considered in [2], an approach based on Chebyshev expansion remains less explored. Recently, it has been considered in [3] for a single-asset option contract and in a multiasset setting in [4]. The latter combines with a Fourier series development, offering an interesting analysis of the error in the approximation.…”

Section: Introductionmentioning

confidence: 99%

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Pricing Basket Options by Polynomial Approximations

Olivares¹,

Alvarez²

2021

Preprint

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“…where (1) , (2) , and (3) are, respectively, the spot prices of gasoline, heating oil, and crude oil. Exchange options are spread options with = 0; see [15].…”

Section: Basket Derivatives and Taylor Expansionsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Pricing Basket Options by Polynomial Approximations

Olivares¹,

Alvarez²

2021

Preprint

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“…Pistorius and Stolte (2012) use Chebyshev interpolation of Black&Scholes prices in the volatility as an intermediate step to derive a pricing methodology for a time-changed model. Independently from us, Pachon (2016) recently proposed Chebyshev interpolation as a quadrature rule for the computation of option prices with a Fourier type representation, which is comparable to the cosine method.…”

Section: Introductionmentioning

confidence: 99%

Chebyshev interpolation for parametric option pricing

et al. 2018

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Recurrent tasks such as pricing, calibration and risk assessment need to be executed accurately and in real time. We concentrate on parametric option pricing (POP) as a generic instance of parametric conditional expectations and show that polynomial interpolation in the parameter space promises to considerably reduce runtimes while maintaining accuracy. The attractive properties of Chebyshev interpolation and its tensorized extension enable us to identify broadly applicable criteria for (sub)exponential convergence and explicit error bounds. The method is most promising when the computation of the prices is most challenging. We therefore investigate its combination with Monte Carlo simulation and analyze the effect of (stochastic) approximations of the interpolation. For a wide and important range of problems, the Chebyshev method turns out to be more efficient than parametric multilevel Monte Carlo. We conclude with a numerical efficiency study.

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