Stochastic Modelling with Applications in Finance and Insurance

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Financial Mathematics".

Deadline for manuscript submissions: closed (31 May 2021) | Viewed by 18253

Special Issue Editors


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Guest Editor
AFI Department, KU Leuven, 3000 Leuven, Belgium
Interests: actuarial science; risk measures; herd behavior; fair valuation; comonotonicity
Special Issues, Collections and Topics in MDPI journals

E-Mail Website
Guest Editor
Department of Applied Mathematics, Computer Science and Statistics, Ghent University, Krijgslaan 281 S9 (WE02), B-9000 Gent, Belgium
Interests: financial mathematics; option pricing; stochastic modelling with applications in finance and insurance; computational finance

Special Issue Information

Dear Colleagues,

Interdisciplinary research in finance and insurance has gained a lot of attention in recent years. Stochastic models have been questioned under the upsurge of machine learning techniques applied to these fields. Nonetheless, stochastic modelling remains a powerful tool to describe a broad range of phenomena in the area of mathematical finance and of insurance separately, as well as in their intersection. The interaction between the theoretical developments on one hand, and numerical computation techniques on the other hand, has led to important results and applications in the above-mentioned fields, including portfolio optimization, risk management and solvency related research questions.

This Special Issue aims at highlighting high-quality papers under the form of an original research article, a state-of-the-art review or an expository dealing with the recent advances on the topic of 'Stochastic Modelling with Applications in Finance and Insurance'. Both theoretical and practice-related developments in the area of modelling in quantitative finance and insurance as well as in the interplay between these fields are welcome. Applications involve pricing, hedging, reserving, valuation and more generally, risk measurement and management.

Prof. Dr. Jan Dhaene
Prof. Dr. Michèle Vanmaele
Guest Editors

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Keywords

  • Mathematical Finance
  • Actuarial Science
  • Interplay between mathematical finance and actuarial science
  • Stochastic modelling
  • Valuation
  • Pricing
  • Reserving
  • Hedging
  • Risk measurement
  • Optimization

Published Papers (7 papers)

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Research

27 pages, 441 KiB  
Article
Mortality/Longevity Risk-Minimization with or without Securitization
by Tahir Choulli, Catherine Daveloose and Michèle Vanmaele
Mathematics 2021, 9(14), 1629; https://doi.org/10.3390/math9141629 - 10 Jul 2021
Cited by 1 | Viewed by 1645
Abstract
This paper addresses the risk-minimization problem, with and without mortality securitization, à la Föllmer–Sondermann for a large class of equity-linked mortality contracts when no model for the death time is specified. This framework includes situations in which the correlation between the market model [...] Read more.
This paper addresses the risk-minimization problem, with and without mortality securitization, à la Föllmer–Sondermann for a large class of equity-linked mortality contracts when no model for the death time is specified. This framework includes situations in which the correlation between the market model and the time of death is arbitrary general, and hence leads to the case of a market model where there are two levels of information—the public information, which is generated by the financial assets, and a larger flow of information that contains additional knowledge about the death time of an insured. By enlarging the filtration, the death uncertainty and its entailed risk are fully considered without any mathematical restriction. Our key tool lies in our optional martingale representation, which states that any martingale in the large filtration stopped at the death time can be decomposed into precise orthogonal local martingales. This allows us to derive the dynamics of the value processes of the mortality/longevity securities used for the securitization, and to decompose any mortality/longevity liability into the sum of orthogonal risks by means of a risk basis. The first main contribution of this paper resides in quantifying, as explicitly as possible, the effect of mortality on the risk-minimizing strategy by determining the optimal strategy in the enlarged filtration in terms of strategies in the smaller filtration. Our second main contribution consists of finding risk-minimizing strategies with insurance securitization by investing in stocks and one (or more) mortality/longevity derivatives such as longevity bonds. This generalizes the existing literature on risk-minimization using mortality securitization in many directions. Full article
(This article belongs to the Special Issue Stochastic Modelling with Applications in Finance and Insurance)
16 pages, 1101 KiB  
Article
Implied Tail Risk and ESG Ratings
by Jingyan Zhang, Jan De Spiegeleer and Wim Schoutens
Mathematics 2021, 9(14), 1611; https://doi.org/10.3390/math9141611 - 8 Jul 2021
Cited by 9 | Viewed by 3917
Abstract
This paper explores whether the high or low ESG rating of a company is related to the level of its implied tail risk, measured on the basis of derivative data by implied skewness and implied kurtosis. Previous research suggests that the ESG rating [...] Read more.
This paper explores whether the high or low ESG rating of a company is related to the level of its implied tail risk, measured on the basis of derivative data by implied skewness and implied kurtosis. Previous research suggests that the ESG rating of a company is indeed connected to some financial risk; however, often, only volatility is used as a risk measure. We examined the relation between ESG ratings and implied volatility, and explore the relation between ESG ratings and financial risk in more depth by looking into higher implied moments accessing financial tail risk. First, we found that higher ESG rated companies have a lower implied volatility connected with them, and exhibit more negative implied skewness and higher implied kurtosis. In other words, we observed a higher negative tail risk for higher ESG rated companies. However, on a midsized company data set, we found that higher ESG rated companies both have lower implied volatility, and exhibit less negative implied skewness and lower implied kurtosis. Hence, negative tail risk is typically lower for high ESG rated companies. Our study further investigated similar effects on individual environmental (E), social (S) and governance (G) scores of the involved companies. Second, we examined whether such a kind of trend exists for different sectors. Our results indicate that the influence of ESG ratings on implied volatility exhibits a similar trend, except for the industrial, information services, and real estate sectors, while for the materials, healthcare, and communication services sectors, the influence of ESG ratings on implied skewness and implied kurtosis is less pronounced. Moreover, the results show that the ESG ratings are correlated with implied moments for companies in consumer discretionary sectors. Full article
(This article belongs to the Special Issue Stochastic Modelling with Applications in Finance and Insurance)
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23 pages, 492 KiB  
Article
An Intrinsic Value Approach to Valuation with Forward–Backward Loops in Dividend Paying Stocks
by Anna Kamille Nyegaard, Johan Raunkjær Ott and Mogens Steffensen
Mathematics 2021, 9(13), 1520; https://doi.org/10.3390/math9131520 - 29 Jun 2021
Cited by 1 | Viewed by 1721
Abstract
We formulate a claim valuation problem where the dynamics of the underlying asset process contain the claim value itself. The problem is motivated here by an equity valuation of a firm, with intermediary dividend payments that depend on both the underlying, that is, [...] Read more.
We formulate a claim valuation problem where the dynamics of the underlying asset process contain the claim value itself. The problem is motivated here by an equity valuation of a firm, with intermediary dividend payments that depend on both the underlying, that is, the assets of the company, and the equity value itself. Since the assets are reduced by the dividend payments, the entanglement of claim, claim value, and underlying is complete and numerically challenging because it forms a forward–backward stochastic system. We propose a numerical approach based on disentanglement of the forward–backward deterministic system for the intrinsic values, a parametric assumption of the claim value in its intrinsic value, and a simulation of the stochastic elements. We illustrate the method in a numerical example where the equity value is approximated efficiently, at least for the relevant ranges of the asset value. Full article
(This article belongs to the Special Issue Stochastic Modelling with Applications in Finance and Insurance)
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17 pages, 559 KiB  
Article
Numerical Valuation of American Basket Options via Partial Differential Complementarity Problems
by Karel J. in’t Hout and Jacob Snoeijer
Mathematics 2021, 9(13), 1498; https://doi.org/10.3390/math9131498 - 26 Jun 2021
Viewed by 1867
Abstract
We study the principal component analysis based approach introduced by Reisinger and Wittum (2007) and the comonotonic approach considered by Hanbali and Linders (2019) for the approximation of American basket option values via multidimensional partial differential complementarity problems (PDCPs). Both approximation approaches require [...] Read more.
We study the principal component analysis based approach introduced by Reisinger and Wittum (2007) and the comonotonic approach considered by Hanbali and Linders (2019) for the approximation of American basket option values via multidimensional partial differential complementarity problems (PDCPs). Both approximation approaches require the solution of just a limited number of low-dimensional PDCPs. It is demonstrated by ample numerical experiments that they define approximations that lie close to each other. Next, an efficient discretisation of the pertinent PDCPs is presented that leads to a favourable convergence behaviour. Full article
(This article belongs to the Special Issue Stochastic Modelling with Applications in Finance and Insurance)
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22 pages, 468 KiB  
Article
A Generalized Weighted Monte Carlo Calibration Method for Derivative Pricing
by Hilmar Gudmundsson and David Vyncke
Mathematics 2021, 9(7), 739; https://doi.org/10.3390/math9070739 - 29 Mar 2021
Cited by 2 | Viewed by 2467
Abstract
The weighted Monte Carlo method is an elegant technique to calibrate asset pricing models to market prices. Unfortunately, the accuracy can drop quite quickly for out-of-sample options as one moves away from the strike range and maturity range of the benchmark options. To [...] Read more.
The weighted Monte Carlo method is an elegant technique to calibrate asset pricing models to market prices. Unfortunately, the accuracy can drop quite quickly for out-of-sample options as one moves away from the strike range and maturity range of the benchmark options. To improve the accuracy, we propose a generalized version of the weighted Monte Carlo calibration method with two distinguishing features. First, we use a probability distortion scheme to produce a non-uniform prior distribution for the simulated paths. Second, we assign multiple weights per path to fit with the different maturities present in the set of benchmark options. Our tests on S&P500 options data show that the new calibration method proposed here produces a significantly better out-of-sample fit than the original method for two commonly used asset pricing models. Full article
(This article belongs to the Special Issue Stochastic Modelling with Applications in Finance and Insurance)
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30 pages, 405 KiB  
Article
Pricing of Commodity and Energy Derivatives for Polynomial Processes
by Fred Espen Benth
Mathematics 2021, 9(2), 124; https://doi.org/10.3390/math9020124 - 7 Jan 2021
Cited by 5 | Viewed by 2540
Abstract
Operating in energy and commodity markets require a management of risk using derivative products such as forward and futures, as well as options on these. Many of the popular stochastic models for spot dynamics and weather variables developed from empirical studies in commodity [...] Read more.
Operating in energy and commodity markets require a management of risk using derivative products such as forward and futures, as well as options on these. Many of the popular stochastic models for spot dynamics and weather variables developed from empirical studies in commodity and energy markets belong to the class of polynomial jump diffusion processes. We derive a tailor-made framework for efficient polynomial approximation of the main derivatives encountered in commodity and energy markets, encompassing a wide range of arithmetic and geometric models. Our analysis accounts for seasonality effects, delivery periods of forwards and exotic temperature forwards where the underlying “spot” is a nonlinear function of the temperature. We also include in our derivations risk management products such as spread, Asian and quanto options. Full article
(This article belongs to the Special Issue Stochastic Modelling with Applications in Finance and Insurance)
18 pages, 426 KiB  
Article
Modeling Recovery Rates of Small- and Medium-Sized Entities in the US
by Aleksey Min, Matthias Scherer, Amelie Schischke and Rudi Zagst
Mathematics 2020, 8(11), 1856; https://doi.org/10.3390/math8111856 - 23 Oct 2020
Cited by 7 | Viewed by 1950
Abstract
A sound statistical model for recovery rates is required for various applications in quantitative risk management, with the computation of capital requirements for loan portfolios as one important example. We compare different models for predicting the recovery rate on borrower level including linear [...] Read more.
A sound statistical model for recovery rates is required for various applications in quantitative risk management, with the computation of capital requirements for loan portfolios as one important example. We compare different models for predicting the recovery rate on borrower level including linear and quantile regressions, decision trees, neural networks, and mixture regression models. We fit and apply these models on the worldwide largest loss and recovery data set for commercial loans provided by GCD, where we focus on small- and medium-sized entities in the US. Additionally, we include macroeconomic information via a predictive Crisis Indicator or Crisis Probability indicating whether economic downturn scenarios are expected within the time of resolution. The horserace is won by the mixture regression model which regresses the densities as well as the probabilities that an observation belongs to a certain component. Full article
(This article belongs to the Special Issue Stochastic Modelling with Applications in Finance and Insurance)
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