![]() You are given two risky bonds with the following specifications: How can one obtain the joint migration probabilities for the relevant credits in a bank's portfolio? 2. How can one obtain the migration matrix for a credit? (c) How would you calculate the default probabilities? (b) Using the data on a corporate financial statement, answer the following questions: (a) This exercise deals with value-at-risk calculations for credit portfolios. This percentage depends on the product type, the time to maturity, the bank’s internal credit rating, and other factors. On the basis of the Basel II Accord rules, one usually derives SSRCs by taking a percentage of the market value. SSRCs include any debt or equity position that has not received a modeled-specific risk charge (i.e., regulatory VaR, SVaR, or IRC). Specific risk is due to loss from changes in the market value of a position that could result from factors other than market movements and includes event risk, default risk, and idiosyncratic risk. They also aim to recognize the impact of correlations between default and migration events among issuers. IRC models are usually designed to capture market-specific and issuer-specific concentrations, credit quality, and liquidity horizons. A constant position assumption means that a bank maintains the same set of positions throughout the 1-year horizon (regardless of the maturity date of the positions) so as to model profit and loss distributions. Liquidity horizons establish the effective holding period of the assets and are defined as the time that would be required to reduce exposure, or hedge all material risks, in a stressed market environment. The IRC is measured over a 1-year horizon at the 99.9% confidence level under the assumption of constant positions. The aim of the IRC is to cover default and credit migration risks. The regulatory SVaR is periodically calibrated by means of internal methods and policies to determine the severest stress period for a bank’s current trading book. More specifically, regulatory SVaR is based on model parameters (such as volatilities and correlations) calibrated on historical data from a continuous 12-month period reflecting significant financial stress. The main difference between VaR and SVaR is in the parameters used for their estimate. The regulatory VaR models are usually used to assess the SVaR. This is a process through which the 1-day VaR, at the 99% confidence level, is compared with the buy-and-hold daily revenue (i.e., the profit and loss impact if the portfolio is held constant at the end of the day and repriced the following day). On this subject, banks are required to perform back-testing to evaluate the effectiveness of their models. ![]() MM is a multiplier ranging between 3 and 4, based on the number of back-testing exceptions that occur in a rolling 12-month period. The other item in the max formula (i.e., 1 60 ∑ r = 1 60 V a R ( 1 − α ), t − r ⋅ M M) is the average 10-day VaR measured over the 60 days before the end of the period. (3.33) V a R r e g, t = max V a R ( 1 − α ), t, 1 60 ∑ r = 1 60 V a R ( 1 − α ), t − r ⋅ M M ,where V aR (1− α), t is the end-period 10-day VaR.
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