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20 pages, 1324 KiB

Open AccessArticle

Deep Hedging under Rough Volatility

by Blanka Horvath, Josef Teichmann and Žan Žurič

Risks 2021, 9(7), 138; https://doi.org/10.3390/risks9070138 - 20 Jul 2021

Cited by 15 | Viewed by 4046

Abstract

We investigate the performance of the Deep Hedging framework under training paths beyond the (finite dimensional) Markovian setup. In particular, we analyse the hedging performance of the original architecture under rough volatility models in view of existing theoretical results for those. Furthermore, we [...] Read more.

We investigate the performance of the Deep Hedging framework under training paths beyond the (finite dimensional) Markovian setup. In particular, we analyse the hedging performance of the original architecture under rough volatility models in view of existing theoretical results for those. Furthermore, we suggest parsimonious but suitable network architectures capable of capturing the non-Markoviantity of time-series. We also analyse the hedging behaviour in these models in terms of Profit and Loss (P&L) distributions and draw comparisons to jump diffusion models if the rebalancing frequency is realistically small. Full article

(This article belongs to the Special Issue Machine Learning in Finance, Insurance and Risk Management)

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20 pages, 661 KiB

Open AccessArticle

Exploiting Distributional Temporal Difference Learning to Deal with Tail Risk

by Peter Bossaerts, Shijie Huang and Nitin Yadav

Risks 2020, 8(4), 113; https://doi.org/10.3390/risks8040113 - 26 Oct 2020

Cited by 1 | Viewed by 2833

Abstract

In traditional Reinforcement Learning (RL), agents learn to optimize actions in a dynamic context based on recursive estimation of expected values. We show that this form of machine learning fails when rewards (returns) are affected by tail risk, i.e., leptokurtosis. Here, we adapt [...] Read more.

In traditional Reinforcement Learning (RL), agents learn to optimize actions in a dynamic context based on recursive estimation of expected values. We show that this form of machine learning fails when rewards (returns) are affected by tail risk, i.e., leptokurtosis. Here, we adapt a recent extension of RL, called distributional RL (disRL), and introduce estimation efficiency, while properly adjusting for differential impact of outliers on the two terms of the RL prediction error in the updating equations. We show that the resulting “efficient distributional RL” (e-disRL) learns much faster, and is robust once it settles on a policy. Our paper also provides a brief, nontechnical overview of machine learning, focusing on RL. Full article

(This article belongs to the Special Issue Machine Learning in Finance, Insurance and Risk Management)

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31 pages, 2911 KiB

Open AccessEditor’s ChoiceArticle

A Generative Adversarial Network Approach to Calibration of Local Stochastic Volatility Models

by Christa Cuchiero, Wahid Khosrawi and Josef Teichmann

Risks 2020, 8(4), 101; https://doi.org/10.3390/risks8040101 - 27 Sep 2020

Cited by 34 | Viewed by 6025

Abstract

We propose a fully data-driven approach to calibrate local stochastic volatility (LSV) models, circumventing in particular the ad hoc interpolation of the volatility surface. To achieve this, we parametrize the leverage function by a family of feed-forward neural networks and learn their parameters [...] Read more.

We propose a fully data-driven approach to calibrate local stochastic volatility (LSV) models, circumventing in particular the ad hoc interpolation of the volatility surface. To achieve this, we parametrize the leverage function by a family of feed-forward neural networks and learn their parameters directly from the available market option prices. This should be seen in the context of neural SDEs and (causal) generative adversarial networks: we generate volatility surfaces by specific neural SDEs, whose quality is assessed by quantifying, possibly in an adversarial manner, distances to market prices. The minimization of the calibration functional relies strongly on a variance reduction technique based on hedging and deep hedging, which is interesting in its own right: it allows the calculation of model prices and model implied volatilities in an accurate way using only small sets of sample paths. For numerical illustration we implement a SABR-type LSV model and conduct a thorough statistical performance analysis on many samples of implied volatility smiles, showing the accuracy and stability of the method. Full article

(This article belongs to the Special Issue Machine Learning in Finance, Insurance and Risk Management)

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18 pages, 3729 KiB

Open AccessArticle

Deep Local Volatility

by Marc Chataigner, Stéphane Crépey and Matthew Dixon

Risks 2020, 8(3), 82; https://doi.org/10.3390/risks8030082 - 3 Aug 2020

Cited by 7 | Viewed by 5238

Abstract

Deep learning for option pricing has emerged as a novel methodology for fast computations with applications in calibration and computation of Greeks. However, many of these approaches do not enforce any no-arbitrage conditions, and the subsequent local volatility surface is never considered. In [...] Read more.

Deep learning for option pricing has emerged as a novel methodology for fast computations with applications in calibration and computation of Greeks. However, many of these approaches do not enforce any no-arbitrage conditions, and the subsequent local volatility surface is never considered. In this article, we develop a deep learning approach for interpolation of European vanilla option prices which jointly yields the full surface of local volatilities. We demonstrate the modification of the loss function or the feed forward network architecture to enforce (hard constraints approach) or favor (soft constraints approach) the no-arbitrage conditions and we specify the experimental design parameters that are needed for adequate performance. A novel component is the use of the Dupire formula to enforce bounds on the local volatility associated with option prices, during the network fitting. Our methodology is benchmarked numerically on real datasets of DAX vanilla options. Full article

(This article belongs to the Special Issue Machine Learning in Finance, Insurance and Risk Management)

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24 pages, 1804 KiB

Open AccessArticle

Neural Network Pricing of American Put Options

by Raquel M. Gaspar, Sara D. Lopes and Bernardo Sequeira

Risks 2020, 8(3), 73; https://doi.org/10.3390/risks8030073 - 2 Jul 2020

Cited by 9 | Viewed by 6084

Abstract

In this study, we use Neural Networks (NNs) to price American put options. We propose two NN models—a simple one and a more complex one—and we discuss the performance of two NN models with the Least-Squares Monte Carlo (LSM) method. This study relies [...] Read more.

In this study, we use Neural Networks (NNs) to price American put options. We propose two NN models—a simple one and a more complex one—and we discuss the performance of two NN models with the Least-Squares Monte Carlo (LSM) method. This study relies on American put option market prices, for four large U.S. companies—Procter and Gamble Company (PG), Coca-Cola Company (KO), General Motors (GM), and Bank of America Corp (BAC). Our dataset is composed of all options traded within the period December 2018 until March 2019. Although on average, both NN models perform better than LSM, the simpler model (NN Model 1) performs quite close to LSM. Moreover, the second NN model substantially outperforms the other models, having an RMSE ca. 40% lower than the presented by LSM. The lower RMSE is consistent across all companies, strike levels, and maturities. In summary, all methods present a good accuracy; however, after calibration, NNs produce better results in terms of both execution time and Root Mean Squared Error (RMSE). Full article

(This article belongs to the Special Issue Machine Learning in Finance, Insurance and Risk Management)

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18 pages, 1499 KiB

Open AccessFeature PaperArticle

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

by Sandrine Gümbel and Thorsten Schmidt

Risks 2020, 8(2), 50; https://doi.org/10.3390/risks8020050 - 21 May 2020

Cited by 2 | Viewed by 3896

Abstract

Calibration is a highly challenging task, in particular in multiple yield curve markets. This paper is a first attempt to study the chances and challenges of the application of machine learning techniques for this. We employ Gaussian process regression, a machine learning methodology [...] Read more.

Calibration is a highly challenging task, in particular in multiple yield curve markets. This paper is a first attempt to study the chances and challenges of the application of machine learning techniques for this. We employ Gaussian process regression, a machine learning methodology having many similarities with extended Kálmán filtering, which has been applied many times to interest rate markets and term structure models. We find very good results for the single-curve markets and many challenges for the multi-curve markets in a Vasiček framework. The Gaussian process regression is implemented with the Adam optimizer and the non-linear conjugate gradient method, where the latter performs best. We also point towards future research. Full article

(This article belongs to the Special Issue Machine Learning in Finance, Insurance and Risk Management)

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30 pages, 615 KiB

Open AccessArticle

Deep Arbitrage-Free Learning in a Generalized HJM Framework via Arbitrage-Regularization

by Anastasis Kratsios and Cody Hyndman

Risks 2020, 8(2), 40; https://doi.org/10.3390/risks8020040 - 23 Apr 2020

Cited by 6 | Viewed by 5901

Abstract

A regularization approach to model selection, within a generalized HJM framework, is introduced, which learns the closest arbitrage-free model to a prespecified factor model. This optimization problem is represented as the limit of a one-parameter family of computationally tractable penalized model selection tasks. [...] Read more.

A regularization approach to model selection, within a generalized HJM framework, is introduced, which learns the closest arbitrage-free model to a prespecified factor model. This optimization problem is represented as the limit of a one-parameter family of computationally tractable penalized model selection tasks. General theoretical results are derived and then specialized to affine term-structure models where new types of arbitrage-free machine learning models for the forward-rate curve are estimated numerically and compared to classical short-rate and the dynamic Nelson-Siegel factor models. Full article

(This article belongs to the Special Issue Machine Learning in Finance, Insurance and Risk Management)

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34 pages, 5590 KiB

Open AccessArticle

Neural Networks for the Joint Development of Individual Payments and Claim Incurred

by Łukasz Delong and Mario V. Wüthrich

Risks 2020, 8(2), 33; https://doi.org/10.3390/risks8020033 - 7 Apr 2020

Cited by 8 | Viewed by 3597

Abstract

The goal of this paper is to develop regression models and postulate distributions which can be used in practice to describe the joint development process of individual claim payments and claim incurred. We apply neural networks to estimate our regression models. As regressors [...] Read more.

The goal of this paper is to develop regression models and postulate distributions which can be used in practice to describe the joint development process of individual claim payments and claim incurred. We apply neural networks to estimate our regression models. As regressors we use the whole claim history of incremental payments and claim incurred, as well as any relevant feature information which is available to describe individual claims and their development characteristics. Our models are calibrated and tested on a real data set, and the results are benchmarked with the Chain-Ladder method. Our analysis focuses on the development of the so-called Reported But Not Settled (RBNS) claims. We show benefits of using deep neural network and the whole claim history in our prediction problem. Full article

(This article belongs to the Special Issue Machine Learning in Finance, Insurance and Risk Management)

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Review

Jump to: Research

46 pages, 664 KiB

Open AccessReview

A Review on Machine Learning for Asset Management

by Pedro M. Mirete-Ferrer, Alberto Garcia-Garcia, Juan Samuel Baixauli-Soler and Maria A. Prats

Risks 2022, 10(4), 84; https://doi.org/10.3390/risks10040084 - 13 Apr 2022

Cited by 7 | Viewed by 11459

Abstract

This paper provides a review on machine learning methods applied to the asset management discipline. Firstly, we describe the theoretical background of both machine learning and finance that will be needed to understand the reviewed methods. Next, the main datasets and sources of [...] Read more.

This paper provides a review on machine learning methods applied to the asset management discipline. Firstly, we describe the theoretical background of both machine learning and finance that will be needed to understand the reviewed methods. Next, the main datasets and sources of data are exposed to help researchers decide which are the best ones to suit their targets. After that, the existing methods are reviewed, highlighting their contribution and significance in the analyzed financial disciplines. Furthermore, we also describe the most common performance criteria that are applied to compare such methods quantitatively. Finally, we carry out a critical analysis to discuss the current state-of-the-art and lay down a set of future research directions. Full article

(This article belongs to the Special Issue Machine Learning in Finance, Insurance and Risk Management)

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