Modern Numerical Techniques and Machine-Learning in Pricing and Risk Management

A special issue of Risks (ISSN 2227-9091).

Deadline for manuscript submissions: closed (31 May 2019) | Viewed by 20261

Special Issue Editors

1. CWI—Centrum Wiskunde & Informatica, 1098 Amsterdam, The Netherlands
2. DIAM, Delft University of Technology, 2628 Delft, The Netherlands
Interests: risk management; computational finance; scientific computing; applied mathematics; numerical mathematics
Dr. Lech A. Grzelak
E-Mail
Guest Editor
Delft and Rabobank Group, Delft University of Technology, Utrecht, The Netherlands

Special Issue Information

Dear Colleagues,

In present day financial practice, we need to model and price the impact of a counterparty going bankrupt. In modern risk management, different valuation adjustments, commonly known as “xVA” (where “VA" stands for valuation adjustment and the "x" means “any letter”, where each letter stands for a different VA component), are added to the fair value of a financial derivative. Accurate pricing and hedging of these VAs is of a high importance and requires sophisticated models and numerical techniques.

At the same time, we observe a high interest in financial machine-learning, both at the level of pricing and price prediction, as on the level of risk management (“learning the client, learning the creditworthiness, etc.”).

We would like to connect both of these recent themes in this Special Issue, which will publish high-quality research papers on machine-learning in computational finance, and on advanced risk management. Combinations of these themes are especially interesting.

Prof. Cornelis W. Oosterlee
Dr. Lech A. Grzelak
Guest Editors

Manuscript Submission Information

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Keywords

  • Numerical methods in computational finance
  • Risk management and derivative valuation 
  • XVA, CVA, FVA, MVA, etc. 
  • Machine-learning in computational finance

Published Papers (3 papers)

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Research

27 pages, 445 KiB  
Article
Can Machine Learning-Based Portfolios Outperform Traditional Risk-Based Portfolios? The Need to Account for Covariance Misspecification
Risks 2019, 7(3), 74; https://doi.org/10.3390/risks7030074 - 03 Jul 2019
Cited by 18 | Viewed by 5641
Abstract
The Hierarchical risk parity (HRP) approach of portfolio allocation, introduced by Lopez de Prado (2016), applies graph theory and machine learning to build a diversified portfolio. Like the traditional risk-based allocation methods, HRP is also a function of the estimate of the covariance [...] Read more.
The Hierarchical risk parity (HRP) approach of portfolio allocation, introduced by Lopez de Prado (2016), applies graph theory and machine learning to build a diversified portfolio. Like the traditional risk-based allocation methods, HRP is also a function of the estimate of the covariance matrix, however, it does not require its invertibility. In this paper, we first study the impact of covariance misspecification on the performance of the different allocation methods. Next, we study under an appropriate covariance forecast model whether the machine learning based HRP outperforms the traditional risk-based portfolios. For our analysis, we use the test for superior predictive ability on out-of-sample portfolio performance, to determine whether the observed excess performance is significant or if it occurred by chance. We find that when the covariance estimates are crude, inverse volatility weighted portfolios are more robust, followed by the machine learning-based portfolios. Minimum variance and maximum diversification are most sensitive to covariance misspecification. HRP follows the middle ground; it is less sensitive to covariance misspecification when compared with minimum variance or maximum diversification portfolio, while it is not as robust as the inverse volatility weighed portfolio. We also study the impact of the different rebalancing horizon and how the portfolios compare against a market-capitalization weighted portfolio. Full article
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21 pages, 480 KiB  
Article
Model-Free Stochastic Collocation for an Arbitrage-Free Implied Volatility, Part II
Risks 2019, 7(1), 30; https://doi.org/10.3390/risks7010030 - 06 Mar 2019
Cited by 4 | Viewed by 4627
Abstract
This paper explores the stochastic collocation technique, applied on a monotonic spline, as an arbitrage-free and model-free interpolation of implied volatilities. We explore various spline formulations, including B-spline representations. We explain how to calibrate the different representations against market option prices, detail how [...] Read more.
This paper explores the stochastic collocation technique, applied on a monotonic spline, as an arbitrage-free and model-free interpolation of implied volatilities. We explore various spline formulations, including B-spline representations. We explain how to calibrate the different representations against market option prices, detail how to smooth out the market quotes, and choose a proper initial guess. The technique is then applied to concrete market options and the stability of the different approaches is analyzed. Finally, we consider a challenging example where convex spline interpolations lead to oscillations in the implied volatility and compare the spline collocation results with those obtained through arbitrage-free interpolation technique of Andreasen and Huge. Full article
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22 pages, 981 KiB  
Article
Pricing Options and Computing Implied Volatilities using Neural Networks
Risks 2019, 7(1), 16; https://doi.org/10.3390/risks7010016 - 09 Feb 2019
Cited by 64 | Viewed by 9475
Abstract
This paper proposes a data-driven approach, by means of an Artificial Neural Network (ANN), to value financial options and to calculate implied volatilities with the aim of accelerating the corresponding numerical methods. With ANNs being universal function approximators, this method trains an optimized [...] Read more.
This paper proposes a data-driven approach, by means of an Artificial Neural Network (ANN), to value financial options and to calculate implied volatilities with the aim of accelerating the corresponding numerical methods. With ANNs being universal function approximators, this method trains an optimized ANN on a data set generated by a sophisticated financial model, and runs the trained ANN as an agent of the original solver in a fast and efficient way. We test this approach on three different types of solvers, including the analytic solution for the Black-Scholes equation, the COS method for the Heston stochastic volatility model and Brent’s iterative root-finding method for the calculation of implied volatilities. The numerical results show that the ANN solver can reduce the computing time significantly. Full article
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