The principle underlying the contingent claims approach to measuring credit risk equates the cost of eliminating credit risk for a firm to be equal to:
Under the contingent claims approach, a firm will default on its debt when the value of its assets fall to less than the face value of the debt. Debt holders can protect themselves against such an event by buying a put on the assets of the firm, where the strike price is equal to the value of the debt. In other words, Risky Debt + Put on the firm's assets = Risk free debt. This is because if the value of the assets is greater than the value of the debt, they will be paid in full. If the value of the assets is lower than the value of the debt, they will exercise the put and be paid in full.
Therefore the value of the put on the firm's assets with a strike equal to the value of the debt represents the cost of eliminating credit risk. Choice 'b' is the correct answer.
Note that it is improbable that a put on the firm's assets is available in real life to debt holders. However, the same effect can be synthetically achieved by using the shares of the firm as a proxy for its assets, and shorting an appropriate number of shares. Such a synthetic put will require frequent readjustments.
Which of the following is not a limitation of the univariate Gaussian model to capture the codependence structure between risk factros used for VaR calculations?
In the univariate Gaussian model, each risk factor is modeled separately independent of the others, and the dependence between the risk factors is captured by the covariance matrix (or its equivalent combination of the correlation matrix and the variance matrix). Risk factors could include interest rates of different tenors, different equity market levels etc.
While this is a simple enough model, it has a number of limitations.
First, it fails to fit to the empirical distributions of risk factors, notably their fat tails and skewness. Second, a single covariance matrix is insufficient to describe the fine codependence structure among risk factors as non-linear dependencies or tail correlations are not captured. Third, determining the covariance matrix becomes an extremely difficult task as the number of risk factors increases. The number of covariances increases by the square of the number of variables.
But an inability to capture linear relationships between the factors is not one of the limitations of the univariate Gaussian approach - in fact it is able to do that quite nicely with covariances.
A way to address these limitations is to consider joint distributions of the risk factors that capture the dynamic relationships between the risk factors, and that correlation is not a static number across an entire range of outcomes, but the risk factors can behave differently with each other at different intersection points.
When fitting a distribution in excess of a threshold as part of the body-tail distribution method described by the equation below, how is the parameter 'p' calculated.
Here, F(x) is the severity distribution. F(Tail) and F(Body) are the parametric distributions selected for the tail and the body, and T is the threshold in excess of which the tail is considered to begin.
p = k/N. If there are N observations of which K are upto T, then p = k/N allows us to have a continuous unbroken curve which gets increasingly weighted towards the distribution selected for the tail as we move towards the 'right', ie the higher values of losses.
The other choices are incorrect and mostly nonsensical.
Under the CreditPortfolio View approach to credit risk modeling, which of the following best describes the conditional transition matrix:
Under the CreditPortfolio View approach, the credit rating transition matrix is adjusted for the state of the economy in a way as to increase the probability of defaults when the economy is not doing well, and vice versa. Therefore Choice 'a' is the correct answer. The other choices represent nonsensical options.
Which of the following distributions is generally not used for frequency modeling for operational risk
Frequency modeling is performed using discrete distributions that have a positive integer as a resultant - this allows for the number of events per period of time to be modeled. Of the distributions listed above, Poisson, negative binomial and binomial can be used for modeling frequency distributions. The Poisson and negative binomial distributions are encountered the most in practice.
The gamma distribution is a continuous distribution and cannot be used for frequency modeling.
