Pricing European Double Barrier Option with Moving Barriers Under a Fractional Black–Scholes Model

Rezaei, Mohammad; Yazdanian, A. R.

doi:10.1007/s00009-022-02104-4

Cited by 2 publications

(2 citation statements)

References 24 publications

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“…As a mathematical model, certain assumptions, such as the log-normality of underlying prices, constant volatility, frictionless market, continuous trading without dividends applied to stocks, etc., are made for the Black-Scholes model to hold [13]. Though the Black-Scholes model has been criticized over the years due to some underlying assumptions, which are not applicable in the realworld scenario, certain recent works are associated with the model [33][34][35][36]. Additionally, Eskiizmirliler et al [37] numerically solved the Black-Scholes equation for the European call options using feed-forward neural networks.…”

Section: Extended Black-scholes Model For Barrier Optionsmentioning

confidence: 99%

Barrier Options and Greeks: Modeling with Neural Networks

Umeorah,

Mashele,

Agbaeze

et al. 2023

Axioms

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This paper proposes a non-parametric technique of option valuation and hedging. Here, we replicate the extended Black–Scholes pricing model for the exotic barrier options and their corresponding Greeks using the fully connected feed-forward neural network. Our methodology involves some benchmarking experiments, which result in an optimal neural network hyperparameter that effectively prices the barrier options and facilitates their option Greeks extraction. We compare the results from the optimal NN model to those produced by other machine learning models, such as the random forest and the polynomial regression; the output highlights the accuracy and the efficiency of our proposed methodology in this option pricing problem. The results equally show that the artificial neural network can effectively and accurately learn the extended Black–Scholes model from a given simulated dataset, and this concept can similarly be applied in the valuation of complex financial derivatives without analytical solutions.

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Section: Extended Black-scholes Model For Barrier Optionsmentioning

confidence: 99%

Barrier Options and Greeks: Modeling with Neural Networks

Umeorah,

Mashele,

Agbaeze

et al. 2023

Axioms

View full text Add to dashboard Cite

show abstract

“…In [171], Equation ( 51) was solved using a reconstructed variational iteration method, which yielded a series solution. Later, Rezaei et al [176] employed a similar technique presented in [118] to evaluate double barrier options in the European market with dynamically adjusting barriers, which are governed by an extension of Equation ( 51) incorporating time-dependent interest rates, volatility, and dividend parameters.…”

Section: Equations Derived By Fractional Taylor Series and Their Solu...mentioning

confidence: 99%

Review of the Fractional Black-Scholes Equations and Their Solution Techniques

Zhang,

Liu

et al. 2024

Fractal Fract

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The pioneering work in finance by Black, Scholes and Merton during the 1970s led to the emergence of the Black-Scholes (B-S) equation, which offers a concise and transparent formula for determining the theoretical price of an option. The establishment of the B-S equation, however, relies on a set of rigorous assumptions that give rise to several limitations. The non-local property of the fractional derivative (FD) and the identification of fractal characteristics in financial markets have paved the way for the introduction and rapid development of fractional calculus in finance. In comparison to the classical B-S equation, the fractional B-S equations (FBSEs) offer a more flexible representation of market behavior by incorporating long-range dependence, heavy-tailed and leptokurtic distributions, as well as multifractality. This enables better modeling of extreme events and complex market phenomena, The fractional B-S equations can more accurately depict the price fluctuations in actual financial markets, thereby providing a more reliable basis for derivative pricing and risk management. This paper aims to offer a comprehensive review of various FBSEs for pricing European options, including associated solution techniques. It contributes to a deeper understanding of financial model development and its practical implications, thereby assisting researchers in making informed decisions about the most suitable approach for their needs.

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Pricing European Double Barrier Option with Moving Barriers Under a Fractional Black–Scholes Model

Cited by 2 publications

References 24 publications

Barrier Options and Greeks: Modeling with Neural Networks

Barrier Options and Greeks: Modeling with Neural Networks

Review of the Fractional Black-Scholes Equations and Their Solution Techniques

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