Risks, Volume 7, Issue 4 (December 2019) – 26 articles

We develop valuation and risk techniques for the future benefits of a retiree who participates in the American Social Security program based on their chosen date of retirement, the term structure of interest rates, and forecasted life expectancy. These valuation methods are then used to determine the optimal retirement time of a beneficiary given a specific wage history and health profile in the sense of maximizing the present value of cash flows received during retirement years. We then examine how a number of risk factors including interest rates, disease diagnosis, and mortality risks impact benefit value. Specifically, we utilize principal component analysis in order to assess both interest rate and mortality risk. We then conduct numerical studies to examine how such risks range over distinct income and demographic groups and finally summarize future research directions. Full article

This paper proposes a new method to model loss given default (LGD) for IFRS 9 purposes. We develop two models for the purposes of this paper—LGD1 and LGD2. The LGD1 model is applied to the non-default (performing) accounts and its empirical value based on a specified reference period using a lookup table. We also segment this across the most important variables to obtain a more granular estimate. The LGD2 model is applied to defaulted accounts and we estimate the model by means of an exposure weighted logistic regression. This newly developed LGD model is tested on a secured retail portfolio from a bank. We compare this weighted logistic regression (WLR) (under the assumption of independence) with generalised estimating equations (GEEs) to test the effects of disregarding the dependence among the repeated observations per account. When disregarding this dependence in the application of WLR, the standard errors of the parameter estimates are underestimated. However, the practical effect of this implementation in terms of model accuracy is found to be negligible. The main advantage of the newly developed methodology is the simplicity of this well-known approach, namely logistic regression of binned variables, resulting in a scorecard format. Full article

The aim of this work is to assess systemic risk of Tunisian listed banks. The goal is to identify the institutions that contribute the most to systemic risk and that are most exposed to it. We use the CoVaR that considered the systemic risk as the value at risk (VaR) of a financial institution conditioned on the VaR of another institution. Thus, if the CoVaR increases with respect to the VaR, the spillover risk also increases among the institutions. The difference between these measurements is termed △CoVaR, and it allows for estimating the exposure and contribution of each bank to systemic risk. Results allow classifying Tunisian banks in terms of systemic risk involvement. They show that public banks occupy the top places, followed by the two largest private banks in Tunisia. These five banks are the main systemic players in the Tunisian banking sector. It seems that they are the least sensitive to the financial difficulties of existing banks and the most important contributors to the distress of the other banks. This work aims to add a broader perspective to the micro prudential application of regulation, including contagion, proposing a macro prudential vision and strengthening of regulatory policy. Supervisors could impose close supervision for institutions considered as potentially systemic banks. Furthermore, regulations should consider the systemic contribution when defining risk requirements to minimize the consequences of possible herd behavior. Full article

This paper considers the Brownian perturbed Cramér–Lundberg risk model with a dividends barrier. We study various types of Padé approximations and Laguerre expansions to compute or approximate the scale function that is necessary to optimize the dividends barrier. We experiment also with a heavy-tailed claim distribution for which we apply the so-called “shifted” Padé approximation. Full article

In this paper, we study a stochastic control problem faced by an insurance company allowed to pay out dividends and make capital injections. As in (Løkka and Zervos (2008); Lindensjö and Lindskog (2019)), for a Brownian motion risk process, and in Zhu and Yang (2016), for diffusion processes, we will show that the so-called Løkka–Zervos alternative also holds true in the case of a Cramér–Lundberg risk process with exponential claims. More specifically, we show that: if the cost of capital injections is low, then according to a double-barrier strategy, it is optimal to pay dividends and inject capital, meaning ruin never occurs; and if the cost of capital injections is high, then according to a single-barrier strategy, it is optimal to pay dividends and never inject capital, meaning ruin occurs at the first passage below zero. Full article

A new Bornhuetter–Ferguson method is suggested herein. This is a variant of the traditional chain ladder method. The actuary can adjust the relative ultimates using externally estimated relative ultimates. These correspond to linear constraints on the Poisson likelihood underpinning the chain ladder method. Adjusted cash flow estimates were obtained as constrained maximum likelihood estimates. The statistical derivation of the new method is provided in the generalised linear model framework. A related approach in the literature, combining unconstrained and constrained maximum likelihood estimates, is presented in the same framework and compared theoretically. A data illustration is described using a motor portfolio from a Greek insurer. Full article

We study the jump behaviour in the sovereign risks of major oil-exporting countries and examine whether it is affected by jumps in the price and volatility of crude oil. Data used are daily from 14 February 2011, to 31 July 2019. We detect the presence of jumps in many oil exporters and find evidence of less frequent jumps in the crude oil market. The jumps in sovereign risks of oil-exporters are significantly affected by oil volatility jumps, not by oil price jumps. These findings suggest that the sovereign risks of oil-exporters are affected by abrupt movements in oil implied volatility, which points to a contagion effect. The findings are useful not only for refining the prediction of the sovereign risks of oil-exporters but also in reducing the potential effect of price discontinuity of sovereign risks on public finances sustainability and financial health. Full article

The Segerdahl-Tichy Process, characterized by exponential claims and state dependent drift, has drawn a considerable amount of interest, due to its economic interest (it is the simplest risk process which takes into account the effect of interest rates). It is also the simplest non-Lévy, non-diffusion example of a spectrally negative Markov risk model. Note that for both spectrally negative Lévy and diffusion processes, first passage theories which are based on identifying two “basic” monotone harmonic functions/martingales have been developed. This means that for these processes many control problems involving dividends, capital injections, etc., may be solved explicitly once the two basic functions have been obtained. Furthermore, extensions to general spectrally negative Markov processes are possible; unfortunately, methods for computing the basic functions are still lacking outside the Lévy and diffusion classes. This divergence between theoretical and numerical is strikingly illustrated by the Segerdahl process, for which there exist today six theoretical approaches, but for which almost nothing has been computed, with the exception of the ruin probability. Below, we review four of these methods, with the purpose of drawing attention to connections between them, to underline open problems, and to stimulate further work. Full article

This article is concerned with the study of the tail correlation among equity indices by means of dynamic copula functions. The main idea is to consider the impact of the use of copula functions in the accuracy of the model’s parameters and in the computation of Value-at-Risk (VaR). Results show that copulas provide more sophisticated results in terms of the accuracy of the forecasted VaR, in particular, if they are compared with the results obtained from Dynamic Conditional Correlation (DCC) model. Full article

In modern market conditions, customers who purchase banking products require a high level of service. In particular, they require continuous real-time service with the ability to instantly “switch” between service channels. The article analyzed the economic component of the omnichannel sales management system in banking. The existing barriers to introducing omnichannels to the practice of banking management have been identified. The features of the calculation of individual elements of the cost of sales at various stages of the life cycle of sales (sales funnel) are considered. An economic–mathematical model for managing the cost and profitability of sales by selecting the optimal omnichannel chains was proposed. The omnichannel model of interaction with customers enables banks to simultaneously achieve several key goals of increasing their own business efficiency: increase sales while reducing their cost and improving the quality of customer service. The model can be used not only in banking, but also in other forms of retail business where it is possible to collect detailed statistics and build a factor analysis of conversion through a sales funnel. Full article

In the mandatory health insurance market in Switzerland, a range of insurers offer policies that differ in characteristics like premium and service level while benefits are the same and regulated by law. In this paper, we give an overview of the market and analyse the relationship between insurers’ characteristics and the evolution of their market shares. Indeed, in view of substantial differences between the players, the risk that policyholders change their provider is important. We develop a linear model with two-sided lognormally distributed errors and use publicly available data on the Swiss mandatory health insurance market for the years from 2002 to 2015. Thereby we identify and quantify the main drivers for the policyholders’ switching behavior that reflect in changes in market shares. The results suggest that market share changes are particularly linked to the difference between an insurer’s premium and the overall market premium. In addition, the difference to the previous year’s premium also has an impact on the market share while the service level as well as the group affiliation of a provider turn out not be significant in explaining annual market share changes. Full article

In this paper, we apply machine learning to forecast the conditional variance of long-term stock returns measured in excess of different benchmarks, considering the short- and long-term interest rate, the earnings-by-price ratio, and the inflation rate. In particular, we apply in a two-step procedure a fully nonparametric local-linear smoother and choose the set of covariates as well as the smoothing parameters via cross-validation. We find that volatility forecastability is much less important at longer horizons regardless of the chosen model and that the homoscedastic historical average of the squared return prediction errors gives an adequate approximation of the unobserved realised conditional variance for both the one-year and five-year horizon. Full article

The purpose of this paper is to evaluate and estimate market risk for the ten major industries in Vietnam. The focus of the empirical analysis is on the energy sector, which has been designated as one of the four key industries, together with services, food, and telecommunications, targeted for economic development by the Vietnam Government through to 2020. The oil and gas industry is a separate energy-related major industry, and it is evaluated separately from energy. The data set is from 2009 to 2017, which is decomposed into two distinct sub-periods after the Global Financial Crisis (GFC), namely the immediate post-GFC (2009–2011) period and the normal (2012–2017) period, in order to identify the behavior of market risk for Vietnam’s major industries. For the stock market in Vietnam, the website used in this paper provided complete and detailed data for each stock, as classified by industry. Two widely used approaches to measure and analyze risk are used in the empirical analysis, namely Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR). The empirical findings indicate that Energy and Pharmaceuticals are the least risky industries, whereas oil and gas and securities have the greatest risk. In general, there is strong empirical evidence that the four key industries display relatively low risk. For public policy, the Vietnam Government’s proactive emphasis on the targeted industries, including energy, to achieve sustainable economic growth and national economic development, seems to be working effectively. This paper presents striking empirical evidence that Vietnam’s industries have substantially improved their economic performance over the full sample, moving from relatively higher levels of market risk in the immediate post-GFC period to a lower risk environment in a normal period several years after the end of the calamitous GFC. Full article

The study of connectedness is key to assess spillover effects and identify lead-lag relationships among market exchanges trading the same asset. By means of an extension of Diebold and Yilmaz (2012) econometric connectedness measures, we examined the relationships of five major Bitcoin exchange platforms during two periods of main interest: the 2017 surge in prices and the 2018 decline. We concluded that Bitfinex and Gemini are leading exchanges in terms of return spillover transmission during the analyzed time-frame, while Bittrexs act as a follower. We also found that connectedness of overall returns fell substantially right before the Bitcoin price hype, whereas it leveled out during the period the down market period. We confirmed that the results are robust with regards to the modeling strategies. Full article

In this paper, we solve the problem of mid price movements arising in high-frequency and algorithmic trading using real data. Namely, we introduce different new types of General Compound Hawkes Processes (GCHPDO, GCHP2SDO, GCHPnSDO) and find their diffusive limits to model the mid price movements of 6 stocks-EBAY, FB, MU, PCAR, SMH, CSCO. We also define error rates to estimate the models fitting accuracy. Maximum Likelihood Estimation (MLE) and Particle Swarm Optimization (PSO) are used for Hawkes processes and models parameters’ calibration. Full article

The misestimation of rating transition probabilities may lead banks to lend money incoherently with borrowers’ default trajectory, causing both a deterioration in asset quality and higher system distress. Applying a Mover-Stayer model to determine the migration risk of small and medium enterprises, we find that banks are over-estimating their credit risk resulting in excessive regulatory capital. This has important macroeconomic implications due to the fact that holding a large capital buffer is costly for banks and this in turn influences their ability to lend in the wider economy. This conclusion is particularly true during economic downturns with the consequence of exacerbating the cyclicality in risk capital that therefore acts to aggravate economic conditions further. We also explain part of the misevaluation of borrowers and the actual relevant weight of non-performing loans within banking portfolios: some of the prudential requirements, at least as regards EMS credit portfolios, cannot be considered effective as envisaged by the regulators who developed the “new” regulation in response to the most recent crisis. The Mover-Stayers approach helps to reduce calculation inaccuracy when analyzing the historical movements of borrowers’ ratings and consequently, improves the efficacy of the resource allocation process and banking industry stability. Full article

This paper investigates option valuation when the underlying market suffers from illiquidity of price impact. Using option data, I infer trading activities and price impacts on the buy side and the sell side in the stock market from option prices across maturities. The finding displays that the stock market is active when the stock prices plummet, but becomes silent after the market crashes. In addition, the difference of option implied price impacts between the buy side and the sell side, which indicates asymmetric liquidity, increases with the time to maturity, especially on the day of the market crisis. Moreover, investors have different perspectives on the future liquidity after liquidity shocks when they are in a bull market or in a bear market according to the option implied price impact (or market depth) curves. I also calibrate three market indices simultaneously and reach the same conclusion that the three markets become erratic on the event date and calm down in the aftermath. Full article

The aggregation of individual risks into total risk using a weighting variable multiplied by two ratio variables representing incidence and intensity is an important task for risk professionals. For example, expected loss (EL) of a loan is the product of exposure at default (EAD), probability of default (PD), and loss given default (LGD) of the loan. Simple weighted (by EAD) means of PD and LGD are intuitive summaries however they do not satisfy a reconciliation property whereby their product with the total EAD equals the sum of the individual expected losses. This makes their interpretation problematic, especially when trying to ascertain whether changes in EAD, PD, or LGD are responsible for a change in EL. We propose means for PD and LGD that have the property of reconciling at the aggregate level. Properties of the new means are explored, including how changes in EL can be attributed to changes in EAD, PD, and LGD. Other applications such as insurance where the incidence ratio is utilization rate (UR) and the intensity ratio is an average benefit (AB) are discussed and the generalization to products of more than two ratio variables provided. Full article

The purpose of this study is to examine the volatility-timing performance of Singapore-based funds under the Central Provident Fund (CPF) Investment Scheme and non-CPF linked funds by taking into account the currency risk effect on internationally managed funds. In particular, we empirically assess whether the funds under the CPF Investment Scheme outperform non-CPF funds by examining the volatility-timing performance associated with these funds. The volatility-timing ability of CPF funds will provide the CPF board with a new method for risk classification. We employ the GARCH models and modified factor models to capture the response of funds to market abnormal conditional volatility including the weekday effect. The SMB and HML factors for non-US based funds are constructed from stock market data to exclude the contribution of the size effect and the BE/ME effect. The results show that volatility timing is one of the factors contributing to the excess return of funds. However, funds’ volatility-timing seems to be country-specific. Most of the Japanese equity funds and global equity funds under the CPF Investment Scheme are found to have the ability of volatility timing. This finding contrasts with the existing studies on Asian, ex-Japan funds and Greater China funds. Moreover, there is no evidence that funds under the CPF Investment Scheme show a better group performance of volatility timing. Full article

First, we give a closed-form formula for first passage time of a reflected Brownian motion with drift. This corrects a formula by Perry et al. (2004). Second, we show that the maximum before a fixed drawdown is exponentially distributed for any drawdown, if and only if the diffusion characteristic $\mu /{\sigma }^2$ is constant. This complements the sufficient condition formulated by Lehoczky (1977). Third, we give an alternative proof for the fact that the maximum before a fixed drawdown is exponentially distributed for any spectrally negative Lévy process, a result due to Mijatović and Pistorius (2012). Our proof is similar, but simpler than Lehoczky (1977) or Landriault et al. (2017). Full article

We consider the Sparre Andersen risk process with interclaim times that belong to the class of distributions with rational Laplace transform. We construct error bounds for the ruin probability based on the Pollaczek–Khintchine formula, and develop an efficient algorithm to approximate the ruin probability for completely monotone claim size distributions. Our algorithm improves earlier results and can be tailored towards achieving a predetermined accuracy of the approximation. Full article

In this paper, we study a generalised CIR process with externally-exciting and self-exciting jumps, and focus on the distributional properties and applications of this process and its aggregated process. The aim of the paper is to introduce a more general process that includes many models in the literature with self-exciting and external-exciting jumps. The first and second moments of this jump-diffusion process are used to calculate the insurance premium based on mean-variance principle. The Laplace transform of aggregated process is derived, and this leads to an application for pricing default-free bonds which could capture the impacts of both exogenous and endogenous shocks. Illustrative numerical examples and comparisons with other models are also provided. Full article

We present an approach to individual claims reserving and claim watching in general insurance based on classification and regression trees (CART). We propose a compound model consisting of a frequency section, for the prediction of events concerning reported claims, and a severity section, for the prediction of paid and reserved amounts. The formal structure of the model is based on a set of probabilistic assumptions which allow the provision of sound statistical meaning to the results provided by the CART algorithms. The multiperiod predictions required for claims reserving estimations are obtained by compounding one-period predictions through a simulation procedure. The resulting dynamic model allows the joint modeling of the case reserves, which usually yields useful predictive information. The model also allows predictions under a double-claim regime, i.e., when two different types of compensation can be required by the same claim. Several explicit numerical examples are provided using motor insurance data. For a large claims portfolio we derive an aggregate reserve estimate obtained as the sum of individual reserve estimates and we compare the result with the classical chain-ladder estimate. Backtesting exercises are also proposed concerning event predictions and claim-reserve estimates. Full article

Global investors’ investment in local currency bonds, especially Korea Treasury Bonds, has increased significantly since the mid-2000s, and their influence on bonds and financial markets has grown consistently. In this paper, we investigate global investor’s priority of decision factors in investing in Korea Treasury Bonds by distributing a pairwise comparative survey to experts and analyzing the results using the analytical hierarchy process technique. For analysis, we created model frames with experts in the field of investment based on literature analysis, selected survey participants by considering their institution of their employment, work experience and region, and obtained responses. We find that investors with short-term investment propensities are more sensitive to international and domestic factors and less to risk factors, and more heavily influenced by U.S. dollar funding conditions. On the other hand, investors with long-term investment tendencies are found to be more sensitive to international and risk factors as opposed to domestic factors, and influenced by: global policy rate decisions and fiscal soundness, sovereign credit rating, possible global economic recession, and geographical risks. Our findings not only contribute to enhancing investors’ understanding of the Korean bond market by discussing consensus among investors, but also provide policy implications for Korean government policymakers who need stable and sustained funding. Full article

Since the 2008–2009 financial crisis, banks have introduced a family of X-valuation adjustments (XVAs) to quantify the cost of counterparty risk and of its capital and funding implications. XVAs represent a switch of paradigm in derivative management, from hedging to balance sheet optimization. They reflect market inefficiencies that should be compressed as much as possible. In this work, we present a genetic algorithm applied to the compression of credit valuation adjustment (CVA), the expected cost of client defaults to a bank. The design of the algorithm is fine-tuned to the hybrid structure, both discrete and continuous parameter, of the corresponding high-dimensional and nonconvex optimization problem. To make intensive trade incremental XVA computations practical in real-time as required for XVA compression purposes, we propose an approach that circumvents portfolio revaluation at the cost of disk memory, storing the portfolio exposure of the night so that the exposure of the portfolio augmented by a new deal can be obtained at the cost of computing the exposure of the new deal only. This is illustrated by a CVA compression case study on real swap portfolios. Full article

In this paper, a new heavy-tailed distribution, the mixture Pareto-loggamma distribution, derived through an exponential transformation of the generalized Lindley distribution is introduced. The resulting model is expressed as a convex sum of the classical Pareto and a special case of the loggamma distribution. A comprehensive exploration of its statistical properties and theoretical results related to insurance are provided. Estimation is performed by using the method of log-moments and maximum likelihood. Also, as the modal value of this distribution is expressed in closed-form, composite parametric models are easily obtained by a mode matching procedure. The performance of both the mixture Pareto-loggamma distribution and composite models are tested by employing different claims datasets. Full article