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# 7 creditmetrics it is based on an analysis of credit

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7. CreditMetrics. It is based on an analysis of credit migration. This is the probability of a firm moving from one rating category to another during a certain period of time. Calculating a one-year VaR for the portfolio using CreditMetrics involves carrying out Monte Carlo simulation of ratings transitions for bonds in the portfolio over a one-year period. On each simulation trial the final credit rating of all bonds is calculated and the bonds are revalued to determine total credit losses for the year. The 99% worst result is the one-year 99% VaR for the portfolio. - The credit rating changes for different counterparties should not be assumed to be independent. Æ use Gaussian copula model Æ The copula correlation between the - 21 -

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Study Notes: Risk Management and Financial Institutions By Zhipeng Yan rating transitions for two companies is typically set equal to the correlation between their equity returns using a factor model. Chapter 13 Credit Derivatives 1. Credit derivatives are contracts where the payoff depends on the creditworthiness of one or more companies or countries. Banks have been the largest buyers of CDS credit protection and insurance companies have been the largest sellers. - The n-year CDS spread should be approximately equal to the excess of the par yield on an n-year corporate bond over the par yield on an n-year risk-free bond . If it is markedly less than this, an investor can earn more than the risk-free rate by buying the corporate bond and buying protection. If it is markedly great than this, an investor can borrow at less than the risk-free rate by shorting the corporate bond and selling CDS protection. - The payoff from a CDS in a credit event is notional principal*(1-recovery rate). Usually a CDS specifies that a number of different bonds can be delivered in the credit event. This gives the holder of CDS a cheapest-to-deliver bond option . Therefore, recovery rate should be the lowest recovery rate applicable to a deliverable bond. 2. Valuation of credit default swaps - CDS can be analyzed by calculating the present value of the expected payments (including accrued interests) and the present value of the expected payoff . - The default probabilities used to value a CDS should be risk-neutral default probabilities, which can be estimated from bond prices or asset swaps. An alternative is to imply them from CDS quotes. - Binary CDS: it is similar to a regular CDS except that the payoff is a fixed dollar amount. - Is the recovery rate important? – whether we use CDS spreads or bond prices to estimate default probabilities, we need an estimate of the recovery rate. However, provided that we use the same recovery rate for (a) estimating risk-neutral default probabilities and (b) valuing a CDS, the value of the CDS is not very sensitive to the recovery rate. This is because the implied probabilities of default are approximately proportional to 1/(1-R) and the payoffs from a CDS are proportional to 1-R.
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• Spring '10
• NanLi
• Normal Distribution, ........., Risk Management and Financial Institutions, Zhipeng Yan

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