A computationally efficient numerical approach for multi-asset option pricing

Khodayari, Leila; Ranjbar, Mojtaba

doi:10.1080/00207160.2018.1458096

Cited by 9 publications

(3 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Some subsequent models (Leland 1985) have been proposed to address its limitations and better align with observed market characteristics. One interesting extension of the Black-Scholes models in option pricing is the modeling of multiple underlying assets, which is commonly referred to as the multi-asset Black-Scholes model (Khodayari and Ranjbar 2018).…”

Section: Introductionmentioning

confidence: 99%

Evolutionary Neural Networks for Option Pricing: Multi-Assets Option and Exotic Option

Li,

Wu,

2023

AAAI-SS

View full text Add to dashboard Cite

This paper presents a novel framework based on the evolutionary neural network to solve the generalized Black-Scholes equation arising in the financial market efficiently and accurately. We first employ evolutionary neural networks to parameterize the Partial Differential Equations (PDEs) involved in option pricing. This approach allows us to simplify the Black-Scholes PDEs and convert them into the corresponding Ordinary Differential Equations (ODEs). Thus we can use standard ODE solvers such as Euler’s method to solve the simplified ODE problem. The proposed framework is flexible and can handle various boundary conditions and terminal conditions, allowing customization based on specific market requirements and scenarios. Moreover, our method offers a reliable and deterministic solution methodology for the pricing framework, as it does not rely on stochastic training. Unlike other approaches that incorporate stochastic elements in their training process, our method eliminates the need for such training and provides consistent results. This deterministic nature enhances the reliability and stability of our approach, making it well-suited for real-world applica- tions in option pricing and financial markets. The experiments on multiple settings are carried out to illustrate the applicability and accuracy of the proposed framework.

show abstract

Section: Introductionmentioning

confidence: 99%

Evolutionary Neural Networks for Option Pricing: Multi-Assets Option and Exotic Option

Li,

Wu,

2023

AAAI-SS

View full text Add to dashboard Cite

show abstract

“…, s n , t) be the value of the option, where s i is the underlying i-th asset value. We consider the following generalized n-asset BS equation [3,4]:…”

Section: Introductionmentioning

confidence: 99%

Finite Difference Method for the Multi-Asset Black–Scholes Equations

et al. 2020

View full text Add to dashboard Cite

In this paper, we briefly review the finite difference method (FDM) for the Black–Scholes (BS) equations for pricing derivative securities and provide the MATLAB codes in the Appendix for the one-, two-, and three-dimensional numerical implementation. The BS equation is discretized non-uniformly in space and implicitly in time. The two- and three-dimensional equations are solved using the operator splitting method. In the numerical tests, we show characteristic examples for option pricing. The computational results are in good agreement with the closed-form solutions to the BS equations.

show abstract

“…Several numerical studies have been done to predict the European/American options. In most cases, the numerical schemes used are based on the finite difference method: (Acevedo and Lelièvre, 2018;Akpan and Fatokun, 2015;Anwar and Andallah, 2018;Company et al, 2009;Dilloo and Tangman, 2017;Khodayari and Ranjbar, 2018;Kiyoumarsi, 2018;Koleva and Vulkov, 2016;Matus et al, 2017;Rao and Manisha, 2018;Vahdati et al, 2018;Yousuf, 2018;Phaochoo et al, 2016;Zhang et al, 2016).…”

Section: Introductionmentioning

confidence: 99%

Numerical analysis of the European and American options with the SPH method

Idrissi

Achchab

Maloum

2020

IJMMNO

View full text Add to dashboard Cite

In this paper, we propose a numerical method to solve the European and the American options by using the SPH method. Because its robustness and efficacy, this numerical method has been widely applied in the computation of partial differential equations particularly in fluid dynamic. To model these financial options, we use the Black Scholes equation. It is a mathematical model consisting of a set of partial differential equation supplemented by some boundary conditions. We evaluate the accuracy of our numerical method by giving some comparisons between the analytic solution and the numerical simulation.

show abstract

A computationally efficient numerical approach for multi-asset option pricing

Cited by 9 publications

References 25 publications

Evolutionary Neural Networks for Option Pricing: Multi-Assets Option and Exotic Option

Evolutionary Neural Networks for Option Pricing: Multi-Assets Option and Exotic Option

Finite Difference Method for the Multi-Asset Black–Scholes Equations

Numerical analysis of the European and American options with the SPH method

Contact Info

Product

Resources

About