Actuarial Science Project Topics

Credit Risk Modelling Techniques for Life Insurers

Credit Risk Modelling Techniques for Life Insurers


Objectives of the study

The following are the aims and objectives of the study

  • To know the best techniques of credit risk modeling for life insurers.
  • To examine the impact of credit risks on life insurers.
  • To examine the benefits of credit to life insurer.
  • To examine the relationship between credit and performance of insurers.
  • To know if credit facilities are readily made available to insurers.




This chapter gives an insight into various studies conducted by outstanding researchers, as well as explained terminologies with regards to the influence of management on academic performance of secondary school students in Port Harcourt Local Government area in Rivers State, Nigeria. The chapter also gives a resume of the history and present status of the problem delineated by a concise review of previous studies into closely related problems.


The quantitative credit analysis literature began with Altman (1968), where the author proposes discriminant analysis to determine combinations of observable characteristics that may best differentiate between defaulted and non-defaulted firms. This paper was one of the first examples of a quantitative, “credit-scoring” approach to credit assessment. This approach has fallen out of favor in recent decades, in part because of the descriptive focus. Discriminant analysis characterizes a firm’s likely observable characteristics given the current default status, while a credit analyst is generally interested in the converse: a firm’s likely default status given its observable characteristics. In addition to this point, Lo (1986) proves that discriminant analysis is consistent in a much more limited set of circumstances relative to other, more modern approaches. One such approach is logistic regression models that afford a methodology to estimate directly the effects of particular variables on default probabilities (or in the case of logistic regression, the log odds-ratios of the default probabilities).

The 1970s saw the broad application of stochastic calculus into the theoretical finance toolkit. This led to many breakthroughs throughout the field, including in the assessment of credit risk. Merton (1974) is the canonical example. In this paper, Merton applies the option-pricing framework from Black and Scholes (1973) to a firm’s balance sheet. Given standard assumptions governing frictionless markets, full information, and the assumption that firms will default when and if their asset value falls below their liabilities, Merton demonstrates how one can calculate a default rate for any firm. These assumptions about the nature of the markets and the nature of economic behavior cause these models to be called “structural models.” The additional structural assumptions allow the analyst to calculate credit risk given relatively parsimonious data requirements (one needed only the risk-free rate, and firm-level leverage, value of assets and volatility of assets), and the theoretical appeal of the assumed structure led to this model’s wide acceptance and the development of further “structural” models of credit risk. Of course, further developments in the literature investigated the reasonableness of the key structural assumptions with fairly disappointing results (Shumway and Bharath (2008)).

With this foundation, the literature began to apply credit risk in new arenas and relax some key assumptions. Hull and White (1995) discuss how one can incorporate counterparty credit risk in derivative securities, while Duffie and Singleton (1999), and Jarrow and Turnbull (1997) focus on the dynamic nature of credit risk through credit spreads. Duffie and Singleton prove the uniqueness of credit spreads and apply them to a variety of contexts, including term structure models and derivative products; Jarrow and Turnbull develop a model that allows for dynamic credit spreads and calculate the associated impacts on pricing. Lando (1998) demonstrates how risk-free interest rates can be incorporated into quantitative credit analysis. This generalization dramatically increased the potential for quantitative default modeling: now, one can reasonably look at a variety of inputs or “state variables” when characterizing credit risk rather than asset value, volatility and leverage as in Merton (1974). Shumway (2001) and Jarrow and Chava (2004) estimate flexible, “reduced form” models of default intensity that characterize default risk in a statistical model based on firm- and economy-level detail. Shumway notes that reduced form hazard models appear to have superior out-of-sample performance, and the additional information incorporated in the default prediction, such as size, historical stock returns, and the variation in stock returns all appear very important. Jarrow and Chava validate these results, apply this methodology to a monthly frequency for the first time, incorporate industry-level heterogeneity for the first time, and take Shumway’s information conclusions a step further: it appears that given available market prices, standard accounting ratios (such as one would see in Altman (1968) or Merton (1974)) add fairly little explanatory power to default estimation equations. In their credit modeling summary, Altman, Resti, and Sironi (2004) reiterate Shumway’s and Jarrow and Chava’s findings on the sufficiency of the Merton structural approach in characterizing corporate default risk and the relative performance of structural and reduced form models in default modeling. However, the performance for recovery rates is more mixed. In the literature, recovery rate modeling is surrounded by data issues. In addition to the much smaller universe of data, recoveries also have timing issues and intra-firm heterogeneity across securities, as well as tremendous variation across firms and industries both at a point in as well as over time. Jarrow (2001) attempts to detangle default and recovery risk by

examining debt and equity prices with the assumption that in the event of default, the equity value is zero. This is complicated somewhat by the variation in volume between these markets, which necessitates some way to incorporate liquidity risk and liquidity spreads, which we see in much more detail further in the decade. Araten, Jacobs and Varshney (2004) detail the results of an 18-year study of commercial loan recovery rates. They find that the distribution of recoveries tends to be bimodal, varies tremendously by industry and geography (though they do not have enough power to detect a statistical effect), and that the secured or unsecured nature of the credit seems to affect the macroeconomic sensitivity of the recovery rate. Altman (2006) discusses the need for recovery rates to be an independent variable for both structural and reduced form default probability models, as his research shows that there is a statistically significant inverse relationship between recovery and default rates. Finally, Guo, Jarrow, and Zeng (2009) develop a model for pricing distressed debt under default and recovery risk with complete and incomplete information. Recent literature seems to favor the reduced form approach in data rich environments, such as corporate defaults. Shumway and Bharath (2008) demonstrate that structural models are outperformed by reduced form models to such an extent that it is possible to outperform Merton (1974) and its modern-day implementations both in-sample and out-of-sample with a much simpler alternative that does not require the stringent assumptions or simultaneous non-linear equations of the structural approach. Campbell, Hilscher and Szilagyi (2008) even illustrate how one can identify “distressed” firms based on observable characteristics and generate a profitable trading strategy through the application of reduced form models. Recent developments in credit-related assets such as credit default swaps (CDS) have led to a great deal of academic work. Interestingly, much of the work on the CDS market focuses on the shortcomings of these market prices as sources of credit information rather than their strengths. Longstaff, Mithal, and Neis (2005) find that a substantial fraction of quoted corporate yield spreads (through the CDS market) can only be explained by an appeal to non-credit-related, or “liquidity” components. Jarrow (2012) describes how inferring default rates from CDS quotes is fraught with theoretical issues in addition to the empirical inadequacies. Finally, Campbell, Hilscher, and Szilagyi (2008) take issues with the efficiency of prices outside of the CDS market. They illustrate how one can use a reduced form framework to identify observably distressed firms, and then demonstrate that these distressed firms have lower-thanaverage returns, even after accounting for typical factors such as volatility and size.

2.3   Economics and Finance Literature: Current Consensus

The general consensus from the literature on the relative empirical performance of “structural” and “reduced form” default probability modeling, the relative accessibility of data and modeling software all combined to lead to a rapid expansion in the credit modeling literature in the mid-2000s. Cetin, Jarrow, Protter, and Yilidrim (2004) motivate a reduced form modeling approach through the lens of incomplete information. As the analyst does not observe the market value of the assets of the firm or their

volatilities, a true implementation of Merton (1974) is impossible, and instead one would like to condition on as many observable covariates that are correlated with asset value and asset volatility as possible. Duffie, Wang, and Saita (2007) illustrate how to incorporate default risk that varies over time through a conditional term structure of default probabilities based on observable characteristics. This naturally leads to questions concerning correlation in default intensities over time. Das, Duffie, Kapadia, and Saita (2007) and Jarrow and van Deventer (2005) examine endogenous correlation in a reduced form model through dependence on common covariates. After the recession of the late 2000s, regulatory agencies have focused a great deal of energy on incorporating macroeconomic sensitivity into credit models. Reduced form models are naturally suited to this approach as well. In fact, Figlewski, Frydman, and Liang (2012) demonstrate the sensitivity of default rates to common macroeconomic variables within a given ratings grade, suggesting that ratings themselves are not well suited to this new focus.

Modern quantitative credit risk modeling in economics and finance has evolved from describing observable characteristics of defaulted firms to inferring default intensities by assuming a certain structure to the markets and to the underlying processes that govern asset values, and finally to a point where the analyst can broadly describe and accurately estimate an entire high frequency term structure of default probabilities with endogenous cross-sectional default correlations through reliance on a generalized set of observable characteristics, including macroeconomic factors. More than that, recent research trends have also highlighted potential pitfalls for the conscientious analyst when inferring credit parameters from certain market prices. Still, there is a great deal of research to be done outside of the corporate default space, where data quality and/or availability concerns slow the rate of academic research.

2.4   Industry Literature: Principal Sources

Interestingly, the applied and insurance industry research has followed a much more diverse trend. Some organizations and publications have had fairly light coverage of credit, or have only recently begun to include credit research, though this is certainly not the case across the board. Industry organizations place a great deal of emphasis on credit risk. The American Academy of Actuaries Actuarial Standards of Practice, while not recommending any particular models, require the actuary to consider the impact on cash flow associated with asset quality and the risk of asset default. The SOA exam syllabus includes knowledge of both structural and reduced form models, loss given default, correlation, and credit derivatives.




This chapter states the various methods used in research, as well as the population of the study, and sampling techniques used in determining the sample size for the research. How data was collected and analysed is also discussed in this chapter.

The main objectives of this research were achieved through quantitative methods, as inferential statistics were used to measure the level of accuracy and validate responses from the respondents in accordance to the objectives of the research.


Abuja, the capital of Nigeria was the study area for this research. It is located in the centre of Nigeria, within the Federal Capital Territory (FCT). Abuja is a planned city, and was built mainly in the 1980s. It officially became Nigeria’s capital on 12 December 1991, replacing Lagos, though the latter remains the country’s most populous city. At the 2006 census, the city of Abuja had a population of 776,298, making it one of the ten most populous cities in Nigeria. Abuja has witnessed a huge influx of people into the city; the growth has led to the emergence of satellite towns such as Karu Urban Area, Suleja, Gwagwalada, Lugbe, Kuje and smaller settlements to which the planned city is sprawling. The unofficial metropolitan area of Abuja has a population of well over three million and comprises the fourth largest urban area in Nigeria, surpassed only by Lagos, Kano and Ibadan.



This chapter is devoted to the presentation, analysis and interpretation of the data gathered in the course of this study. The data are based on the number of copies of the questionnaire completed and returned by the respondents. The data are presented in tables and the analysis is done using the Pearson correlation test.



The objectives of the study were to

  • To know the best techniques of credit risk modeling for life insurers.
  • To examine the impact of credit risks on life insurers.
  • To examine the benefits of credit to life insurer.
  • To examine the relationship between credit and performance of insurers.
  • To know if credit facilities are readily made available to insurers.

Findings from the study revealed the following

  1. Credit facilities are readily made available to insurers.
  2. There is a relationship between credit and performance of insurance companies
  3. Credit risks negatively affect insurance companies.
  4. Credit risks taken by insurance institutions are high
  5. There are models that can help reduce the risks taken by insurers.


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