Solvency II: stability problems with the SCR aggregation formula

One of the central issues in the Solvency II process will be an appropriate calculation of the Solvency Capital Requirement (SCR). This is the economic capital that an insurance company must hold in order to guarantee a one-year ruin probability of at most 0.5%. In the so-called standard formula, the overall SCR is calculated from individual SCRs in a particular way that imitates the calculation of the standard deviation for a sum of normally distributed risks (SCR aggregation formula). However, in order to cope with skewness in the individual risk distributions, this formula must be calibrated accordingly in order to maintain the prescribed level of confidence. In this paper, we want to show that the methods proposed and discussed thus far still show stability problems within the general setup.     

Topical modelling issues in Solvency II

The main reasons for giving European insurance companies the option to apply internal models for calculating the main solvency requirement within the Solvency II framework is to enhance better risk management in the firms, and to provide the opportunity to derive a more accurate risk-oriented capital requirement than the standard Solvency Capital Requirement (SCR) could provide. The possibility to use internal models within pillar 1 basically means freedom to calculate the solvency requirement using some other formula and even principles than those given by the standard formula. This freedom is more limited with partial models.

This paper gives a brief introduction and update to the Solvency II project, reviews and discusses some topical aspects of internal models from the supervisory point of view, and points out some relating results of the Quantitative Impact Studies carried out, thus far, in the EU by CEIOPS.     

Flexible dependence modeling of operational risk losses and its impact on total capital requirements

Operational risk data, when available, are usually scarce, heavy-tailed and possibly dependent. In this work, we introduce a model that captures such real-world characteristics and explicitly deals with heterogeneous pairwise and tail dependence of losses. By considering flexible families of copulas, we can easily move beyond modeling bivariate dependence among losses and estimate the total risk capital for the seven- and eight-dimensional distributions of event types and business lines. Using real-world data, we then evaluate the impact of realistic dependence modeling on estimating the total regulatory capital, which turns out to be up to 38% smaller than what the standard Basel approach would prescribe.     

Ultimate Government Control Structures and Firm Value: Evidence from Chinese Listed Companies

We show that 70% of Chinese listed companies are ultimately controlled by government agencies, thereby indicating that state ownership remains widespread in China's stock markets. Three questions are considered that are related to government control structures and their impact on firm value: (1) how do government agencies maintain their control of listed companies; (2) what are the impacts of different government control structures on firm value; and (3) are these impacts different in local government and central government-controlled firms? We find that the Chinese government controls listed companies directly or indirectly through solely state-owned enterprises (SSOEs). Taking into account the trade-off between political and agency costs, we show that firm value increases when some control rights are decentralized from the government to state-owned enterprises (SOEs). Moreover, decentralization improves significantly the performance of local government- controlled, but not central government-controlled firms.     

Government Regulation,Enforcement, and Economic Consequences in a Transition Economy: Empirical Evidence from Chinese Listed Companies Implementing the Split Share Structure Reform

In a changing transition economy, Chinese government regulations that adopt the relatively simple bright line rule formula are enforceable in practice. Taking the early reform-oriented policies of the China Securities Regulatory Commission (CSRC) as an example, we find that the CSRC did not consider local enthusiasm for reform when allocating IPO resources because of the high enforcement costs involved. We also find that CSRC listed company regulations were enforced due to the lower costs involved in verifying regulatory violations, and that listed companies that completed the reform process were given priority in public refinancing. We present empirical evidence supporting the theoretical basis for the hypotheses outlined above. We also conclude that companies that completed the reform process in 2005 were of significantly higher quality and that the SEO regulation did not affect stock market efficiency. These findings enhance our understanding of the efficiency of government regulation in a transition economy.     

Bayesian estimation of truncated data with applications to operational risk measurement

Data insufficiency and reporting threshold are two main issues in operational risk modelling. When these conditions are present, maximum likelihood estimation (MLE) may produce very poor parameter estimates. In this study, we first investigate four methods to estimate the parameters of truncated distributions for small samples—MLE, expectation-maximization algorithm, penalized likelihood estimators, and Bayesian methods. Without any proper prior information, Jeffreys’ prior for truncated distributions is used. Based on a simulation study for the log-normal distribution, we find that the Bayesian method gives much more credible and reliable estimates than the MLE method. Finally, an application to the operational loss severity estimation using real data is conducted using the truncated log-normal and log-gamma distributions. With the Bayesian method, the loss distribution parameters and value-at-risk measure for every cell with loss data can be estimated separately for internal and external data. Moreover, confidence intervals for the Bayesian estimates are obtained via a bootstrap method.     

Hierarchical structures in the aggregation of premium risk for insurance underwriting

In the valuation of the Solvency II capital requirement, the correct appraisal of risk dependencies acquires particular relevance. These dependencies refer to the recognition of risk diversification in the aggregation process and there are different levels of aggregation and hence different types of diversification. For instance, for a non-life company at the first level the risk components of each single line of business (e.g. premium, reserve, and CAT risks) need to be combined in the overall portfolio, the second level regards the aggregation of different kind of risks as, for example, market and underwriting risk, and finally various solo legal entities could be joined together in a group.

Solvency II allows companies to capture these diversification effects in capital requirement assessment, but the identification of a proper methodology can represent a delicate issue. Indeed, while internal models by simulation approaches permit usually to obtain the portfolio multivariate distribution only in the independence case, generally the use of copula functions can consent to have the multivariate distribution under dependence assumptions too.

However, the choice of the copula and the parameter estimation could be very problematic when only few data are available. So it could be useful to find a closed formula based on Internal Models independence results with the aim to obtain the capital requirement under dependence assumption.

A simple technique, to measure the diversification effect in capital requirement assessment, is the formula, proposed by Solvency II quantitative impact studies, focused on the aggregation of capital charges, the latter equal to percentile minus average of total claims amount distribution of single line of business (LoB), using a linear correlation matrix.

On the other hand, this formula produces the correct result only for a restricted class of distributions, while it may underestimate the diversification effect.

In this paper we present an alternative method, based on the idea to adjust that formula with proper calibration factors (proposed by Sandström (2007)) and appropriately extended with the aim to consider very skewed distribution too.

In the last part considering different non-life multi-line insurers, we compare the capital requirements obtained, for only premium risk, applying the aggregation formula to the results derived by elliptical copulas and hierarchical Archimedean copulas.     

Mandatory Corporate Social Responsibility: The Indian experience

The question we raise is what to do when companies fail to keep pace with societal expectations with respect to their corporate social responsibility (CSR). The response of the Indian government was to make it mandatory for large corporations to spend funds on CSR activities. In this paper, we investigate the success of this legislation both for the companies and the intended beneficiaries. We find that the impact of the legislation has fallen short of expectations both in terms of the volume of CSR expenditure generated and the activities to which it has been directed. In particular, we find that the legislation has had a negative corporate profitability which can impact on the willingness of companies to spend in this area. We conclude that greater care must be taken when implementing mandatory CSR if it is to be effective.     

Estimating Portfolio Credit Losses in Downturns

This paper suggests formulas able to capture potential strong connection among credit losses in downturns without assuming any specific distribution for the variables involved. We first show that the current model adopted by regulators (Basel) is equivalent to a conditional distribution derived from the Gaussian Copula (which does not identify tail dependence). We then use conditional distributions derived from copulas that express tail dependence (stronger dependence across higher losses) to estimate the probability of credit losses in extreme scenarios (crises). Next, we use data on historical credit losses incurred in American banks to compare the suggested approach to the Basel formula with respect to their performance when predicting the extreme losses observed in 2009 and 2010. Our results indicate that, in general, the copula approach outperforms the Basel method in two of the three credit segments investigated. The proposed method is extendable to other differentiable copula families and this gives flexibility to future practical applications of the model.     

Extreme dependence in investor attention and stock returns – consequences for forecasting stock returns and measuring systemic risk

We characterize co-movements in investor attention by modeling multivariate internet search volume data. Using a variety of copula models that can capture both asymmetric and skewed dependence, we find empirical evidence of strong non-linear and asymmetric dependence in the attention investors give to companies. Modeling three years of daily stock returns and search volumes from Google Trends for 29 bank names, we find a striking similarity between the dependence structure inherent in stock returns and the dependence in the corresponding time series of search queries. We then document the existence of significant asymmetric and skewed tail dependence in the joint distribution of stock returns and investor attention. Finally, stock returns and internet search volumes appear to evolve concurrently in real time with neither one leading the other. Our findings have important implications, e.g. for the analysis of banks' interconnectedness based on equity data and the pricing of investor attention in the cross-section of stock returns.     

Finance company failure in New Zealand during 2006–2009: Predictable failures?

Over 31 finance companies (non-bank deposit takers) failed in New Zealand over the 2006–2009 period. With an estimated loss of over NZ$3 billion, there was public outcry and a parliamentary inquiry into the causes of the failures, but few have asked if this was a predictable event. We find that failed finance companies have lower capital adequacy, inferior asset quality, more loans falling due, higher earnings and lower cash flows. Furthermore, failed companies have a longer audit lag and some trustees appear to have a greater percentage of failed firms than others. Our logistic model can successfully classify failure one year before for 88.7% of companies. Our logistic model (neural network) can also correctly classify up to 87.5% (83.3%) of a holdout sample. Our results are of interest to regulators and practitioners, as we show that publicly available data could distinguish between failed and non-failed finance companies.     

Pricing catastrophe risk in life (re)insurance

What is the catastrophe risk a life insurance company faces? What is the correct price of a catastrophe cover? During a review of the current standard model, due to Strickler, we found that this model has some serious shortcomings. We therefore present a new model for the pricing of catastrophe excess of loss cover (Cat XL). The new model for annual claim cost C is based on a compound Poisson process of catastrophe costs. To evaluate the distribution of the cost of each catastrophe, we use the Peaks Over Threshold model for the total number of lost lives in each catastrophe and the beta binomial model for the proportion of these corresponding to customers of the insurance company. To be able to estimate the parameters of the model, international and Swedish data were collected and compiled, listing accidents claiming at least twenty and four lives, respectively. Fitting the new model to data, we find the fit to be good. Finally we give the price of a Cat XL contract and perform a sensitivity analysis of how some of the parameters affect the expected value and standard deviation of the cost and thus the price.     

SPAC merger announcement returns and subsequent performance

Special purpose acquisition companies (SPACs) are created to raise capital and then find non-listed operating companies with which to merge. While most of the extant research has focused on SPAC initial public offerings, we study what happens when SPACs announce business combinations. Our analysis of 236 ‘deSPACs’ completed between January 2012 and June 2021 in the United States documents an average short-term announcement return of +7.4% and a 1-year abnormal return of −14.1% (−18.0% over 2 years) for public investors beginning from the merger announcement. Short-term returns decrease with longer times from initial public offering until announcement.     

Modeling Operational Risk With Bayesian Networks

Bayesian networks is an emerging tool for a wide range of risk management applications, one of which is the modeling of operational risk. This comes at a time when changes in the supervision of financial institutions have resulted in increased scrutiny on the risk management of banks and insurance companies, thus giving the industry an impetus to measure and manage operational risk. The more established methods for risk quantification are linear models such as time series models, econometric models, empirical actuarial models, and extreme value theory. Due to data limitations and complex interaction between operational risk variables, various nonlinear methods have been proposed, one of which is the focus of this article: Bayesian networks. Using an idealized example of a fictitious on line business, we construct a Bayesian network that models various risk factors and their combination into an overall loss distribution. Using this model, we show how established Bayesian network methodology can be applied to: (1) form posterior marginal distributions of variables based on evidence, (2) simulate scenarios, (3) update the parameters of the model using data, and (4) quantify in real‐time how well the model predictions compare to actual data. A specific example of Bayesian networks application to operational risk in an insurance setting is then suggested.     

Selection bias and the perils of benchmarking

To find the secrets of business success, what could be more natural than studying successful businesses? In fact, nothing could be more dangerous, warns this Stanford professor. Generalizing from the examples of successful companies is like generalizing about New England weather from data taken only in the summer. That's essentially what businesspeople do when they learn from good examples and what consultants, authors, and researchers do when they study only existing companies or--worse yet--only high-performing companies. They reach conclusions from unrepresentative data samples, falling into the classic statistical trap of selection bias. Drawing on a wealth of case studies, for instance, one researcher concluded that great leaders share two key traits: They persist, often despite initial failures, and they are able to persuade others to join them. But those traits are also the hallmarks of spectacularly unsuccessful entrepreneurs, who must persist in the face of failure to incur large losses and must be able to persuade others to pour their money down the drain. To discover what makes a business successful, then, managers should look at both successes and failures. Otherwise, they will overvalue risky business practices, seeing only those companies that won big and not the ones that lost dismally. They will not be able to tell if their current good fortune stems from smart business practices or if they are actually coasting on past accomplishments or good luck. Fortunately, economists have developed relatively simple tools that can correct for selection bias even when data about failed companies are hard to come by. Success may be inspirational, but managers are more likely to find the secrets of high performance if they give the stories of their competitors'failures as full a hearing as they do the stories of dazzling successes.     

Displaced lognormal volatility skews: analysis and applications to stochastic volatility simulations

We analyze the implied volatility skews generated by displaced lognormal diffusions. In particular, we prove the global monotonicity of implied volatility, and an at-the-money bound on the steepness of downward volatility skews, under displaced lognormal dynamics, which therefore cannot reproduce some features observed in equity markets. A variant, the displaced anti-lognormal, overcomes the steepness constraint, but its state space is bounded above and unbounded below. In light of these limitations on what features the displaced (anti-)lognormal (DL) can model, we exploit the DL, not as a model, but as a control variate, to reduce variance in Monte Carlo simulations of the CEV and SABR local/stochastic volatility models. For either use—as model, or as control variate—the DL’s parameters require estimation. We find an explicit formula for the DL’s short-expiry limiting volatility skew, which allows direct calibration of its parameters to volatility skews implied by market data or by other models.     

Correlation smile matching for collateralized debt obligation tranches with α-stable distributions and fitted Archimedean copula models

As an extension of the standard Gaussian copula model to price collateralized debt obligation (CDO) tranche swaps we present a generalization of a one-factor copula model based on stable distributions. For special parameter values these distributions coincide with Gaussian or Cauchy distributions, but changing the parameters allows a continuous deformation away from the Gaussian copula. All these factor copulas are embedded in a framework of stochastic correlations. We furthermore generalize the linear dependence in the usual factor approach to a more general Archimedean copula dependence between the individual trigger variable and the common latent factor. Our analysis is carried out on a non-homogeneous correlation structure of the underlying portfolio. CDO tranche market premia, even throughout the correlation crisis in May 2005, can be reproduced by certain models. From a numerical perspective, all these models are simple, since calculations can be reduced to one-dimensional numerical integrals.     

A note on the price- and cost structure of retail payment services in the Swedish banking sector 2002

We estimate private costs in the Swedish banking sector for the production of payment services and investigate to what extent the price structure reflects the estimated cost structure. We find that (i) banks tend to use two-part tariffs but (ii) variable costs are poorly reflected in transaction fees towards both consumers and corporate customers. (iii) There exist large cross subsidies between different payment services, foremost from acquiring card payments to cash distribution to the public, while payment services as a whole are not subsidized.     

Auditors' Affirmations of Compliance with IFRS around the World: An Exploratory Study*

It is widely believed that international financial reporting standards (IFRS) have been adopted in many countries, at least for the consolidated reporting of listed companies. However, in nearly all cases, what the rules require is some national or supranational version of IFRS. This might create problems for investor confidence and comparability. We examine what companies and auditors report concerning compliance with IFRS, focusing on the first full year of IFRS reporting by companies in the stock market indices of four major European countries and Australia. We find that, even when companies were complying with IFRS, they were generally not saying so, which seems to miss part of the point of the 35‐year project on international harmonization. In a small number of cases, auditors provided dual reports: on full IFRS in addition to the mandated reference to national GAAP where the latter corresponds with full IFRS. These cases were found only in Germany and the United Kingdom, and mainly related to companies that filed with the Securities and Exchange Commission as foreign private issuers. We propose explanations for the general lack of dual reports and for the exceptions. We call for widespread adoption of dual reporting where a plain report on IFRS is not yet possible.     

Long memory and tail dependence in trading volume and volatility

We investigate the relationship between volatility, measured by realized volatility, and trading volume for 25 NYSE stocks. We show that volume and volatility are long memory but not fractionally cointegrated in most cases. We also find right tail dependence in the volatility and volume innovations. Tail dependence is informative on the behavior of the volatility and volume when large surprising news impact the market. We estimate a fractionally integrated VAR with shock distributions modeled with a mixture of copula functions. The model is able to capture the main characteristics of the series, say long memory, marginal non-normality and tail dependence. A simulation and forecasting exercise highlight the importance of modeling both long memory and tail dependence to capture extreme events.