This section provides sample simulations illustrating the generation of value distributions using the option framework of default. The simulations require three steps: summarizing the general framework, defining our set of simplifying assumptions and providing sample simulations.
A summarized description of a simplified econometric structure serves to define the simulation framework. After making explicit the set of simplifying assumptions, we present simulations for a two-segment portfolio.
The transition matrices of rating agency data are unconditional on the state of the economy and reflect historical data. They provide the probabilities that an obligor in risk class k moves to risk class l during a certain period. Joint transition matrices provide the probability that a pair of obligors moves from one pair of […]
The example is a portfolio of two obligors X and Y, with a small number of credit states to make the calculations tractable. Using the joint migration matrix above, we have a probability for each cell, and all sum to 1. Mapping credit spreads with ratings serves to value exposures.
In order to get a value distribution for the portfolio, using the joint migration probability matrix, we consider all combinations of risk classes of X and Y, including default. When a facility defaults, its value drops to zero. When it migrates to the risk class 1 or 2, its value discounts the final 100 flow […]
Portfolio models generate a loss distribution at a future horizon selected by the end-user. This horizon applies to all facilities regardless of their maturity. Maturities of facilities serve to assign default probabilities as a function of time and to date the exposures.
The loss distribution results from the portfolio value distribution. The loss distribution is the mirror image of the portfolio value distribution. From the loss distribution, all loss statistics, including credit risk VaR and economic capital, derive. However, there are several alternative options for calculating them.
The RaRoC ratio depends on consistent definitions of the numerator and the denominator. If the revenues are net of expected loss, the capital should also be, otherwise the expected loss would count twice. If the revenues are the contractual revenues, not netting the expected loss, capital should include both expected and unexpected losses.
Capital allocation aims at allocating both credit and market risk to the business units and the transactions that originate them. They provide the top-down and bottom-up links between the post-diversification risk of the bank and individual transactions. The relationship is far from obvious because the risks do not add up arithmetically, so that the total […]
DEFINITIONS AND NOTATION In this section, we define the standalone risk of a facility, the risk contribution of an existing facility i within a portfolio P, orRCp, also named Absolute Risk Contributions (ARC), and the marginal risk contribution of the facility f added to a portfolio P ,or MRCp+f.
