Pricing Barrier Options with DeepBSDEs

Ganesan, Narayan; Yan, Yu; Hientzsch, Bernhard

doi:10.48550/arxiv.2005.10966

Cited by 3 publications

(3 citation statements)

References 8 publications

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“…The DeepBSDE concept initially proposed by Han et al in [28] converted high-dimensional PDE into BSDE, intending to reduce the dimensionality constraint, and they redesigned the solution of the PDE problem as a deeplearning problem. Further implementation of the BSDE-based using the numerical method with deep-learning techniques in the valuation of the barrier options is found in [29,30].…”

Section: Introductionmentioning

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: Introductionmentioning

confidence: 99%

Barrier Options and Greeks: Modeling with Neural Networks

Umeorah,

Mashele,

Agbaeze

et al. 2023

Axioms

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“…Neural networks are used to approximate the diffusion term in the stochastic differential equations, which is related to the gradient of the solution. Since then, some variants have been applied to the barrier options in [32,13].…”

Section: Introductionmentioning

confidence: 99%

Solving barrier options under stochastic volatility using deep learning

Fu¹,

Hirsa²

2022

Preprint

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We develop an unsupervised deep learning method to solve the barrier options under the Bergomi model. The neural networks serve as the approximate option surfaces and are trained to satisfy the PDE as well as the boundary conditions. Two singular terms are added to the neural networks to deal with the non-smooth and discontinuous payoff at the strike and barrier levels so that the neural networks can replicate the asymptotic behaviors of barrier options at short maturities. After that, vanilla options and barrier options are priced in a single framework. Also, neural networks are employed to deal with the high dimensionality of the function input in the Bergomi model. Once trained, the neural network solution yields fast and accurate option values.

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“…Numerical approximation of barrier options is not new in finance since a lot of research has been done extensively. For instance, numerical methods such as the continuous Fourier sine transform, 1 Crank-Nicolson finite difference method (FDM), 2,3 binomial method, 4 deep backward stochastic differential equation techniques 5,6 have been applied in the barrier options pricing process. For comparison purposes, we will employ the extended Black-Scholes pricing formula as the closed-form benchmark of the pricing process, and these analytical formulas have been presented explicitly in References 7 and 8.…”

Section: Introductionmentioning

confidence: 99%

Approximation of single‐barrier options partial differential equations using feed‐forward neural network

Umeorah

Clément

2022

Appl Stoch Models Bus & Ind

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Artificial neural networks are generally employed in the numerical solution of differential equation problems. In this article, we propose an approach that deals with the combination of the feed-forward neural network method and the optimization technique in solving the partial differential equation arising from the valuation of barrier options. The methodology entails transforming the extended Black-Scholes partial differential equations (PDE), which defines a barrier option, into a constrained optimization problem, and then proposing a trial solution that reduces the differential equation problem to an unconstrained one. This trial function consists of the adjustable and non-adjustable neural network parameters. We design it to be differentiable, analytic, and satisfy the initial and boundary conditions of the corresponding option pricing PDE. We compare the corresponding option values to the Monte-Carlo simulated values, Crank-Nicolson finite-difference values and the exact Black-Scholes prices.Numerical results presented in this research show that neural networks can sufficiently solve PDE-related problems with sufficient precision and accuracy. Furthermore, they can be applied in the fast and accurate valuation of financial derivatives without closed analytic forms.

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Pricing Barrier Options with DeepBSDEs

Cited by 3 publications

References 8 publications

Barrier Options and Greeks: Modeling with Neural Networks

Barrier Options and Greeks: Modeling with Neural Networks

Solving barrier options under stochastic volatility using deep learning

Approximation of single‐barrier options partial differential equations using feed‐forward neural network

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