Research

33 pages, 5115 KiB

Open AccessArticle

The Regime-Switching Structural Default Risk Model

by Andreas Milidonis and Kevin Chisholm

Risks 2024, 12(3), 48; https://doi.org/10.3390/risks12030048 - 04 Mar 2024

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We develop the regime-switching default risk (RSDR) model as a generalization of Merton’s default risk (MDR) model. The RSDR model supports an expanded range of asset probability density functions. First, we show using simulation that the RSDR model incorporates [...] Read more.

We develop the regime-switching default risk (RSDR) model as a generalization of Merton’s default risk (MDR) model. The RSDR model supports an expanded range of asset probability density functions. First, we show using simulation that the RSDR model incorporates sudden changes in asset values faster than the MDR model. Second, we empirically implement the RSDR, MDR and an extension of the MDR model with changes in drift parameters, using maximum likelihood estimation. Focusing on the period before and after corporate rating downgrades used primarily for investment advice, we find that the RSDR model uses changes in equity mean returns and volatility to produce higher estimated default probabilities, faster, than both benchmark models. Full article

(This article belongs to the Special Issue Risks Journal: A Decade of Advancing Knowledge and Shaping the Future)

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28 pages, 10433 KiB

Open AccessArticle

L₁ Regularization for High-Dimensional Multivariate GARCH Models

by Sijie Yao, Hui Zou and Haipeng Xing

Risks 2024, 12(2), 34; https://doi.org/10.3390/risks12020034 - 04 Feb 2024

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Abstract

The complexity of estimating multivariate GARCH models increases significantly with the increase in the number of asset series. To address this issue, we propose a general regularization framework for high-dimensional GARCH models with BEKK representations, and obtain a penalized quasi-maximum likelihood (PQML) estimator. [...] Read more.

The complexity of estimating multivariate GARCH models increases significantly with the increase in the number of asset series. To address this issue, we propose a general regularization framework for high-dimensional GARCH models with BEKK representations, and obtain a penalized quasi-maximum likelihood (PQML) estimator. Under some regularity conditions, we establish some theoretical properties, such as the sparsity and the consistency, of the PQML estimator for the BEKK representations. We then carry out simulation studies to show the performance of the proposed inference framework and the procedure for selecting tuning parameters. In addition, we apply the proposed framework to analyze volatility spillover and portfolio optimization problems, using daily prices of 18 U.S. stocks from January 2016 to January 2018, and show that the proposed framework outperforms some benchmark models. Full article

(This article belongs to the Special Issue Risks Journal: A Decade of Advancing Knowledge and Shaping the Future)

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17 pages, 414 KiB

Open AccessArticle

Invariance of the Mathematical Expectation of a Random Quantity and Its Consequences

by Pierpaolo Angelini

Risks 2024, 12(1), 14; https://doi.org/10.3390/risks12010014 - 18 Jan 2024

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Abstract

Possibility and probability are the two aspects of uncertainty, where uncertainty represents the ignorance of a given individual. The notion of alternative (or event) belongs to the domain of possibility. An event is intrinsically subdivisible and a quadratic metric, whose value is intrinsic [...] Read more.

Possibility and probability are the two aspects of uncertainty, where uncertainty represents the ignorance of a given individual. The notion of alternative (or event) belongs to the domain of possibility. An event is intrinsically subdivisible and a quadratic metric, whose value is intrinsic or invariant, is used to study it. By subdividing the notion of alternative, a joint (bivariate) distribution of mass appears. The mathematical expectation of X is proved to be invariant using joint distributions of mass. The same is true for

X_{12}

and

X_{12 \dots m}

. This paper describes the notion of

α

-product, which refers to joint distributions of mass, as a way to connect the concept of probability with multilinear matters that can be treated through statistical inference. This multilinear approach is a meaningful innovation with regard to the current literature. Linear spaces over

R

with a different dimension can be used as elements of probability spaces. In this study, a more general expression for a measure of variability referred to a single random quantity is obtained. This multilinear measure is obtained using different joint distributions of mass, which are all considered together. Full article

(This article belongs to the Special Issue Risks Journal: A Decade of Advancing Knowledge and Shaping the Future)

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17 pages, 446 KiB

Open AccessFeature PaperArticle

The Applications of Generalized Poisson Regression Models to Insurance Claim Data

by Pouya Faroughi, Shu Li and Jiandong Ren

Risks 2023, 11(12), 213; https://doi.org/10.3390/risks11120213 - 07 Dec 2023

Viewed by 1593

Abstract

Predictive modeling has been widely used for insurance rate making. In this paper, we focus on insurance claim count data and address their common issues with more flexible modeling techniques. In particular, we study the zero-inflated and hurdle-generalized Poisson and negative binomial distributions [...] Read more.

Predictive modeling has been widely used for insurance rate making. In this paper, we focus on insurance claim count data and address their common issues with more flexible modeling techniques. In particular, we study the zero-inflated and hurdle-generalized Poisson and negative binomial distributions in a functional form for modeling insurance claim count data. It is shown that these models are useful in addressing the problem of excess zeros and over-dispersion of the claim count variable. In addition, we show that including the exposure as a covariate in both the zero and the count part of the model is an effective approach to incorporating exposure information in zero-inflated and hurdle models. We illustrate the effectiveness and versatility of the introduced models using three real datasets. The results suggest their promising applications in insurance risk classification and beyond. Full article

(This article belongs to the Special Issue Risks Journal: A Decade of Advancing Knowledge and Shaping the Future)

20 pages, 1528 KiB

Open AccessFeature PaperArticle

Coupled Price–Volume Equity Models with Auto-Induced Regime Switching

by Manuel L. Esquível, Nadezhda P. Krasii, Pedro P. Mota and Victoria V. Shamraeva

Risks 2023, 11(11), 203; https://doi.org/10.3390/risks11110203 - 17 Nov 2023

Viewed by 1412

Abstract

In this work, we present a rigorous development of a model for the Price–Volume relationship of transactions introduced in 2009. For this development, we rely on the precise formulation of diffusion auto-induced regime-switching models presented in our previous work of 2020. The auto-induced [...] Read more.

In this work, we present a rigorous development of a model for the Price–Volume relationship of transactions introduced in 2009. For this development, we rely on the precise formulation of diffusion auto-induced regime-switching models presented in our previous work of 2020. The auto-induced regime-switching models referred to may be based on a finite set of stochastic differential equations (SDE)—all defined on the same bounded time interval—and a sequence of interlacing stopping times defined by the hitting threshold times of the trajectories of the solutions of the SDE. The coupling between price and volume—which we take as a proxy of liquidity—is assumed to be the following: the regime switching in the price variable occurs at the stopping times for which there is a change of region—in the product state space of price and liquidity—for the liquidity variable (and vice versa). The regimes may be defined parametrically—that is, the SDE coefficients keep the same functional form but with varying parameters—or the functional form of the SDE coefficients may change with each regime. By using the same noise source for both the price and the liquidity regime-switching models—volume (liquidity), which, in general, is not a tradable asset—we ensure that despite incorporating information on liquidity, the price part of the coupled model can be assumed to be arbitrage free and complete, allowing the pricing and hedging of derivatives in a simple way. Full article

(This article belongs to the Special Issue Risks Journal: A Decade of Advancing Knowledge and Shaping the Future)

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26 pages, 5597 KiB

Open AccessArticle

Macroeconomic Risks and Monetary Policy in Central European Countries: Parallels in the Czech Republic, Hungary, and Poland

by István Ábel and Pierre Siklos

Risks 2023, 11(11), 200; https://doi.org/10.3390/risks11110200 - 15 Nov 2023

Viewed by 1479

Abstract

Changes in interest rates, inflation, and exchange rates are the main components of macroeconomic risks (financial risks) in projects evaluation. However, the conduct of monetary policy as well as its impact on the economic environment is seldom considered as an important component of [...] Read more.

Changes in interest rates, inflation, and exchange rates are the main components of macroeconomic risks (financial risks) in projects evaluation. However, the conduct of monetary policy as well as its impact on the economic environment is seldom considered as an important component of macroeconomic risks. In this paper, we offer a simple framework to analyze the conduct of monetary policy. We examine the stabilizing properties of monetary policy, its impact, and the parallels in the monetary policy approaches taken in the Czech Republic, Hungary, and Poland until the pandemic. We provide a simple theoretical background to motivate the main elements of the debate and the choice of policy strategy. We then rationalize the adoption of a form of flexible inflation targeting (FIT). It is characterized by an explicit concern over exchange rates. The empirical evidence, consisting of calibrated and extended Taylor rules, together with local projections estimates, suggests that monetary policy has been practiced with considerable flexibility by all three central banks and has contributed to business cycle stabilization in the region. Most notably, the exchange rate plays an important role in the conduct of monetary policy. Full article

(This article belongs to the Special Issue Risks Journal: A Decade of Advancing Knowledge and Shaping the Future)

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17 pages, 2980 KiB

Open AccessFeature PaperArticle

Discovering Intraday Tail Dependence Patterns via a Full-Range Tail Dependence Copula

by Lei Hua

Risks 2023, 11(11), 195; https://doi.org/10.3390/risks11110195 - 11 Nov 2023

Viewed by 1292

Abstract

In this research, we employ a full-range tail dependence copula to capture the intraday dynamic tail dependence patterns of 30 s log returns among stocks in the US market in the year of 2020, when the market experienced a significant sell-off and a [...] Read more.

In this research, we employ a full-range tail dependence copula to capture the intraday dynamic tail dependence patterns of 30 s log returns among stocks in the US market in the year of 2020, when the market experienced a significant sell-off and a rally thereafter. We also introduce a model-based unified tail dependence measure to directly model and compare various tail dependence patterns. Using regression analysis of the upper and lower tail dependence simultaneously, we have identified some interesting intraday tail dependence patterns, such as interactions between the upper and lower tail dependence over time among growth and value stocks and in different market regimes. Our results indicate that tail dependence tends to peak towards the end of the regular trading hours, and, counter-intuitively, upper tail dependence tends to be stronger than lower tail dependence for short-term returns during a market sell-off. Furthermore, we investigate how the Fama–French five factors affect the intraday tail dependence patterns and provide plausible explanations for the occurrence of these phenomena. Among these five factors, the market excess return plays the most important role, and our study suggests that when there is a moderate positive excess return, both the upper and lower tails tend to reach their lowest dependence levels. Full article

(This article belongs to the Special Issue Risks Journal: A Decade of Advancing Knowledge and Shaping the Future)

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25 pages, 857 KiB

Open AccessFeature PaperArticle

Assessing the Impact of Credit Risk on Equity Options via Information Contents and Compound Options

by Federico Maglione and Maria Elvira Mancino

Risks 2023, 11(10), 183; https://doi.org/10.3390/risks11100183 - 20 Oct 2023

Viewed by 1574

Abstract

This work aims to develop a measure of how much credit risk is priced into equity options. Such a measure appears particularly appealing when applied to a portfolio of equity options, as it allows for the factoring in of firm-specific default dynamics, thus [...] Read more.

This work aims to develop a measure of how much credit risk is priced into equity options. Such a measure appears particularly appealing when applied to a portfolio of equity options, as it allows for the factoring in of firm-specific default dynamics, thus producing a comparable statistic across different equities. As a matter of fact, comparing options written on different equities based on their moneyness does offer much guidance in understanding which option offers a better hedging against default. Our newly-introduced measure aims to fulfil this gap: it allows us to rank options written on different names based on the amount of default risk they carry, incorporating firm-specific characteristics such as leverage and asset risk. After having computed this measure using data from the US market, several empirical tests confirm the economic intuition of puts being more sensitive to changes in the default risk as well as a good integration of the CDS and option markets. We further document cross-sectional sectorial differences based on the industry the companies operate in. Moreover, we show that this newly-introduced measure displays forecasting power in explaining future changes in the skew of long-term maturity options. Full article

(This article belongs to the Special Issue Risks Journal: A Decade of Advancing Knowledge and Shaping the Future)

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