PRM Certification 8008 Release Date

The CDS rate is approximated by the [Loss given default x Default hazard rate]. Thus Choice 'b' is the correct answer.

Note that this is also equal to the credit spread on the reference bond over the risk free rate. Therefore credit spreads and CDS rates are generally the same. Also, 'loss given default' is nothing but (1 - Recovery rate). This can be substituted in the formula for the credit spread to get an alternative expression that directly refers to the recovery rate. Therefore all other choices are incorrect.

Bank B's exposure is measured by the price it paid for the bonds, which in this case is $7m ($10m x 70/100). Hence Choice 'c' represents the correct answer.

(Note that the question is asking for 'exposure' and not the legal claim in the event of default. The legal claim in the event of default would be the full notional of $10m. )

The initial issue price and issue size are irrelevant.

The probability of default would make the future cash flows from both the bonds identical. If p be the probability of default, the cash flows from the risky corporate bond would be

= (cash flows in the event of default x probability of default) + (cash flows without default x (1 - probability of default))

=> p*0 + (1 - p)*(1 + 8.5%) = (1 - p)*1.085.

The cash flows from the treasury bond would be 1.04. These two should be equal, ie,

1.04 = (1- p)*1.085, implying p = 4.15%.

(Note: The above is a simplification intended for the exam. In reality investors would demand a 'credit risk premium' for the corporate bond over and above the expected default loss rate. They are unlikely to be happy with just being compensated with exactly the expected default loss rate plus the risk-fre rate because the expected default loss rate itself is uncertain. They would demand some premium over and above what the default rate alone might mathematically imply above the risk free rate. In this question, this credit risk premium is ignored.)

When we do a Monte Carlo simulation, the statistic we obtain (eg, the expected price) is an estimate of the real variable. The difference between the real value (which would be what we would get if we had access to the entire population) and that estimated by the Monte Carlo simulation is measured by the 'standard error', which is the standard deviation of the difference between the 'real' value and the simulated value (ie, the 'error').

As we increase the number of draws in a Monte Carlo simulation, the closer our estimate will be to the true value of the variable we are trying to estimate. But increasing the sample size does not reduce the error in a linear way, ie doubling the sample size does not halve the error, but reduces it by the inverse of the square root of the sample size. So if we have a sample size of 1000, going up to a sample size of 100,000 will reduce the standard error by a factor of 10 (and not 100), ie, SQRT(1/100) = 1/10. In other words, standard error is proportional to 1/√N, where N is the sample size.

Therefore Choice 'c' is correct and the others are incorrect.