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# P2.T7.519. Basel II credit risk parameters and Solvency II (Hull)

#### Nicole Seaman

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Learning outcomes: Define in the context of Basel II and calculate where appropriate: Probability of default (PD), Loss given default (LGD), Exposure at default (EAD), Worst-case probability of default. Differentiate between solvency capital requirements (SCR) and minimum capital requirements (MCR) in the Solvency II framework, and describe the repercussions to an insurance company for breaching the SCR and MCR. Compare the standardized approach and the internal models approach for calculating the SCR in Solvency II.

Questions:
(Source: John Hull, Risk Management and Financial Institutions, 5th Edition (New York: John Wiley & Sons, 2018))

519.1. Under the Basel II internal ratings-based (IRB) approach, the capital required is the excess of the 99.9% worst-case loss over the expected loss. The key parameters in the formula are: the probability that the counterparty will default within one year (PD), the exposure at default (EAD), the loss given default or the proportion of the exposure that is lost if there is a default (LGD), and the “worst-case probability of default” defined so that the bank is 99.9% certain it will not be exceeded next year for the counterparty (WCDR). Consider the following three specific applications:

I. For Corporate, Sovereign, and Bank Exposures under the Foundation IRB approach, banks supply PD while LGD, EAD, and maturity (M) are supervisory values set by the Basel Committee. PD is subject to a floor of 0.03% for bank and corporate exposures. LGD is set at 45% for senior claims and 75% for subordinated claims. M is set at 2.5 in most circumstances.

II. For Corporate, Sovereign and Bank Exposures under the Advanced IRB approach, banks supply their own estimates of the PD, LGD, EAD, and maturity (M) for corporate, sovereign, and bank exposures. The PD can be reduced by credit mitigants such as credit triggers. The two main factors influencing the LGD are the seniority of the debt and the collateral. In calculating EAD, banks can with regulatory approval use their own estimates of credit conversion factors.

III. For Retail Exposures, the model underlying the calculation of capital for retail exposures is similar to that underlying the calculation of corporate, sovereign, and banking exposures. However, the Foundation IRB and Advanced IRB approaches are merged and all banks using the IRB approach provide their own estimates of PD, EAD, and LGD. There is no maturity adjustment, MA.

Which of the above is (are) essentially true statements?

a. None are true
b. Only I. is true
c. Only II. is true
d. All are true

519.2. Solvency II has three pillars which are analogous to Basel II's three pillars. Pillar 1 (in Solvency II) is concerned with the calculation of capital requirements and the types of capital that are eligible. Pillar 2 is concerned with the supervisory review process. Pillar 3 is concerned with the disclosure of risk management information to the market. Pillar 1 specifies both a minimum capital requirement (MCR) and a solvency capital requirement (SCR). Each of the following is true about the SCR or MCR EXCEPTwhich is false?

a. If capital drops below the solvency capital requirements (SCR) level, the supervisor might require the insurance company to take particular measures to correct the situation
b. If capital drops below the solvency capital requirements (SCR) level, an insurance company should, at minimum, deliver to the supervisor a plan to restore capital to above the SCR level
c. If capital drops below the minimum capital requirement (MCR) level, supervisors is likely to insist that the insurance company add new businesses and underwriting additional policies in order to increase earned premiums
d. If capital drops below the minimum capital requirement (MCR) level, supervisors might force the insurance company into liquidation, transferring its policies to another company

519.3. Pillar 1 of Solvency II specifies both a minimum capital requirement (MCR) and a solvency capital requirement (SCR). The SCR involves a capital charge for investment risk, underwriting risk, and operational risk. Investment risk is subdivided into market risk and credit risk. Underwriting risk is subdivided into risk arising from life insurance, non-life insurance (i.e., property and casualty), and health insurance. There are two ways to calculate the SCR: the standardized approach and the internal models approach. In regard to the capital and the internal models approach, each of the following is true EXCEPT which is false?

a. The internal models approach involves a VaR calculation with a one-year time horizon and a 99.5% confidence limit. The confidence level is, therefore, less than the 99.9% confidence level used for credit and operational risk in Pillar 1 of Basel II. Longer time horizons with lower confidence levels are also allowed when the protection provided is considered equivalent
b. The internal models are required to satisfy three tests. The first is a statistical quality test. This is a test of the soundness of the data and methodology used in calculating VaR. The second is a calibration test. This is a test of whether risks have been assessed in accordance with a common SCR target criterion. The third is a use test. This is a test of whether the model is genuinely relevant to and used by risk managers
c. All qualifying capital must be "Tier 1" which can only consist of liabilities that are subordinated to policyholders and satisfy certain criteria concerning their availability in wind-down scenarios
d. Capital should be adequate to deal with large adverse events. Examples of the events considered in quantitative impact studies include: a 32% decrease in global stock markets; a 20% decrease in real estate prices; a 20% change in foreign exchange rates; specified catastrophic risk scenarios affecting property and casualty payouts; health care costs increasing by a factor times the historical standard deviation of costs; a 10% increase in mortality rates; a 25% decrease in mortality rates; a 10% increase in expenses.