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Risks
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Applying Stochastic Models in Practice: Empirics and Numerics
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Applying Stochastic Models in Practice: Empirics and Numerics

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

Deadline for manuscript submissions: closed (30 June 2016) | Viewed by 41582

Special Issue Editor

Prof. Dr. Alexander Szimayer

E-Mail Website
Guest Editor
Faculty of Economics and Social Sciences, University of Hamburg, 20146 Hamburg, Germany
Interests: financial econometrics; mathematical finance; economics of risk and insurance
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The ongoing development of novel stochastic models is essential to better understand and quantify newly emerging risks in finance and insurance. To ensure the practical use of these models, it is of particular importance that potential users be equipped with tools necessary for estimation and/or calibration of a specific model, and with efficient numerical algorithms that employ a certain model for an ensuing application. Prominent examples for recent advances in stochastic modeling include models for extreme dependence in finance and insurance (credit contagion or clustering of natural disasters), the effect of lapse risk or longevity risk on insurance companies, and capital/credit/debt/funding value adjustments in finance. The aim of this Special Issue is to highlight empirical results and methods, as well as numerical algorithms related to novel stochastic models in finance and insurance with a focus on the application of such models in practice.

Prof. Dr. Alexander Szimayer
Guest Editor

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Keywords

  • Empirical Finance
  • Empirical Studies in Insurance
  • Numerical Methods in Finance
  • Numerical Methods in Insurance

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Published Papers (7 papers)

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Research

1910 KiB  
Article
Nested MC-Based Risk Measurement of Complex Portfolios: Acceleration and Energy Efficiency
by Sascha Desmettre, Ralf Korn, Javier Alejandro Varela and Norbert Wehn
Risks 2016, 4(4), 36; https://doi.org/10.3390/risks4040036 - 18 Oct 2016
Cited by 3 | Viewed by 7271
Abstract
Risk analysis and management currently have a strong presence in financial institutions, where high performance and energy efficiency are key requirements for acceleration systems, especially when it comes to intraday analysis. In this regard, we approach the estimation of the widely-employed portfolio risk [...] Read more.
Risk analysis and management currently have a strong presence in financial institutions, where high performance and energy efficiency are key requirements for acceleration systems, especially when it comes to intraday analysis. In this regard, we approach the estimation of the widely-employed portfolio risk metrics value-at-risk (VaR) and conditional value-at-risk (cVaR) by means of nested Monte Carlo (MC) simulations. We do so by combining theory and software/hardware implementation. This allows us for the first time to investigate their performance on heterogeneous compute systems and across different compute platforms, namely central processing unit (CPU), many integrated core (MIC) architecture XeonPhi, graphics processing unit (GPU), and field-programmable gate array (FPGA). To this end, the OpenCL framework is employed to generate portable code, and the size of the simulations is scaled in order to evaluate variations in performance. Furthermore, we assess different parallelization schemes, and the targeted platforms are evaluated and compared in terms of runtime and energy efficiency. Our implementation also allowed us to derive a new algorithmic optimization regarding the generation of the required random number sequences. Moreover, we provide specific guidelines on how to properly handle these sequences in portable code, and on how to efficiently implement nested MC-based VaR and cVaR simulations on heterogeneous compute systems. Full article
(This article belongs to the Special Issue Applying Stochastic Models in Practice: Empirics and Numerics)
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929 KiB  
Article
Choosing Markovian Credit Migration Matrices by Nonlinear Optimization
by Maximilian Hughes and Ralf Werner
Risks 2016, 4(3), 31; https://doi.org/10.3390/risks4030031 - 30 Aug 2016
Cited by 9 | Viewed by 5497
Abstract
Transition matrices, containing credit risk information in the form of ratings based on discrete observations, are published annually by rating agencies. A substantial issue arises, as for higher rating classes practically no defaults are observed yielding default probabilities of zero. This does not [...] Read more.
Transition matrices, containing credit risk information in the form of ratings based on discrete observations, are published annually by rating agencies. A substantial issue arises, as for higher rating classes practically no defaults are observed yielding default probabilities of zero. This does not always reflect reality. To circumvent this shortcoming, estimation techniques in continuous-time can be applied. However, raw default data may not be available at all or not in the desired granularity, leaving the practitioner to rely on given one-year transition matrices. Then, it becomes necessary to transform the one-year transition matrix to a generator matrix. This is known as the embedding problem and can be formulated as a nonlinear optimization problem, minimizing the distance between the exponential of a potential generator matrix and the annual transition matrix. So far, in credit risk-related literature, solving this problem directly has been avoided, but approximations have been preferred instead. In this paper, we show that this problem can be solved numerically with sufficient accuracy, thus rendering approximations unnecessary. Our direct approach via nonlinear optimization allows one to consider further credit risk-relevant constraints. We demonstrate that it is thus possible to choose a proper generator matrix with additional structural properties. Full article
(This article belongs to the Special Issue Applying Stochastic Models in Practice: Empirics and Numerics)
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Graphical abstract

1159 KiB  
Article
Lead–Lag Relationship Using a Stop-and-Reverse-MinMax Process
by Stanislaus Maier-Paape and Andreas Platen
Risks 2016, 4(3), 27; https://doi.org/10.3390/risks4030027 - 7 Jul 2016
Cited by 1 | Viewed by 4820
Abstract
The intermarket analysis, in particular the lead–lag relationship, plays an important role within financial markets. Therefore, a mathematical approach to be able to find interrelations between the price development of two different financial instruments is developed in this paper. Computing the differences of [...] Read more.
The intermarket analysis, in particular the lead–lag relationship, plays an important role within financial markets. Therefore, a mathematical approach to be able to find interrelations between the price development of two different financial instruments is developed in this paper. Computing the differences of the relative positions of relevant local extrema of two charts, i.e., the local phase shifts of these price developments, gives us an empirical distribution on the unit circle. With the aid of directional statistics, such angular distributions are studied for many pairs of markets. It is shown that there are several very strongly correlated financial instruments in the field of foreign exchange, commodities and indexes. In some cases, one of the two markets is significantly ahead with respect to the relevant local extrema, i.e., there is a phase shift unequal to zero between them. Full article
(This article belongs to the Special Issue Applying Stochastic Models in Practice: Empirics and Numerics)
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Graphical abstract

2861 KiB  
Article
Survey on Log-Normally Distributed Market-Technical Trend Data
by René Brenner and Stanislaus Maier-Paape
Risks 2016, 4(3), 20; https://doi.org/10.3390/risks4030020 - 4 Jul 2016
Cited by 1 | Viewed by 5326
Abstract
In this survey, a short introduction of the recent discovery of log-normally-distributed market-technical trend data will be given. The results of the statistical evaluation of typical market-technical trend variables will be presented. It will be shown that the log-normal assumption fits better to [...] Read more.
In this survey, a short introduction of the recent discovery of log-normally-distributed market-technical trend data will be given. The results of the statistical evaluation of typical market-technical trend variables will be presented. It will be shown that the log-normal assumption fits better to empirical trend data than to daily returns of stock prices. This enables one to mathematically evaluate trading systems depending on such variables. In this manner, a basic approach to an anti-cyclic trading system will be given as an example. Full article
(This article belongs to the Special Issue Applying Stochastic Models in Practice: Empirics and Numerics)
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Graphical abstract

523 KiB  
Article
Improving Convergence of Binomial Schemes and the Edgeworth Expansion
by Alona Bock and Ralf Korn
Risks 2016, 4(2), 15; https://doi.org/10.3390/risks4020015 - 23 May 2016
Cited by 6 | Viewed by 4921
Abstract
Binomial trees are very popular in both theory and applications of option pricing. As they often suffer from an irregular convergence behavior, improving this is an important task. We build upon a new version of the Edgeworth expansion for lattice models to construct [...] Read more.
Binomial trees are very popular in both theory and applications of option pricing. As they often suffer from an irregular convergence behavior, improving this is an important task. We build upon a new version of the Edgeworth expansion for lattice models to construct new and quickly converging binomial schemes with a particular application to barrier options. Full article
(This article belongs to the Special Issue Applying Stochastic Models in Practice: Empirics and Numerics)
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976 KiB  
Article
Inflation Protected Investment Strategies
by Mirco Mahlstedt and Rudi Zagst
Risks 2016, 4(2), 9; https://doi.org/10.3390/risks4020009 - 28 Mar 2016
Cited by 1 | Viewed by 7591
Abstract
In this paper, a dynamic inflation-protected investment strategy is presented, which is based on traditional asset classes and Markov-switching models. Different stock market, as well as inflation regimes are identified, and within those regimes, the inflation hedging potential of stocks, bonds, real estate, [...] Read more.
In this paper, a dynamic inflation-protected investment strategy is presented, which is based on traditional asset classes and Markov-switching models. Different stock market, as well as inflation regimes are identified, and within those regimes, the inflation hedging potential of stocks, bonds, real estate, commodities and gold are investigated. Within each regime, we determine optimal investment portfolios driven by the investment idea of protection from losses due to changing inflation if inflation is rising or high, but decoupling the performance from inflation if inflation is low. The results clearly indicate that these asset classes behave differently in different stock market and inflation regimes. Whereas in the long-run, we agree with the general opinion in the literature that stocks and bonds are a suitable hedge against inflation, we observe for short time horizons that the hedging potential of each asset class, especially of real estate and commodities, depend strongly on the state of the current market environment. Thus, our approach provides a possible explanation for different statements in the literature regarding the inflation hedging properties of these asset classes. A dynamic inflation-protected investment strategy is developed, which combines inflation protection and upside potential. This strategy outperforms standard buy-and-hold strategies, as well as the well-known 1 N -portfolio. Full article
(This article belongs to the Special Issue Applying Stochastic Models in Practice: Empirics and Numerics)
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372 KiB  
Article
Modified Munich Chain-Ladder Method
by Michael Merz and Mario V. Wüthrich
Risks 2015, 3(4), 624-646; https://doi.org/10.3390/risks3040624 - 21 Dec 2015
Cited by 2 | Viewed by 5221
Abstract
The Munich chain-ladder method for claims reserving was introduced by Quarg and Mack on an axiomatic basis. We analyze these axioms, and we define a modified Munich chain-ladder method which is based on an explicit stochastic model. This stochastic model then allows us [...] Read more.
The Munich chain-ladder method for claims reserving was introduced by Quarg and Mack on an axiomatic basis. We analyze these axioms, and we define a modified Munich chain-ladder method which is based on an explicit stochastic model. This stochastic model then allows us to consider claims prediction and prediction uncertainty for the Munich chain-ladder method in a consistent way. Full article
(This article belongs to the Special Issue Applying Stochastic Models in Practice: Empirics and Numerics)
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