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Risks, Volume 8, Issue 3 (September 2020) – 18 articles

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Open AccessFeature PaperArticle
Variance and Interest Rate Risk in Unit-Linked Insurance Policies
Risks 2020, 8(3), 84; https://doi.org/10.3390/risks8030084 - 06 Aug 2020
Viewed by 164
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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Open AccessArticle
Nagging Predictors
Risks 2020, 8(3), 83; https://doi.org/10.3390/risks8030083 (registering DOI) - 04 Aug 2020
Viewed by 160
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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Open AccessArticle
Deep Local Volatility
Risks 2020, 8(3), 82; https://doi.org/10.3390/risks8030082 - 03 Aug 2020
Viewed by 174
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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Open AccessArticle
Joshi’s Split Tree for Option Pricing
Risks 2020, 8(3), 81; https://doi.org/10.3390/risks8030081 - 01 Aug 2020
Viewed by 205
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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Open AccessArticle
The Impact of Model Uncertainty on Index-Based Longevity Hedging and Measurement of Longevity Basis Risk
Risks 2020, 8(3), 80; https://doi.org/10.3390/risks8030080 - 01 Aug 2020
Viewed by 199
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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Open AccessArticle
Fiscal Responsibility Legal Framework—New Paradigm for Fiscal Discipline in the EU
Risks 2020, 8(3), 79; https://doi.org/10.3390/risks8030079 - 21 Jul 2020
Viewed by 285
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
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Open AccessArticle
Tail Risk Transmission: A Study of the Iran Food Industry
Risks 2020, 8(3), 78; https://doi.org/10.3390/risks8030078 (registering DOI) - 20 Jul 2020
Viewed by 313
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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Open AccessCommunication
A Poisson Autoregressive Model to Understand COVID-19 Contagion Dynamics
Risks 2020, 8(3), 77; https://doi.org/10.3390/risks8030077 - 16 Jul 2020
Viewed by 328
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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Open AccessArticle
Price Discovery and Market Reflexivity in Agricultural Futures Contracts with Different Maturities
Risks 2020, 8(3), 75; https://doi.org/10.3390/risks8030075 - 11 Jul 2020
Viewed by 401
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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Open AccessArticle
How Risky Are the Options? A Comparison with the Underlying Stock Using MaxVaR as a Risk Measure
Risks 2020, 8(3), 76; https://doi.org/10.3390/risks8030076 - 10 Jul 2020
Viewed by 558
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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Open AccessArticle
Estimating the Volatility of Non-Life Premium Risk Under Solvency II: Discussion of Danish Fire Insurance Data
Risks 2020, 8(3), 74; https://doi.org/10.3390/risks8030074 - 06 Jul 2020
Viewed by 394
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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Open AccessArticle
Neural Network Pricing of American Put Options
Risks 2020, 8(3), 73; https://doi.org/10.3390/risks8030073 - 02 Jul 2020
Viewed by 371
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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Open AccessFeature PaperArticle
Numerical Algorithms for Reflected Anticipated Backward Stochastic Differential Equations with Two Obstacles and Default Risk
Risks 2020, 8(3), 72; https://doi.org/10.3390/risks8030072 - 01 Jul 2020
Viewed by 418
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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Open AccessArticle
The Dynamics of the S&P 500 under a Crisis Context: Insights from a Three-Regime Switching Model
Risks 2020, 8(3), 71; https://doi.org/10.3390/risks8030071 - 01 Jul 2020
Viewed by 551
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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Open AccessArticle
Effect of Variance Swap in Hedging Volatility Risk
Risks 2020, 8(3), 70; https://doi.org/10.3390/risks8030070 - 01 Jul 2020
Viewed by 354
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
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Open AccessFeature PaperArticle
Retiree Mortality Forecasting: A Partial Age-Range or a Full Age-Range Model?
Risks 2020, 8(3), 69; https://doi.org/10.3390/risks8030069 - 01 Jul 2020
Viewed by 303
Abstract
An essential input of annuity pricing is the future retiree mortality. From observed age-specific mortality data, modeling and forecasting can take place in two routes. On the one hand, we can first truncate the available data to retiree ages and then produce mortality [...] Read more.
An essential input of annuity pricing is the future retiree mortality. From observed age-specific mortality data, modeling and forecasting can take place in two routes. On the one hand, we can first truncate the available data to retiree ages and then produce mortality forecasts based on a partial age-range model. On the other hand, with all available data, we can first apply a full age-range model to produce forecasts and then truncate the mortality forecasts to retiree ages. We investigate the difference in modeling the logarithmic transformation of the central mortality rates between a partial age-range and a full age-range model, using data from mainly developed countries in the Human Mortality Database (2020). By evaluating and comparing the short-term point and interval forecast accuracies, we recommend the first strategy by truncating all available data to retiree ages and then produce mortality forecasts. However, when considering the long-term forecasts, it is unclear which strategy is better since it is more difficult to find a model and parameters that are optimal. This is a disadvantage of using methods based on time-series extrapolation for long-term forecasting. Instead, an expectation approach, in which experts set a future target, could be considered, noting that this method has also had limited success in the past. Full article
(This article belongs to the Special Issue Mortality Forecasting and Applications)
Open AccessArticle
Neural Networks and Betting Strategies for Tennis
Risks 2020, 8(3), 68; https://doi.org/10.3390/risks8030068 - 29 Jun 2020
Viewed by 393
Abstract
Recently, the interest of the academic literature on sports statistics has increased enormously. In such a framework, two of the most significant challenges are developing a model able to beat the existing approaches and, within a betting market framework, guarantee superior returns than [...] Read more.
Recently, the interest of the academic literature on sports statistics has increased enormously. In such a framework, two of the most significant challenges are developing a model able to beat the existing approaches and, within a betting market framework, guarantee superior returns than the set of competing specifications considered. This contribution attempts to achieve both these results, in the context of male tennis. In tennis, several approaches to predict the winner are available, among which the regression-based, point-based and paired comparison of the competitors’ abilities play a significant role. Contrary to the existing approaches, this contribution employs artificial neural networks (ANNs) to forecast the probability of winning in tennis matches, starting from all the variables used in a large selection of the previous methods. From an out-of-sample perspective, the implemented ANN model outperforms four out of five competing models, independently of the considered period. For what concerns the betting perspective, we propose four different strategies. The resulting returns on investment obtained from the ANN appear to be more broad and robust than those obtained from the best competing model, irrespective of the betting strategy adopted. Full article
(This article belongs to the Special Issue Risks in Gambling)
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Open AccessFeature PaperArticle
A Two-Population Extension of the Exponential Smoothing State Space Model with a Smoothing Penalisation Scheme
Risks 2020, 8(3), 67; https://doi.org/10.3390/risks8030067 - 29 Jun 2020
Viewed by 386
Abstract
The joint modelling of mortality rates for multiple populations has gained increasing popularity in areas such as government planning and insurance pricing. Sub-groups of a population often preserve similar mortality features with short-term deviations from the common trend. Recent studies indicate that the [...] Read more.
The joint modelling of mortality rates for multiple populations has gained increasing popularity in areas such as government planning and insurance pricing. Sub-groups of a population often preserve similar mortality features with short-term deviations from the common trend. Recent studies indicate that the exponential smoothing state space (ETS) model can produce outstanding prediction performance, while it fails to guarantee the consistency across neighbouring ages. Apart from that, single-population models such as the famous Lee-Carter (LC) may produce divergent forecasts between different populations in the long run and thus lack the property of the so-called coherence. This study extends the original ETS model to a two-population version (2-ETS) and imposes a smoothing penalisation scheme to reduce inconsistency of forecasts across adjacent ages. The exponential smoothing parameters in the 2-ETS model are fitted by a Fourier functional form to reduce dimensionality and thus improve estimation efficiency. We evaluate the performance of the proposed model via an empirical study using Australian female and male population data. Our results demonstrate the superiority of the 2-ETS model over the LC and ETS as well as two multi-population methods - the augmented common factor model (LL) and coherent functional data model (CFDM) regarding forecast accuracy and coherence. Full article
(This article belongs to the Special Issue Mortality Forecasting and Applications)
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