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Volume 8
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Risks, Volume 8, Issue 3 (September 2020) – 33 articles

Cover Story (view full-size image): Deep learning is used to jointly meta-model no-arbitrage vanilla option prices and the local volatility surface through a neural network representation of the Dupire formula. View this paper.
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10 pages, 876 KiB  
Article
Criminal Investigation and Criminal Intelligence: Example of Adaptation in the Prevention and Repression of Cybercrime
by Barlatier Jerome
Risks 2020, 8(3), 99; https://doi.org/10.3390/risks8030099 - 18 Sep 2020
Cited by 8 | Viewed by 7078
Abstract
In the context of the digitization of delinquent activities, perpetrated via the internet, the question of the most appropriate means of crime prevention and crime repression is once again being raised. Studies performed on police investigations have highlighted the over-determining nature of circumstantial [...] Read more.
In the context of the digitization of delinquent activities, perpetrated via the internet, the question of the most appropriate means of crime prevention and crime repression is once again being raised. Studies performed on police investigations have highlighted the over-determining nature of circumstantial factors in crime as a condition for their elucidation for more than fifty years. The emergence of mass delinquency, such as cybercrime, has thus strongly altered the role of investigation as a useful mode of knowledge production. This obsolescence has appeared gradually and can be summarized in four stages, which generates a suspicion about the social relevance of the investigation. It seems that the holistic approach of criminal intelligence is more adapted to the fight against new forms of crime. The investigation becomes a precision instrument assigned to functions that become more specific. This article considers this paradigm shift by the approaches to knowledge management of crime control. Cybercrime is then emblematic of this shift. This study is based on the criminological review and the delinquency analysis led by the central criminal intelligence service of the national gendarmerie. Its premise may likely guide the strategy of French law enforcement agencies. Full article
(This article belongs to the Special Issue Cyber Risk and Security)
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20 pages, 693 KiB  
Article
Multivariate General Compound Point Processes in Limit Order Books
by Qi Guo, Bruno Remillard and Anatoliy Swishchuk
Risks 2020, 8(3), 98; https://doi.org/10.3390/risks8030098 - 11 Sep 2020
Cited by 3 | Viewed by 3307
Abstract
In this paper, we focus on a new generalization of multivariate general compound Hawkes process (MGCHP), which we referred to as the multivariate general compound point process (MGCPP). Namely, we applied a multivariate point process to model the order flow instead of the [...] Read more.
In this paper, we focus on a new generalization of multivariate general compound Hawkes process (MGCHP), which we referred to as the multivariate general compound point process (MGCPP). Namely, we applied a multivariate point process to model the order flow instead of the Hawkes process. The law of large numbers (LLN) and two functional central limit theorems (FCLTs) for the MGCPP were proved in this work. Applications of the MGCPP in the limit order market were also considered. We provided numerical simulations and comparisons for the MGCPP and MGCHP by applying Google, Apple, Microsoft, Amazon, and Intel trading data. Full article
(This article belongs to the Special Issue Stochastic Modelling in Financial Mathematics)
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23 pages, 673 KiB  
Article
EM Estimation for the Poisson-Inverse Gamma Regression Model with Varying Dispersion: An Application to Insurance Ratemaking
by George Tzougas
Risks 2020, 8(3), 97; https://doi.org/10.3390/risks8030097 - 11 Sep 2020
Cited by 15 | Viewed by 4214
Abstract
This article presents the Poisson-Inverse Gamma regression model with varying dispersion for approximating heavy-tailed and overdispersed claim counts. Our main contribution is that we develop an Expectation-Maximization (EM) type algorithm for maximum likelihood (ML) estimation of the Poisson-Inverse Gamma regression model with varying [...] Read more.
This article presents the Poisson-Inverse Gamma regression model with varying dispersion for approximating heavy-tailed and overdispersed claim counts. Our main contribution is that we develop an Expectation-Maximization (EM) type algorithm for maximum likelihood (ML) estimation of the Poisson-Inverse Gamma regression model with varying dispersion. The empirical analysis examines a portfolio of motor insurance data in order to investigate the efficiency of the proposed algorithm. Finally, both the a priori and a posteriori, or Bonus-Malus, premium rates that are determined by the Poisson-Inverse Gamma model are compared to those that result from the classic Negative Binomial Type I and the Poisson-Inverse Gaussian distributions with regression structures for their mean and dispersion parameters. Full article
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27 pages, 492 KiB  
Article
Optimal Dividend Payment in De Finetti Models: Survey and New Results and Strategies
by Christian Hipp
Risks 2020, 8(3), 96; https://doi.org/10.3390/risks8030096 - 10 Sep 2020
Cited by 4 | Viewed by 2377
Abstract
We consider optimal dividend payment under the constraint that the with-dividend ruin probability does not exceed a given value α. This is done in most simple discrete De Finetti models. We characterize the value function V(s,α) for [...] Read more.
We consider optimal dividend payment under the constraint that the with-dividend ruin probability does not exceed a given value α. This is done in most simple discrete De Finetti models. We characterize the value function V(s,α) for initial surplus s of this problem, characterize the corresponding optimal dividend strategies, and present an algorithm for its computation. In an earlier solution to this problem, a Hamilton-Jacobi-Bellman equation for V(s,α) can be found which leads to its representation as the limit of a monotone iteration scheme. However, this scheme is too complex for numerical computations. Here, we introduce the class of two-barrier dividend strategies with the following property: when dividends are paid above a barrier B, i.e., a dividend of size 1 is paid when reaching B+1 from B, then we repeat this dividend payment until reaching a limit L for some 0≤L≤B. For these strategies we obtain explicit formulas for ruin probabilities and present values of dividend payments, as well as simplifications of the above iteration scheme. The results of numerical experiments show that the values V(s,α) obtained in earlier work can be improved, they are suboptimal. Full article
(This article belongs to the Special Issue Computational Finance and Risk Analysis in Insurance)
14 pages, 2071 KiB  
Article
Least Quartic Regression Criterion to Evaluate Systematic Risk in the Presence of Co-Skewness and Co-Kurtosis
by Giuseppe Arbia, Riccardo Bramante and Silvia Facchinetti
Risks 2020, 8(3), 95; https://doi.org/10.3390/risks8030095 - 8 Sep 2020
Cited by 4 | Viewed by 3407
Abstract
This article proposes a new method for the estimation of the parameters of a simple linear regression model which is based on the minimization of a quartic loss function. The aim is to extend the traditional methodology, based on the normality assumption, to [...] Read more.
This article proposes a new method for the estimation of the parameters of a simple linear regression model which is based on the minimization of a quartic loss function. The aim is to extend the traditional methodology, based on the normality assumption, to also take into account higher moments and to provide a measure for situations where the phenomenon is characterized by strong non-Gaussian distribution like outliers, multimodality, skewness and kurtosis. Although the proposed method is very general, along with the description of the methodology, we examine its application to finance. In fact, in this field, the contribution of the co-moments in explaining the return-generating process is of paramount importance when evaluating the systematic risk of an asset within the framework of the Capital Asset Pricing Model. We also illustrate a Monte Carlo test of significance on the estimated slope parameter and an application of the method based on the top 300 market capitalization components of the STOXX® Europe 600. A comparison between the slope coefficients evaluated using the ordinary Least Squares (LS) approach and the new Least Quartic (LQ) technique shows that the perception of market risk exposure is best captured by the proposed estimator during market turmoil, and it seems to anticipate the market risk increase typical of these periods. Moreover, by analyzing the out-of-sample risk-adjusted returns we show that the proposed method outperforms the ordinary LS estimator in terms of the most common performance indices. Finally, a bootstrap analysis suggests that significantly different Sharpe ratios between LS and LQ yields and Value at Risk estimates can be considered more accurate in the LQ framework. This study adds insights into market analysis and helps in identifying more precisely potentially risky assets whose extreme behavior is strongly dependent on market behavior. Full article
(This article belongs to the Special Issue Financial Networks in Fintech Risk Management II)
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20 pages, 538 KiB  
Review
Bank Risk Determinants in Latin America
by Mariña Martínez-Malvar and Laura Baselga-Pascual
Risks 2020, 8(3), 94; https://doi.org/10.3390/risks8030094 - 7 Sep 2020
Cited by 5 | Viewed by 3809
Abstract
Systemic Banking crises are a recurrent phenomenon that affects society, and there is a need for a better understanding of the risk factors to support prudential regulation and reduce unnecessary risk intake in the financial system. This paper examines the main bank risk [...] Read more.
Systemic Banking crises are a recurrent phenomenon that affects society, and there is a need for a better understanding of the risk factors to support prudential regulation and reduce unnecessary risk intake in the financial system. This paper examines the main bank risk determinants in Latin America. The period analysed covers the timespan from 1999 to 2013, including the systemic banking crisis episodes in Argentina (2001–2003) and Uruguay (2002–2005). We apply a new data-driven comparable methodology to classify and select commercial banks from the sample. We study bank risk proxied by the Z-score. We use the system-GMM estimator as our main empirical analysis method. According to our results, well capitalized, liquid, and traditional commercial banks are less risky. We perform robustness tests by applying OLS, and the results resemble our original model. Full article
(This article belongs to the Special Issue Credit Risk Modeling and Management in Banking Business)
21 pages, 436 KiB  
Article
Measuring the Performance of Bank Loans under Basel II/III and IFRS 9/CECL
by Bernd Engelmann and Ha Pham
Risks 2020, 8(3), 93; https://doi.org/10.3390/risks8030093 - 2 Sep 2020
Cited by 3 | Viewed by 5270
Abstract
In the last two decades, both internal and external risk management of banks have undergone significant developments. Banking supervision encourages banks to use a risk-based approach for computing minimum regulatory capital. Accounting rules have been tightened requiring more timely loss reserves for impaired [...] Read more.
In the last two decades, both internal and external risk management of banks have undergone significant developments. Banking supervision encourages banks to use a risk-based approach for computing minimum regulatory capital. Accounting rules have been tightened requiring more timely loss reserves for impaired loans. In this article, we propose a comprehensive scheme for calculating the profitability of a loan that could be used both for setting risk-based interest rates when originating a loan and for accurately determining the profitability of existing clients. The scheme utilizes the credit models developed for regulatory purposes and takes the impact of regulation on loan performance into account. We show that accounting loan loss provisions cannot be applied in a performance measurement scheme because they do not reflect the true economic loss. In addition, we demonstrate that it is crucial to measure loan performance over the full life cycle of a loan. Restricting profitability measurement to a time horizon of one year as often observed in practice could be misleading. Although our focus is on profitability measurement, the framework could be applied in a wider context, i.e., for macroeconomic stress tests, bank balance sheet projections, capital management, or evaluating the impact of securitizing parts of a bank’s loan portfolio. Full article
(This article belongs to the Special Issue Credit Risk Modeling and Management in Banking Business)
12 pages, 827 KiB  
Article
Address Identification Using Telematics: An Algorithm to Identify Dwell Locations
by Christopher Grumiau, Mina Mostoufi, Solon Pavlioglou and Tim Verdonck
Risks 2020, 8(3), 92; https://doi.org/10.3390/risks8030092 - 1 Sep 2020
Cited by 1 | Viewed by 3386
Abstract
In this work, a method is proposed for exploiting the predictive power of a geo-tagged dataset as a means of identification of user-relevant points of interest (POI). The proposed methodology is subsequently applied in an insurance context for the automatic identification of a [...] Read more.
In this work, a method is proposed for exploiting the predictive power of a geo-tagged dataset as a means of identification of user-relevant points of interest (POI). The proposed methodology is subsequently applied in an insurance context for the automatic identification of a driver’s residence address, solely based on his pattern of movements on the map. The analysis is performed on a real-life telematics dataset. We have anonymized the considered dataset for the purpose of this study to respect privacy regulations. The model performance is evaluated based on an independent batch of the dataset for which the address is known to be correct. The model is capable of predicting the residence postal code of the user with a high level of accuracy, with an f1 score of 0.83. A reliable result of the proposed method could generate benefits beyond the area of fraud, such as general data quality inspections, one-click quotations, and better-targeted marketing. Full article
(This article belongs to the Special Issue Data Mining in Actuarial Science: Theory and Applications)
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19 pages, 1920 KiB  
Article
A Longitudinal Analysis of the Impact of Distance Driven on the Probability of Car Accidents
by Jean-Philippe Boucher and Roxane Turcotte
Risks 2020, 8(3), 91; https://doi.org/10.3390/risks8030091 - 1 Sep 2020
Cited by 20 | Viewed by 4795
Abstract
Using telematics data, we study the relationship between claim frequency and distance driven through different models by observing smooth functions. We used Generalized Additive Models (GAM) for a Poisson distribution, and Generalized Additive Models for Location, Scale, and Shape (GAMLSS) that we generalize [...] Read more.
Using telematics data, we study the relationship between claim frequency and distance driven through different models by observing smooth functions. We used Generalized Additive Models (GAM) for a Poisson distribution, and Generalized Additive Models for Location, Scale, and Shape (GAMLSS) that we generalize for panel count data. To correctly observe the relationship between distance driven and claim frequency, we show that a Poisson distribution with fixed effects should be used because it removes residual heterogeneity that was incorrectly captured by previous models based on GAM and GAMLSS theory. We show that an approximately linear relationship between distance driven and claim frequency can be derived. We argue that this approach can be used to compute the premium surcharge for additional kilometers the insured wants to drive, or as the basis to construct Pay-as-you-drive (PAYD) insurance for self-service vehicles. All models are illustrated using data from a major Canadian insurance company. Full article
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19 pages, 841 KiB  
Article
A Note on Simulation Pricing of π-Options
by Zbigniew Palmowski and Tomasz Serafin
Risks 2020, 8(3), 90; https://doi.org/10.3390/risks8030090 - 28 Aug 2020
Cited by 1 | Viewed by 2767
Abstract
In this work, we adapt a Monte Carlo algorithm introduced by Broadie and Glasserman in 1997 to price a π-option. This method is based on the simulated price tree that comes from discretization and replication of possible trajectories of the underlying asset’s [...] Read more.
In this work, we adapt a Monte Carlo algorithm introduced by Broadie and Glasserman in 1997 to price a π-option. This method is based on the simulated price tree that comes from discretization and replication of possible trajectories of the underlying asset’s price. As a result, this algorithm produces the lower and the upper bounds that converge to the true price with the increasing depth of the tree. Under specific parametrization, this π-option is related to relative maximum drawdown and can be used in the real market environment to protect a portfolio against volatile and unexpected price drops. We also provide some numerical analysis. Full article
(This article belongs to the Special Issue Quantitative Methods in Economics and Finance)
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16 pages, 1149 KiB  
Article
Modelling Australian Dollar Volatility at Multiple Horizons with High-Frequency Data
by Long Hai Vo and Duc Hong Vo
Risks 2020, 8(3), 89; https://doi.org/10.3390/risks8030089 - 26 Aug 2020
Cited by 1 | Viewed by 3358
Abstract
Long-range dependency of the volatility of exchange-rate time series plays a crucial role in the evaluation of exchange-rate risks, in particular for the commodity currencies. The Australian dollar is currently holding the fifth rank in the global top 10 most frequently traded currencies. [...] Read more.
Long-range dependency of the volatility of exchange-rate time series plays a crucial role in the evaluation of exchange-rate risks, in particular for the commodity currencies. The Australian dollar is currently holding the fifth rank in the global top 10 most frequently traded currencies. The popularity of the Aussie dollar among currency traders belongs to the so-called three G’s—Geology, Geography and Government policy. The Australian economy is largely driven by commodities. The strength of the Australian dollar is counter-cyclical relative to other currencies and ties proximately to the geographical, commercial linkage with Asia and the commodity cycle. As such, we consider that the Australian dollar presents strong characteristics of the commodity currency. In this study, we provide an examination of the Australian dollar–US dollar rates. For the period from 18:05, 7th August 2019 to 9:25, 16th September 2019 with a total of 8481 observations, a wavelet-based approach that allows for modelling long-memory characteristics of this currency pair at different trading horizons is used in our analysis. Findings from our analysis indicate that long-range dependence in volatility is observed and it is persistent across horizons. However, this long-range dependence in volatility is most prominent at the horizon longer than daily. Policy implications have emerged based on the findings of this paper in relation to the important determinant of volatility dynamics, which can be incorporated in optimal trading strategies and policy implications. Full article
(This article belongs to the Special Issue Quantitative Methods in Economics and Finance)
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14 pages, 364 KiB  
Article
Hedging on Betting Markets
by Gustav Axén and Dominic Cortis
Risks 2020, 8(3), 88; https://doi.org/10.3390/risks8030088 - 25 Aug 2020
Cited by 5 | Viewed by 6583
Abstract
The possibility to use hedging strategies is an often neglected aspect in the literature on prediction/betting markets, as most papers assume that bettors will bet according to their beliefs about the probability of the outcome of the event, as opposed to the direction [...] Read more.
The possibility to use hedging strategies is an often neglected aspect in the literature on prediction/betting markets, as most papers assume that bettors will bet according to their beliefs about the probability of the outcome of the event, as opposed to the direction in which the odds will move. This ignores strategies that try to buy low and sell high through exploiting price changes, which is an important aspect to incorporate to fully understand market pricing. In this paper, we derive the key mathematical results in using hedging strategies through taking opposite positions to an initial bet after the market odds have changed and show that a profit can be made without explicitly speculating on the probability of the outcomes. We also discuss two sources of inefficiency that can arise when using hedging strategies in practice: (i) the need to pay a fee when using a betting exchange and (ii) the lack of a lay option (the possibility to bet against outcomes) on some markets, and we analyze how they affect the possibilities to hedge. Many of the results have interesting properties when expressed in terms of the naive probabilities implied by the odds. Full article
(This article belongs to the Special Issue Risks in Gambling)
13 pages, 386 KiB  
Article
Comparison of Home Advantage in European Football Leagues
by Patrice Marek and František Vávra
Risks 2020, 8(3), 87; https://doi.org/10.3390/risks8030087 - 21 Aug 2020
Cited by 5 | Viewed by 5407
Abstract
Home advantage in sports is important for coaches, players, fans, and commentators and has a key role in sports prediction models. This paper builds on results of recent research that—instead of points gained—used goals scored and goals conceded to describe home advantage. This [...] Read more.
Home advantage in sports is important for coaches, players, fans, and commentators and has a key role in sports prediction models. This paper builds on results of recent research that—instead of points gained—used goals scored and goals conceded to describe home advantage. This offers more detailed look at this phenomenon. Presented description understands a home advantage in leagues as a random variable that can be described by a trinomial distribution. The paper uses this description to offer new ways of home advantage comparison—based on the Jeffrey divergence and the test for homogeneity—in different leagues. Next, a heuristic procedure—based on distances between probability descriptions of home advantage in leagues—is developed for identification of leagues with similar home advantage. Publicly available data are used for demonstration of presented procedures in 19 European football leagues between the 2007/2008 and 2016/2017 seasons, and for individual teams of one league in one season. Overall, the highest home advantage rate was identified in the highest Greek football league, and the lowest was identified in the fourth level English football league. Full article
(This article belongs to the Special Issue Risks in Gambling)
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16 pages, 694 KiB  
Article
Exchange Rate, Gold Price, and Stock Market Nexus: A Quantile Regression Approach
by Rizwan Ali, Inayat Ullah Mangla, Ramiz Ur Rehman, Wuzhao Xue, Muhammad Akram Naseem and Muhammad Ishfaq Ahmad
Risks 2020, 8(3), 86; https://doi.org/10.3390/risks8030086 - 17 Aug 2020
Cited by 23 | Viewed by 6476
Abstract
In this study, we examine an empirical relationship between stock market volatility with the exchange rate and gold prices of an emerging market, “Pakistan”, employing daily and monthly data (PSX-100 Index) covering from 2001: Q3 to 2018: Q2. The study explains the average [...] Read more.
In this study, we examine an empirical relationship between stock market volatility with the exchange rate and gold prices of an emerging market, “Pakistan”, employing daily and monthly data (PSX-100 Index) covering from 2001: Q3 to 2018: Q2. The study explains the average stock returns by applying MGARCH. Further, it investigates that the volatility in the exchange rate (Rs/US $) and gold prices remain equally strong in bearish and bullish conditions of the stock market by using a quantile regression approach (2001–2018). Additionally, the sample period is divided into two split samples that cover (2001–2007) and (2008–2018) respectively, based on global financial crises and applied similar analysis. The overall results show the negative impact of the exchange rate and gold price volatility on the stock market performance daily (monthly), supporting the argument that the stock market considers the exchange rate and gold price fluctuations as an adverse indicator and reacts negatively. Full article
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14 pages, 327 KiB  
Article
How Does Split Announcement Affect Stock Liquidity? Evidence from Bursa Malaysia
by S. Amir Tabibian, Zhaoyong Zhang and Mohsen Jafarian
Risks 2020, 8(3), 85; https://doi.org/10.3390/risks8030085 - 13 Aug 2020
Cited by 3 | Viewed by 3978
Abstract
This study examines the impact of stock splits on stock liquidity in Bursa Malaysia from 2004–2018. The study uses event study methodology and investigates liquidity changes, the role of liquidity, and the relationship between abnormal returns and liquidity as well. We found a [...] Read more.
This study examines the impact of stock splits on stock liquidity in Bursa Malaysia from 2004–2018. The study uses event study methodology and investigates liquidity changes, the role of liquidity, and the relationship between abnormal returns and liquidity as well. We found a significant liquidity improvement on the splits announcement, announcement of book closing date and split execution date (Ex-date), while it declined after the split Ex-date. The findings also indicate that firms with a low-level liquidity prior to split announcements experienced an increase in liquidity after Ex-date. Using panel data analysis, we find that the fixed effect model is more appropriate than the pooled OLS, and the abnormal announcement returns are driven by stock liquidity. Full article
(This article belongs to the Special Issue Measuring and Modelling Financial Risk and Derivatives)
23 pages, 865 KiB  
Article
Variance and Interest Rate Risk in Unit-Linked Insurance Policies
by David Baños, Marc Lagunas-Merino and Salvador Ortiz-Latorre
Risks 2020, 8(3), 84; https://doi.org/10.3390/risks8030084 - 6 Aug 2020
Cited by 2 | Viewed by 4407
Abstract
One of the risks derived from selling long-term policies that any insurance company has arises from interest rates. In this paper, we consider a general class of stochastic volatility models written in forward variance form. We also deal with stochastic interest rates to [...] Read more.
One of the risks derived from selling long-term policies that any insurance company has arises from interest rates. In this paper, we consider a general class of stochastic volatility models written in forward variance form. We also deal with stochastic interest rates to obtain the risk-free price for unit-linked life insurance contracts, as well as providing a perfect hedging strategy by completing the market. We conclude with a simulation experiment, where we price unit-linked policies using Norwegian mortality rates. In addition, we compare prices for the classical Black-Scholes model against the Heston stochastic volatility model with a Vasicek interest rate model. Full article
(This article belongs to the Special Issue Interplay between Financial and Actuarial Mathematics)
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26 pages, 1640 KiB  
Article
Nagging Predictors
by Ronald Richman and Mario V. Wüthrich
Risks 2020, 8(3), 83; https://doi.org/10.3390/risks8030083 - 4 Aug 2020
Cited by 41 | Viewed by 5156
Abstract
We define the nagging predictor, which, instead of using bootstrapping to produce a series of i.i.d. predictors, exploits the randomness of neural network calibrations to provide a more stable and accurate predictor than is available from a single neural network run. Convergence results [...] Read more.
We define the nagging predictor, which, instead of using bootstrapping to produce a series of i.i.d. predictors, exploits the randomness of neural network calibrations to provide a more stable and accurate predictor than is available from a single neural network run. Convergence results for the family of Tweedie’s compound Poisson models, which are usually used for general insurance pricing, are provided. In the context of a French motor third-party liability insurance example, the nagging predictor achieves stability at portfolio level after about 20 runs. At an insurance policy level, we show that for some policies up to 400 neural network runs are required to achieve stability. Since working with 400 neural networks is impractical, we calibrate two meta models to the nagging predictor, one unweighted, and one using the coefficient of variation of the nagging predictor as a weight, finding that these latter meta networks can approximate the nagging predictor well, only with a small loss of accuracy. Full article
(This article belongs to the Special Issue Computational Finance and Risk Analysis in Insurance)
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18 pages, 3729 KiB  
Article
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 6 | Viewed by 5161
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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26 pages, 557 KiB  
Article
Joshi’s Split Tree for Option Pricing
by Guillaume Leduc and Merima Nurkanovic Hot
Risks 2020, 8(3), 81; https://doi.org/10.3390/risks8030081 - 1 Aug 2020
Cited by 3 | Viewed by 3414
Abstract
In a thorough study of binomial trees, Joshi introduced the split tree as a two-phase binomial tree designed to minimize oscillations, and demonstrated empirically its outstanding performance when applied to pricing American put options. Here we introduce a “flexible” version of Joshi’s tree, [...] Read more.
In a thorough study of binomial trees, Joshi introduced the split tree as a two-phase binomial tree designed to minimize oscillations, and demonstrated empirically its outstanding performance when applied to pricing American put options. Here we introduce a “flexible” version of Joshi’s tree, and develop the corresponding convergence theory in the European case: we find a closed form formula for the coefficients of 1/n and 1/n3/2 in the expansion of the error. Then we define several optimized versions of the tree, and find closed form formulae for the parameters of these optimal variants. In a numerical study, we found that in the American case, an optimized variant of the tree significantly improved the performance of Joshi’s original split tree. Full article
(This article belongs to the Special Issue Computational Finance and Risk Analysis in Insurance)
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27 pages, 2892 KiB  
Article
The Impact of Model Uncertainty on Index-Based Longevity Hedging and Measurement of Longevity Basis Risk
by Uditha Balasooriya, Johnny Siu-Hang Li and Jackie Li
Risks 2020, 8(3), 80; https://doi.org/10.3390/risks8030080 - 1 Aug 2020
Cited by 1 | Viewed by 3207
Abstract
We investigate the impact of model uncertainty on hedging longevity risk with index-based derivatives and assessing longevity basis risk, which arises from the mismatch between the hedging instruments and the portfolio being hedged. We apply the bivariate Lee–Carter model, the common factor model, [...] Read more.
We investigate the impact of model uncertainty on hedging longevity risk with index-based derivatives and assessing longevity basis risk, which arises from the mismatch between the hedging instruments and the portfolio being hedged. We apply the bivariate Lee–Carter model, the common factor model, and the M7-M5 model, with separate cohort effects between the two populations, and various time series processes and simulation methods, to build index-based longevity hedges and measure the hedge effectiveness. Based on our modeling and simulations on hypothetical scenarios, the estimated levels of hedge effectiveness are around 50% to 80% for a large pension plan, and the model selection, particularly in dealing with the computed time series, plays a very important role in the estimation. We also experiment with a modified bootstrapping approach to incorporate the uncertainty of model selection into the modeling of longevity basis risk. The hedging results under this approach may approximately be seen as a “weighted” average of those calculated from the different model candidates. Full article
(This article belongs to the Special Issue Mortality Forecasting and Applications)
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18 pages, 669 KiB  
Article
Fiscal Responsibility Legal Framework—New Paradigm for Fiscal Discipline in the EU
by Mihaela Tofan, Mihaela Onofrei and Anca-Florentina Vatamanu
Risks 2020, 8(3), 79; https://doi.org/10.3390/risks8030079 - 21 Jul 2020
Cited by 3 | Viewed by 5740
Abstract
This paper aims at studying the legal aspects of the European Union (EU)’s fiscal policy, analyzing the statute of fiscal responsibility legal framework, the different measures undertaken in the last years with respect to European trends in fiscal governance and their implications for [...] Read more.
This paper aims at studying the legal aspects of the European Union (EU)’s fiscal policy, analyzing the statute of fiscal responsibility legal framework, the different measures undertaken in the last years with respect to European trends in fiscal governance and their implications for challenges in public finance sustainability. The research started from the presupposition that there is a lack of mechanisms capable of enforcing the area of public finance sustainability, and the implication of the events that created the economic conjuncture of recent years reveals that the solidity of public finances has reached an impasse and needs to be enhanced. The analyzed documents from the area of fiscal responsibility show formal respect for the legislative framework aimed at consolidating public finance sustainability and accentuate the need to use fiscal laws, independent institutions and mechanisms that put constraints on policymakers and determine them to spend more efficiently, invest more wisely, and obtain better results regarding public finance sustainability. We conclude that future policymaking processes need to consider the consolidation of independent fiscal institutions founded by Fiscal Responsibility Law framework, completed by fiscal rules and, therefore, need to redesign the fiscal risk management process. Full article
(This article belongs to the Special Issue The Nexus of Financial Stability and Financial Access: The Role of Financial Infrastructure)
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17 pages, 613 KiB  
Article
Tail Risk Transmission: A Study of the Iran Food Industry
by Fatemeh Mojtahedi, Seyed Mojtaba Mojaverian, Daniel F. Ahelegbey and Paolo Giudici
Risks 2020, 8(3), 78; https://doi.org/10.3390/risks8030078 - 20 Jul 2020
Cited by 1 | Viewed by 3442
Abstract
This paper extends the extreme downside correlation (EDC) and extreme downside hedge (EDH) methodology to model the interdependence in the sensitivity of assets to the downside risk of other financial assets under severe firm-level and market conditions. The model is applied to analyze [...] Read more.
This paper extends the extreme downside correlation (EDC) and extreme downside hedge (EDH) methodology to model the interdependence in the sensitivity of assets to the downside risk of other financial assets under severe firm-level and market conditions. The model is applied to analyze both systematic and systemic exposures in the Iranian Food Industry. The empirical application investigates (1) which company is the safest for investors to diversify their investment, and (2) which companies are the “transmitters” and “receivers” of downside risk. We study the return series of 11 companies and the Food Industry index publicly listed on the Tehran Stock Exchange. The data covers daily close prices from 2015–2020. The result shows that Mahram Manufacturing is the safest to hedge equity risk, and Glucosan and Behshahr Industries are the riskiest, while Gorji Biscuit is central to risk transmission, and Pegah Fars Diary is the main “receiver” of risk in turbulent times. Full article
(This article belongs to the Special Issue Financial Networks in Fintech Risk Management II)
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8 pages, 474 KiB  
Communication
A Poisson Autoregressive Model to Understand COVID-19 Contagion Dynamics
by Arianna Agosto and Paolo Giudici
Risks 2020, 8(3), 77; https://doi.org/10.3390/risks8030077 - 16 Jul 2020
Cited by 42 | Viewed by 5514
Abstract
We present a statistical model which can be employed to understand the contagion dynamics of the COVID-19, which can heavily impact health, economics and finance. The model is a Poisson autoregression of the daily new observed cases, and can reveal whether contagion has [...] Read more.
We present a statistical model which can be employed to understand the contagion dynamics of the COVID-19, which can heavily impact health, economics and finance. The model is a Poisson autoregression of the daily new observed cases, and can reveal whether contagion has a trend, and where is each country on that trend. Model results are exemplified from some observed series. Full article
(This article belongs to the Special Issue Risks: Feature Papers 2020)
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17 pages, 2017 KiB  
Article
Price Discovery and Market Reflexivity in Agricultural Futures Contracts with Different Maturities
by Steffen Volkenand, Günther Filler and Martin Odening
Risks 2020, 8(3), 75; https://doi.org/10.3390/risks8030075 - 11 Jul 2020
Cited by 2 | Viewed by 3660
Abstract
The purpose of this paper is to analyze market reflexivity in agricultural futures contracts with different maturities. To this end, we apply a four-dimensional Hawkes model to storable and non-storable agricultural commodities. We find market reflexivity for both storable and non-storable commodities. Reflexivity [...] Read more.
The purpose of this paper is to analyze market reflexivity in agricultural futures contracts with different maturities. To this end, we apply a four-dimensional Hawkes model to storable and non-storable agricultural commodities. We find market reflexivity for both storable and non-storable commodities. Reflexivity accounts for about 50 to 70% of the total trading activity. Differences between nearby and deferred contracts are less pronounced for non-storable than for storable commodities. We conclude that the co-existence of exogenous and endogenous price dynamics does not change qualitative characteristics of the price discovery process that have been observed earlier without the consideration of market reflexivity. Full article
(This article belongs to the Special Issue Risks: Feature Papers 2020)
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17 pages, 1771 KiB  
Article
How Risky Are the Options? A Comparison with the Underlying Stock Using MaxVaR as a Risk Measure
by Saswat Patra and Malay Bhattacharyya
Risks 2020, 8(3), 76; https://doi.org/10.3390/risks8030076 - 10 Jul 2020
Cited by 1 | Viewed by 4586
Abstract
This paper investigates the risk exposure for options and proposes MaxVaR as an alternative risk measure which captures the risk better than Value-at-Risk especially. While VaR is a measure of end-of-horizon risk, MaxVaR captures the interim risk exposure of a position or a [...] Read more.
This paper investigates the risk exposure for options and proposes MaxVaR as an alternative risk measure which captures the risk better than Value-at-Risk especially. While VaR is a measure of end-of-horizon risk, MaxVaR captures the interim risk exposure of a position or a portfolio. MaxVaR is a more stringent risk measure as it assesses the risk during the risk horizon. For a 30-day maturity option, we find that MaxVaR can be 40% higher than VaR at a 5% significance level. It highlights the importance of MaxVaR as a risk measure and shows that the risk is vastly underestimated when VaR is used as the measure for risk. The sensitivity of MaxVaR with respect to option characteristics like moneyness, time to maturity and risk horizons at different significance levels are observed. Further, interestingly enough we find that the MaxVar to VaR ratio is higher for stocks than the options and we can surmise that stock returns are more volatile than options. For robustness, the study is carried out under different distributional assumptions on residuals and for different stock index options. Full article
(This article belongs to the Special Issue Measuring and Modelling Financial Risk and Derivatives)
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19 pages, 1435 KiB  
Article
Estimating the Volatility of Non-Life Premium Risk Under Solvency II: Discussion of Danish Fire Insurance Data
by Rocco Roberto Cerchiara and Francesco Acri
Risks 2020, 8(3), 74; https://doi.org/10.3390/risks8030074 - 6 Jul 2020
Cited by 1 | Viewed by 3795
Abstract
We studied the volatility assumption of non-life premium risk under the Solvency II Standard Formula and developed an empirical model on real data, the Danish fire insurance data. Our empirical model accomplishes two things. Primarily, compared to the present literature, this paper innovates [...] Read more.
We studied the volatility assumption of non-life premium risk under the Solvency II Standard Formula and developed an empirical model on real data, the Danish fire insurance data. Our empirical model accomplishes two things. Primarily, compared to the present literature, this paper innovates the fitting of Danish fire insurance data using a composite model with a random threshold. Secondly we prove, by fitting the Danish fire insurance data, that for large insurance companies the volatility of the standard formula is higher than the volatility estimated with internal models such as composite models, also taking into account the dependence between attritional and large claims. Full article
(This article belongs to the Special Issue Capital Requirement Evaluation under Solvency II framework)
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24 pages, 1804 KiB  
Article
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 5993
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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30 pages, 830 KiB  
Article
Numerical Algorithms for Reflected Anticipated Backward Stochastic Differential Equations with Two Obstacles and Default Risk
by Jingnan Wang and Ralf Korn
Risks 2020, 8(3), 72; https://doi.org/10.3390/risks8030072 - 1 Jul 2020
Cited by 2 | Viewed by 3447
Abstract
We study numerical algorithms for reflected anticipated backward stochastic differential equations (RABSDEs) driven by a Brownian motion and a mutually independent martingale in a defaultable setting. The generator of a RABSDE includes the present and future values of the solution. We introduce two [...] Read more.
We study numerical algorithms for reflected anticipated backward stochastic differential equations (RABSDEs) driven by a Brownian motion and a mutually independent martingale in a defaultable setting. The generator of a RABSDE includes the present and future values of the solution. We introduce two main algorithms, a discrete penalization scheme and a discrete reflected scheme basing on a random walk approximation of the Brownian motion as well as a discrete approximation of the default martingale, and we study these two methods in both the implicit and explicit versions respectively. We give the convergence results of the algorithms, provide a numerical example and an application in American game options in order to illustrate the performance of the algorithms. Full article
(This article belongs to the Special Issue Computational Finance and Risk Analysis in Insurance)
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15 pages, 597 KiB  
Article
The Dynamics of the S&P 500 under a Crisis Context: Insights from a Three-Regime Switching Model
by Lorenzo Cerboni Baiardi, Massimo Costabile, Domenico De Giovanni, Fabio Lamantia, Arturo Leccadito, Ivar Massabó, Massimiliano Menzietti, Marco Pirra, Emilio Russo and Alessandro Staino
Risks 2020, 8(3), 71; https://doi.org/10.3390/risks8030071 - 1 Jul 2020
Cited by 10 | Viewed by 4586
Abstract
This paper provides an econometric analysis aiming at evidencing the dynamics showed by the S&P 500 market index during the period of 4 January 2001–28 April 2020, in which the subprime crisis has taken place and the COVID-19 crisis has begun. In particular, [...] Read more.
This paper provides an econometric analysis aiming at evidencing the dynamics showed by the S&P 500 market index during the period of 4 January 2001–28 April 2020, in which the subprime crisis has taken place and the COVID-19 crisis has begun. In particular, we fit a three-regime switching model that allows market parameters to behave differently during economic downturns, with the regimes representative of the tranquil, volatile, and turbulent states. We document that the tranquil regime is the most frequent for the whole period, while the dominant regime is the volatile one for the crisis of 2008 and the turbulent one for the first four months of 2020. We fit the same model to the returns of the Dow Jones Industrial Average index and find that during the same period of investigation, the most frequent regime has been the tranquil one, while the volatile and turbulent regimes share the same frequencies. Additionally, we use a multinomial logit model to describe the probabilities of volatile or turbulent regimes. We show that, in the case of the S&P 500 index, the returns from the Volatility Index (VIX) index are significant for both the volatile and the turbulent regimes, while the gold, WTI oil, and the dollar indices have some explanatory power only for the turbulent regime. Full article
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34 pages, 623 KiB  
Article
Effect of Variance Swap in Hedging Volatility Risk
by Yang Shen
Risks 2020, 8(3), 70; https://doi.org/10.3390/risks8030070 - 1 Jul 2020
Cited by 1 | Viewed by 4042
Abstract
This paper studies the effect of variance swap in hedging volatility risk under the mean-variance criterion. We consider two mean-variance portfolio selection problems under Heston’s stochastic volatility model. In the first problem, the financial market is complete and contains three primitive assets: a [...] Read more.
This paper studies the effect of variance swap in hedging volatility risk under the mean-variance criterion. We consider two mean-variance portfolio selection problems under Heston’s stochastic volatility model. In the first problem, the financial market is complete and contains three primitive assets: a bank account, a stock and a variance swap, where the variance swap can be used to hedge against the volatility risk. In the second problem, only the bank account and the stock can be traded in the market, which is incomplete since the idiosyncratic volatility risk is unhedgeable. Under an exponential integrability assumption, we use a linear-quadratic control approach in conjunction with backward stochastic differential equations to solve the two problems. Efficient portfolio strategies and efficient frontiers are derived in closed-form and represented in terms of the unique solutions to backward stochastic differential equations. Numerical examples are provided to compare the solutions to the two problems. It is found that adding the variance swap in the portfolio can remarkably reduce the portfolio risk. Full article
(This article belongs to the Special Issue Frontiers of Interdisciplinary Research on Financial and Insurance Risk Management)
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