Machine Learning for Multiple Yield Curve Markets: Fast Calibration in the Gaussian Affine Framework

Gümbel, Sandrine; Schmidt, Thorsten

doi:10.3390/risks8020050

Cited by 3 publications

(1 citation statement)

References 21 publications

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“…Further, our paper contributes to the recent literature on deep learning approaches in hedging, starting from the seminal work Buehler et al (2019) and followed by Gümbel and Schmidt (2020), Cuchiero et al (2020), Cao et al (2021), Carbonneau (2021), Carbonneau and Godin (2021), Chen and Wan (2021), Horváth et al (2021), Neufeld and Sester (2021a), amongst many others (see also Ruf and Wang (2020) for a review).…”

Section: Introductionmentioning

confidence: 93%

Robust deep hedging

Lütkebohmert¹,

Schmidt²,

Sester³

2021

Preprint

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We study pricing and hedging under parameter uncertainty for a class of Markov processes which we call generalized affine processes and which includes the Black-Scholes model as well as the constant elasticity of variance (CEV) model as special cases. Based on a general dynamic programming principle, we are able to link the associated nonlinear expectation to a variational form of the Kolmogorov equation which opens the door for fast numerical pricing in the robust framework.The main novelty of the paper is that we propose a deep hedging approach which efficiently solves the hedging problem under parameter uncertainty. We numerically evaluate this method on simulated and real data and show that the robust deep hedging outperforms existing hedging approaches, in particular in highly volatile periods.

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Section: Introductionmentioning

confidence: 93%

Robust deep hedging

Lütkebohmert¹,

Schmidt²,

Sester³

2021

Preprint

Self Cite

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Robust deep hedging

Lütkebohmert

Schmidt

Sester³

2022

Quantitative Finance

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We propose a new deep learning approach for the quantification of name concentration risk in loan portfolios. Our approach is tailored for small portfolios and allows for both an actuarial as well as a mark-to-market definition of loss. The training of our neural network relies on Monte Carlo simulations with importance sampling which we explicitly formulate for the CreditRisk + and the ratings-based CreditMetrics model. Numerical results based on simulated as well as real data demonstrate the accuracy of our new approach and its superior performance compared to existing analytical methods for assessing name concentration risk in small and concentrated portfolios.

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Affine Models With Path-Dependence Under Parameter Uncertainty and Their Application in Finance

GEUCHEN,

OBERPRILLER,

SCHMIDT

2024

Int. J. Theor. Appl. Finan.

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In this paper, we consider one-dimensional generalized affine processes under the paradigm of Knightian uncertainty (the so-called nonlinear generalized affine models). This extends and generalizes previous results in Fadina et al. (2019) and Lütkebohmert et al. (2022). In particular, we study the case when the payoff is allowed to depend on the path, like it is the case for barrier options or Asian options. To this end, we develop the path-dependent setting for the value function relying on functional Itô calculus. We establish a dynamic programming principle which then leads to a functional nonlinear Kolmogorov equation describing the evolution of the value function. While for Asian options, the valuation can be traced back to PDE methods, this is no longer possible for more complicated payoffs like barrier options. To handle such payoffs in an efficient manner, we approximate the functional derivatives with deep neural networks and show that the numerical valuation under parameter uncertainty is highly tractable. Finally, we consider the application to structural modelling of credit and counterparty risk, where both parameter uncertainty and path-dependence are crucial and the approach proposed here opens the door to efficient numerical methods in this field.

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Machine Learning for Multiple Yield Curve Markets: Fast Calibration in the Gaussian Affine Framework

Cited by 3 publications

References 21 publications

Robust deep hedging

Robust deep hedging

Robust deep hedging

Affine Models With Path-Dependence Under Parameter Uncertainty and Their Application in Finance

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