Discontinuous payoff option pricing by Mellin transform: A probabilistic approach

Gzyl, Henryk; Milev, Mariyan; Tagliani, Aldo

doi:10.1016/j.frl.2016.10.011

Cited by 16 publications

(12 citation statements)

References 13 publications

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“…Implementation of the aforementioned Mellin Maximum Entropy algorithm (MME) was done with the following major requirements in mind: a) to apply Mellin transform as described in [9] and [10]; b) to provide sufficient accuracy while maintaining very small error rates and keep the calculation time low; c) to provide a completely open code that relies solely on open packages which makes it possible to reuse the existing solution and reproduce our results;…”

Section: Methodsmentioning

confidence: 99%

“…2) Finite difference method Here we have demonstrated that implementation based on algorithm suggested in [10] can be faster, while keeping sufficient accuracy and can outperform FD approach. For this method we have again used QuantLib implementation BlackScholesMerton and FdBlackScholesBarrierEngine classes [18].…”

Section: -6mentioning

confidence: 95%

“…Although there are many similar implementation available the one shown here is different in the following ways -it uses Mellin transform for option pricing as discussed in [9] and an algorithm developed in [10]; the main focus is put on providing sufficient accuracy while maintaining very small error rates and keeping the calculation time low; code is completely open and relies only on open packages which means that it can be used freely and without limitations or licensing issues.…”

Section: Barrier Option Valuationmentioning

confidence: 99%

See 2 more Smart Citations

Efficient option valuation of single and double barrier options

Kabaivanov

Milev²,

Koleva-Petkova

et al. 2017

AIP Conference Proceedings

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Abstract. In this paper we present an implementation of pricing algorithm for single and double barrier options using Mellin transformation with Maximum Entropy Inversion and its suitability for real-world applications. A detailed analysis of the applied algorithm is accompanied by implementation in C++ that is then compared to existing solutions in terms of efficiency and computational power. We then compare the applied method with existing closed-form solutions and well known methods of pricing barrier options that are based on finite differences.

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Section: Methodsmentioning

confidence: 99%

Section: -6mentioning

confidence: 95%

Section: Barrier Option Valuationmentioning

confidence: 99%

See 1 more Smart Citation

Efficient option valuation of single and double barrier options

Kabaivanov

Milev²,

Koleva-Petkova

et al. 2017

AIP Conference Proceedings

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“…The Nobel Prize-winning Black-Scholes option valuation theory motivates using classical numerical methods for partial differential equations (PDE's) [1]. In computational Finance numerous nonstandard numerical methods are proposed and successfully applied for pricing options [2,3,4,5,6,7,8,9,10,11,12]. Numerical methods are often preferred to closed-form solutions as it they could me more easily extended or adapted to satisfy all the financial requirements of the option contracts and continuously changing conditions imposed by financial institutions and over-the-counter market for controlling trading of derivatives.…”

Section: Introductionmentioning

confidence: 99%

A numerical method for pricing discrete double barrier option by Legendre multiwavelet

Sobhani

Milev

2018

Journal of Computational and Applied Mathematics

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In this paper, a rapid and high accurate numerical method for pricing discrete single and double barrier knock-out call options is presented. According to the well-known Black-Scholes framework, the price of option in each monitoring date could be calculate by computing a recursive integral formula upon the heat equation solution. We have approximated these recursive solutions with the aim of Lagrange interpolation on Jacobi polynomials node. After that, an operational matrix, that makes our computation significantly fast, has been driven. The most important feature of this method is that its CPU time dose not increase when the number of monitoring dates increases. The numerical results confirm the accuracy and efficiency of the presented numerical algorithm.

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“…In Tagliani and Milev, 12 a hybrid method of the Laplace transform and the finite difference was used to solve the Black-Scholes equation. In Gzyl et al, 13 the Mellin transform was applied to solve the Black-Scholes equation with time-dependent parameters and discontinuous payoff. Recently, fractional Black-Scholes equations and their numerical solutions were proposed.…”

Section: Introductionmentioning

confidence: 99%

Fractional model and solution for the Black‐Scholes equation

Duan

Lü

Chen

et al. 2017

Math Methods in App Sciences

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This work presents a new model of the fractional Black-Scholes equation by using the right fractional derivatives to model the terminal value problem. Through nondimensionalization and variable replacements, we convert the terminal value problem into an initial value problem for a fractional convection diffusion equation. Then the problem is solved by using the Fourier-Laplace transform. The fundamental solutions of the derived initial value problem are given and simulated and display a slow anomalous diffusion in the fractional case. KEYWORDS asset pricing models, Black-Scholes equation, fractional derivative, initial value problem, mathematical finance, terminal value problem Math Meth Appl Sci. 2018;41 697-704.wileyonlinelibrary.com/journal/mma

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Discontinuous payoff option pricing by Mellin transform: A probabilistic approach

Cited by 16 publications

References 13 publications

Efficient option valuation of single and double barrier options

Efficient option valuation of single and double barrier options

A numerical method for pricing discrete double barrier option by Legendre multiwavelet

Fractional model and solution for the Black‐Scholes equation

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