1. An Inquiry into Emerging Market Combined Credit &
Political Risk Reinsurance
Athula Alwis, Simon Ying and Vladimir Kremerman
Global Credit, Surety and Political Risk Practice and Willis Analytics
Willis Re
Abstract:
Emerging market combined credit and political risk insurance covers risks associated with non-payment,
bankruptcy and credit default of obligors in emerging market countries, whether it is triggered due to either
commercial credit risk or political risk. Political risk is concerned with the risk associated with government
intervention and restriction of trade and investment into emerging markets. It may encompass long-term perils
(investment related), such as the confiscation, expropriation or nationalization of an infrastructure project in
an emerging market, or short-term perils (export trade related) such as contract frustration, embargo or
currency inconvertibility. Thus, the real risk is a combination of commercial credit risk and emerging market
political risk.
Cross border transactions to, from and between developing / emerging markets have increased exponentially
over the last ten years. Exporters and investors from the developed countries assume billions of dollars worth of
credit exposure every year.
This paper will examine emerging market combined credit and political risk from a financial modeling
perspective and propose a new methodology based on “jump diffusion” to quantify the risk reward profile. It
will recommend a stochastic modeling process to develop economic capital requirements to support this
potentially catastrophic risk.
Key Words: Correlation, Country Risk Ratings, Credit Risk, Default Rates, Emerging Markets, Export Credit,
Gaussian Copula, Jump Diffusion, Political Risk, Pure Diffusion, Recovery Rates, Merton Model, Reinsurance,
Sovereign Ceiling, Student Copula, Trade Credit
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2. Robert Merton
“At times we can lose sight of the ultimate purpose of the models when their mathematics become too
interesting. The mathematics of financial models can be applied precisely, but the models are not all precise in
their application to the complex real world. Their accuracy as a useful approximation to that world varies
significantly across time and place. The models should be applied in practice only tentatively, with careful
assessment of their limitations in each application.”
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3. Section 1: Introduction
The practitioner’s ability to reasonably quantify and manage credit risk in an analytical framework has existed
for close to 20 years. The 2001 paper by David Li is one of the most important contributions to credit analytics
since Robert Merton’s seminal work in early 1970s. Fischer Black, Myron Scholes and Robert Merton developed
and enhanced the “Black-Scholes” option pricing model based on the premise that a company’s equity investors
have a call option on the firm’s value. Vasicek-Kealhofer’s structured model in 1989, Jarrow-Turnbull’s reduced
form model in 1995 and Duffie-Singleton’s 1999 model have been major milestones in the history of credit
modeling. The advancement of powerful computers and computing techniques has tremendously helped
analysts apply mathematical concepts developed decades ago with accuracy and efficiency. David Li’s work
showing how to incorporate a Gaussian copula was an inspiration in credit modeling and paved the way for
broader and more sophisticated credit modeling techniques.
In contrast, the analysis of political risk reinsurance received very little attention until the Argentina crisis in
2001 and the subsequent exodus of capacity from the insurance and reinsurance market. In the early part of
this decade, several reinsurers began the arduous task of quantifying political risk associated with an
investment, loan or trade portfolio. Willis Analytics completed Phase I of its industry political risk study in
2006 to develop the first ever comprehensive industry analysis of default rates, recovery rates and a correlation
matrix for this class of business. Please refer to Appendix A for a definition of political risk.
Until now, there have been no research papers on how to analyze combined political risk and credit risk. At the
same time, the cross border transactions in global trade have become the fastest growing insurance sector
within both credit and political risk in the world today. In a confluence of credit modeling, political risk theory
and option pricing theory, this paper presents a realistic stochastic methodology to model combined credit and
political risk reinsurance for an emerging market portfolio.
Section 2: Combined Political and Credit Risk
Historically, the trade and commodity finance markets supported the imports and exports of emerging market
governments and state-owned entities. The privatization in emerging markets, mainly BRIC countries (Brazil,
Russia, India and China) over the last ten years, has introduced a need for additional insurance protection.
Trade and commodity finance, involving cross border transactions, now requires not only traditional credit
protection covering insolvency, credit default and non-payment, but also political risk insurance covering
contract frustration, currency inconvertibility / exchange transfer, expropriation and war / political violence.
In trade finance, practitioners use insurance to mitigate two main types of risk. The risk of insolvency and non-
payment represented by a local buyer in an import transaction can be mitigated by a local bank that will issue a
payment guarantee to the exporter to cover the imported goods or services. Then the risk of non-honoring the
guarantee by the local bank can be transferred to an insurance company through a combined political risk and
credit risk policy. A multi-national bank’s risk in a pre-export finance transaction into an emerging market
country can be mitigated through a combined political risk and credit cover issued by an insurance company.
There are trade-driven commodity finance transactions that require political and credit risk protection
provided by insurance entities. A large portfolio of these insurance transactions can be pooled together and
structured to obtain risk transfer and capital relief.
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4. Section 3: The Analytical Process
Frequency Severity Pair-wise Correlation
Combined Political Risk & Credit Model
Loss and Counts Distribution
Portfolio Analysis Reinsurance and Capital Markets
Value Based Capital Management Structured Solutions
There are three main drivers of the Combined Political Risk and Credit Model (“the model”).
1. Frequency: Probability of Default
2. Severity: Loss Given Default (1 – Recovery Rate)
3. Correlation: Contagion Risk (Propensity of defaults to group together)
The mechanics of this modeling structure are based on modern collateralized debt obligations (CDO)
technology. One key difference is that the underlying risks here are transparent, thus avoiding the concerns of
traceability evident in the CDO market.
Rating agencies have historically developed credit default rates that have been predictive for the most part.
Several insurers, reinsurers and intermediaries have attempted to develop political risk default rates based on
historical data. However, default rates combining both political risk and credit risk have not yet been
developed. The main technical goal of this paper is to present two methodologies to produce a framework for
combining individual default rates for credit risk and political risk into a joint default rate.
Severity distributions and correlation assumptions for pure credit risk have been analyzed and published by
numerous practitioners and academics over the last decade. For political risk, Willis Analytics conducted an
industry study based on 40 years of data to develop reasonable default rates, loss given default (severity)
indications and a correlation matrix based on regional contagion.
The remainder of the paper will focus on two approaches for developing a joint credit / political risk default rate
based on these separate default parameters.
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5. Section 4: Diffusion Process – A Conservative Approach
The simplest method to represent combined credit and political risk frequency is to sum the default rates and
adjust for double counting by subtracting the probability of both events occurring at the same time.
Pr (A U B) = Pr (A) + Pr (B) – Pr (A ∩ B),
where Pr (A) is the default rate for credit risk excluding political risk, while Pr (B) is the default rate for political
risk. The part that represents the intersection (i.e., both events occurring at the same time: Pr (A ∩ B)) can be
calculated using the two separate default rates and a copula function that describes their dependency. Please
refer to Appendix B for a technical explanation of how to combine these default rates using a Normal copula.
This is a technically sound starting point to model a structure. However, this model does not accurately reflect
the coverage offered under emerging market combined credit and political risk insurance. While any non-
political related credit default (A) is a covered loss, not every political risk event (B) leads to a covered loss. For
example, nationalization of foreign oil companies in an emerging market country may not affect the default
probabilities for companies in other sectors. If the portfolio under analysis has exposure only in sectors and
industries unaffected by the political risk event, then the probability of a default triggered by the political risk
event would be extremely low. Hence, the methodology shown above is clearly conservative.
While this diffusion methodology is simple and practical, its conservatism implies that the calculated mean loss
and other risk parameters, including tail risks, are likely to be overstated. Hence capital allocation based on
Value at Risk (VAR), Tail Value at Risk (TVAR) or similar parameters derived from the diffusion model would
produce overstated capital requirements.
Section 5: Jump Diffusion – A Realistic Approach
In emerging markets, political risk events are more likely to suddenly and markedly increase the likelihood of
credit events, rather than directly causing credit events. Therefore, the financial modeling should reflect credit
defaults due to financial and economic reasons that are represented by traditional credit default rates as well as
the stressed environment during and after a political risk event that could lead to sudden correlated credit
defaults. In other words, the model must be able to represent both traditional credit defaults and the impact of
“jumps” in default scenarios due to political risk events. However, every political risk event does not necessarily
lead to a corresponding credit event (as is the case in the conservative approach of Section 4).
Robert Merton’s 1976 paper “Option Pricing – When Underlying Stock Returns Are Discontinuous” was the
first known application of a jump diffusion model. Robert Merton adjusted the Black-Scholes option pricing
formula to reflect “spikes” in stock prices due to sudden additional information.
Consider stock prices S and the geometric Brownian motion
dS = µSdt + σSdw where µ (drift term) and σ (volatility) are functions of S and t
Then, the jump diffusion model can be shown as
dS = µSdt + σSdw + J΄SdN, where J΄= J -1
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6. and the jump size J (an impulse factor representing the effect precipitated by the arrival of new information in
the stock market) is an independent identically distributed random variable and N is the Poisson process, while
w represents a standard Wiener process.
Through this adjustment, Merton was able to address the issue of option pricing even when the stock price
dynamics cannot be represented by a continuous sample path.
In this application, the size of the political risk jumps would be derived from historical political risk data that
shows the percentage of limits that are in default within a sovereign nation due to a specific political risk event.
The size of the jump would vary by size of the country and region.
The graph in Exhibit 1 presents the change in combined default rate based on the size of the jump (i.e., effect of
the political risk event). At the beginning, when the size of the jump is zero, there is no effect from the political
risk event; thus, the credit default rate is the combined default rate. For example, political violence in one
remote rural corner of an emerging market country may not affect transactions located in other, more urban
areas of the same country. On the right hand side of the curve, when the effect of the jump is 100%, this
framework results in the conservative approach shown in Section 4.
Exhibit 1
0.16
0.14
Probability of credit and
political risk event
0.12
0.1
0.08
0.06
0.04
0 0.2 0.4 0.6 0.8 1
Size of jump (%)
Political Risk default rate = 10.0%
Credit Risk default rate = 5.0%
Section 6: Output: Economic Capital
The immediate output of the model is a correlated multi-variate distribution of losses and counts that reflect
the effects of both credit and political risk exposures in emerging market countries. The distribution can be
summarized to generate benchmarks such as mean, median and standard deviation. But more importantly, it
will present the entire spectrum of the loss distribution including the tail. Exhibit 2 contains an output derived
from a sample distribution.
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7. Exhibit 2
Loss and Counts Distribution
Expected 1,825,527 0.61
Standard Deviation 5,682,749 1.33
CoV 311% 220%
Median – –
Minimum – –
Maximum 54,813,902 18
Return Period Percentile Losses Counts
1 in 2 50.0% – 1
1 in 4 75.0% 379,476 1
1 in 10 90.0% 2,667,853 2
1 in 20 95.0% 11,144,518 3
1 in 50 98.0% 18,632,452 5
1 in 100 99.0% 30,006,859 6
1 in 200 99.5% 38,756,339 11
The standard reinsurance underwriting measures used in decision making can be easily derived from the loss
distribution. Exhibit 3 shows a calculation of “upside” and “downside” risk calibrated by the traditional
reinsurance carriers to reflect the potential risk involved in a reinsurance portfolio. The “upside” represents the
possibility of making an underwriting profit after paying claims and expenses related to the business.
Exhibit 3
Gross Premium 11,250,000
Commission + Expense 20.0%
Gross Capital 29,756,339
Probability of Gross UW Upside 93.7%
Average Gross UW Upside 8,785,246
Probability of Gross UW Downside 6.3%
Average Gross UW Downside (8,147,273)
Average Gross UW Profit / (Loss) 7,174,473
Capital Charge @ 0 % –
Gross Profit Net of Capital Charge 7,174,473
Gross Profit Margin Net of Capital Charge 63.8%
Gross Combined Ratio 36.2%
The reinsurance practitioners use various barriers to determine the risk inherent in an insurance portfolio. The
chance that the probability of downside risk being greater than a pre determined barrier is artificially high
when the conservative approach described in section 4 is applied to a combined credit and political risk
portfolio, perhaps, influencing the risk manager to reject a profitable transaction.
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8. Exhibit 4 contains another view of the loss and counts distribution that is ready to be structured and layered for
risk transfer solutions.
Exhibit 4
Gross Loss Summary
Expected Values in Year of Analysis
Expected Premium 11,250,000
Expected Expenses 2,250,000
Simulation Calculation Summary
Annual Annual # of Size of
Loss Underwriting
Total Large Large Large
Ratio Result
Losses Losses Losses Losses
mean 16.23% 7,174,473 1,825,527 1,825,527 0.6058 3,013,415
st dev 50.51% 5,682,749 5,682,749 5,682,749 1.3329 5,063,648
cov* 3.1129% 0.7921 3.1129 3.1129 2.2002 1.6804
0.1%ile 487.23% (45,813,902) 0 0 0 3,640
0.4%ile 372.37% (32,891,624) 0 0 0 7,878
0.5%ile 344.50% (29,756,339) 0 0 0 9,231
1%ile 266.73% (21,006,859) 0 0 0 13,064
5%ile 99.06% (2,144,518) 0 0 0 42,738
25%ile 3.37% 8,620,524 0 0 0 416,773
50%ile 0.00% 9,000,000 0 0 0 1,253,358
75%ile 0.00% 9,000,000 369,476 369,476 1 3,402,075
95%ile 0.00% 9,000,000 11,144,518 11,144,518 3 11,429,821
99%ile 0.00% 9,000,000 30,006,859 30,006,859 6 26,322,196
99.5%ile 0.00% 9,000,000 38,756,339 38,756,339 8 33,282,391
99.6%ile 0.00% 9,000,000 41,891,624 41,891,624 9 35,683,494
99.9%ile 0.00% 9,000,000 54,813,902 54,813,902 11 47,322,750
Exhibit 4 provides valuable insights to a risk manager to make a decision on various risk transfer mechanisms
such as quota share (QS), excess of loss (XOL), aggregate stop loss or any other combination to get the
appropriate protection for a portfolio of risks. If a valid correlation matrix is used in the analysis, the 99th
percentile (1 in 100 year loss) is a reasonable indicator of capital need on a stand alone basis.
Exhibit 5 on the next page presents various risk transfer options considered for a combined credit and political
risk portfolio by comparing the entire range of the loss distribution.
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9. Exhibit 5
This exhibit was produced by proprietary modeling software, Willis iFM
Exhibit 6 focuses on the amount of capital relief achieved through various risk transfer options. In addition, it
allows the practitioner to estimate the return on capital for the entire gross portfolio and the portfolio net of
reinsurance transactions (i.e., risk transfer mechanisms).
Exhibit 6
Impact on Profitability – Return on Capital
Expected Profit and Loss Account
20% QS 60% QS Pure XL Pure XL
Gross
and XL and XL 21xs4 22.5xl2.5
Gross Premium 11,250,000 11,250,000 11,250,000 11,250,000 11,250,000
Reinsurance Premium 0 4,671,884 7,567,151 2,686,614 3,282,145
Net Premium 11,250,000 6,578,116 3,682,849 8,563,386 7,967,855
Net Retained Loss 1,825,527 802,914 545,675 1,130,014 895,965
Expenses 2,250,000 2,250,000 2,250,000 2,250,000 2,250,000
Ceding Commission 0 562,500 1,687,500 0 0
Profit Commission 0 33,249 99,746 0 0
Underwriting Result (A) 7,174,473 4,120,951 2,674,419 5,183,372 4,821,890
Capital at Risk
Value at Risk (1 in 200 years) 29,756,339 10,902,817 6,896,050 14,988,637 12,660,635
Cost of Capital (B) 4,761,014 1,744,451 1,103,368 2,398,182 2,025,702
Economic Result (A-B) 2,413,459 2,376,500 1,571,051 2,785,190 2,796,188
Economic Return on Capital 24.111% 37.797% 38.782% 34.582% 38.086%
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10. Section 7: Conclusion
It is the authors’ belief that the approach based on “jump diffusion” is a more realistic methodology to model
combined political and credit risk. The goal of the authors is to begin a dialogue on how best to analyze the risk
reward profile of a combined credit and political risk portfolio generated from emerging markets. Cross border
transactions involving both trade and commodity finance will continue to grow as the emerging markets march
towards economic prosperity. In that regard, this paper is a small step in the right direction to provide a
mathematical framework for understanding this important risk.
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11. Appendix A
Definition of Political Risk
Political Risk can be defined as the company’s exposure to the risk of a political event that would diminish the
value of an investment or a loan. The major political risk covers (classes) are:
1. Currency Inconvertibility (CI) and Exchange Transfer (FX)
2. Confiscation, Expropriation and Nationalization (CEN)
3. Political Violence (PV) or War (including revolution, insurrection, politically motivated civil strife,
terrorism)
4. Breach of Contract, Contract Frustration (CF), Contract Repudiation (CR)
5. Wrongful Calling of Guarantee (WCG)
1. Currency Inconvertibility (CI) and Exchange Transfer (FX):
Inability of an investor / lender to convert profits, investment returns and debt service from local
currency to hard currency ($ € £)
Inability of an investor / lender to transfer hard currency out of the country of risk
2. Confiscation, Expropriation and Nationalization (CEN):
Loss of funds or assets due to confiscation, expropriation or nationalization by the host government of
the country of risk
Any unlawful action by the host government depriving the investor of fundamental rights in a project
(creeping expropriation)
3. Political Violence (PV) or War (including revolution, insurrection, politically motivated civil
strife, terrorism)
Loss of funds or assets due to political violence or war
4. Breach of Contract, Contract Frustration (CF), Contract Repudiation (CR)
Loss of funds or assets due to arbitrary non-honoring of a contract by a foreign government (or a semi-
government entity) or breach of contract by a private business entity due to an arbitrary act of a foreign
government
Loss of funds due to non-payment of a loan or guarantee
5. Wrongful Calling of Guarantee (WCG)
Loss of funds or assets due to the host government arbitrarily calling its bonds or a business entity
being forced to call guarantees due to political events (the bonds are generally backed by irrevocable
letters of credit which are callable on demand)
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12. Appendix B – Pure Diffusion
The basis of this approach in the context of quot;pure diffusionquot; for political (P) and credit (C) risks is presented
below. The coupled stochastic differential equations are as follows:
dC = C ( μ dt + σ dW (t )),
c cc
dP = P( μ dt + σ dW (t )).
p p p
The notation is based on the literature from geometric Brownian motion. The correlation expression for
Brownian motion is given by the standard expression,
Cov(Wc (t ),W p (t )) = ρ t.
As a result, the probability of a combined credit and political risk event, taking place when either C or P is below
its corresponding barrier at time t, equals
u = u c + u p − u c, p
The probability of credit and political risk events happening at the same time (at time t) is given by the
following equation,
u c , p = Φ 2 (Φ −1 (u P ), Φ −1 (u C ), ρ ).
Φ2
Here is a normal copula. The probability of a political event equals
ln(K p (t) / P(0)) − (μ p −σ p / 2)t
2
uP = Φ( ),
σp t
K p (t ) is a barrier value for political risk at time t. The probability for a credit event has a similar expression.
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13. Acknowledgements
The authors would like to express their sincere appreciation to Julian Edwards, Steve Capon, Meirion Board,
Esin Celasun, Peter Sprent and Ewa Rose of Ace Global Markets, London for their support, insights and
assistance for this project.
Christophe Meurier, Marina Cottaris and Florence De Rivaz of BNP Paribas deserve sincere appreciation from
the authors for providing valuable insights at the testing stage of the project.
In addition, our colleagues Mark Jenkins, James Cattanach, Andrew Pace, Rick Bowering, Brigitte Jaeger,
Stefania Ilina, Andy Law, Catherine Prevost and Hilary Price deserve sincere appreciation for their
encouragement and support.
The authors are grateful for the time and efforts of Maria Morrill, Harjeet Dhillon, Alice Underwood, Yves
Provencher, Ian Cook, and Rowan Douglas of Willis Analytics in reviewing various drafts of this paper and
providing valuable feedback.
Finally, we want to express our appreciation for the commitment to this project and to long term research and
development demonstrated by Peter Hearn, CEO, Willis Re; James Vickers, Chairman, Willis Re International;
Jason Howard, CEO, Willis Re International and other members of the Willis Re executive team.
The ideas and opinions presented in this paper belong to the authors, as are the errors that have not been
corrected by the time this paper was released for publication.
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14. Bibliography
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– A Capital Market Approach, Forum, International Congress of Actuaries (ICA)
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Forum, Casualty Actuarial Society
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Securities and Graduate School of Business Fordham University
6. Das, S., Freed L., Geng, G., Kapadia, N., (2005): Correlated Default Risk, Santa Clara Univ.
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Tax, Jumps, Liquidity, and Market Factors”, eScholarship Repository, University of California
8. Dhrymes, P. J., (1986): Handbook of Econometrics, Volume III, Elsevier Science Publishers BV
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10. Duffie, D. and Kenneth, J.S. (2003). Credit Risk: Pricing, Measurement, and Management, chapter 3,
Princeton University Press
11. Glasserman, P. (2003): Tail Approximations for Portfolio Credit Risk, Columbia Business School
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15. Glossary
Copula – A function that joins univariate distribution functions to form multivariate distribution functions. A
copula of a multivariate distribution can be thought of as the instrument that describes the dependence
structure.
Credit Risk – The risk due to uncertainty in a counterparty's (also called an obligor or credit's) ability to meet
its obligations. Because there are many types of counterparties, from individuals to sovereign governments, and
many different types of obligations, from auto loans to derivatives transactions, credit risk takes many forms.
Credit Spread – For a bond, this equals the difference between yield on a risky bond and yield on a default-
free government bond with a similar maturity.
Recovery Rate – In the event of a default, the recovery rate is the fraction of the exposure that may be
recovered through bankruptcy proceedings or some other form of settlement.
Biographies of Authors
Athula Alwis is Senior Vice President, Global Credit, Surety and Political Risk Practice at Willis Re Inc. in New
York City, New York. Athula provides capital and risk management services to Willis Re clients worldwide for
credit, D&O, political risk, surety and other financial products lines of business. He is the global coordinator for
credit, surety and political risk practice at Willis Re Inc. Athula has a BS (First Class Honors) in Mathematics
from University of Colombo, Sri Lanka and a MS in Mathematics from Syracuse University, New York. He is an
Associate of the Casualty Actuarial Society (CAS) and a member of the American Academy of Actuaries (AAA).
Athula is a member of the CAS Regional Committees for both Asia and Europe, and is a frequent presenter at
industry conferences. Athula co-authored actuarial papers titled “Credit & Surety Pricing and the Effects of
Financial Market Convergence” in 2002, “D&O Reinsurance Pricing – A Financial Market Approach” in 2005
and “Political Risk Reinsurance – A Capital Market Approach” in 2006.
Vladimir Kremerman is Assistant Vice President, Analytical Services at Willis Re Inc. in New York City, New
York. He is responsible for property / casualty and specialty lines reinsurance analysis. Vladimir has a Ph.D. in
Physics from Vilnius State University. He worked as a physicist at Semiconductor Physics Institute of
Lithuanian Academy of Sciences and at the Center for Ultrafast Photonics in City University, New York. He
authored / coauthored numerous papers on statistical mechanics and actuarial papers on Directors and Officers
Reinsurance Pricing and Political Risk Reinsurance Pricing.
Simon Ying is an actuarial analyst working from the Willis Re New York office. His responsibilities include
reinsurance pricing analyses and research and development projects for the global credit, surety and political
risk practice. He joined Willis Re in July 2007 as an actuarial analyst. Simon is a graduate of the NYU Stern
School of Business in New York City with a major in actuarial science and a minor in philosophy, and is
currently pursuing a fellowship designation in the Casualty Actuarial Society (CAS).
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