Hi, Am I correct in saying that in this 2020 CM2 September exam Q4, essentially the bank has purchased a bond and will receive a payment at maturity, conditioned on weather the person remains solvent? Essentially this is the two-state risk model from chapter 19 of the notes: value of loan at time @ time 0 = e^-r(T-t)*(Expected value of bond at maturity) What I'm struggling with is interpreting the 10% expected return set by the bank (allowing for default) as the risk-free rate of interest, as this is used to discount back the future expected values in all parts of the question? Could this please be explained? Thanks, Darragh
Hi Yes in part (ii) the bank only receives payment if the person remains solvent for whole three years. The formula you've quoted is fine, but remember that the expectation must be calculated using the risk-neutral probabilities, which is then discounted at the risk-free rate. In the question the probability is given as the real-world probability (ie the bank's estimate), and so the real-world expected return is used for the discounting. Hope that helps.
ok thanks for that great. And for part (iii) the formula value of loan at time @ time 0 = e^-r(T-t)*(Expected value of bond at maturity) can be used again we just bear in mind that total expected future value of the bond now is composed of the future expected values of the car for years 1,2&3 if person is insolvent, as well as the future expected value of loan if person remains solvent? And we must just be careful when discounting the future expected values of the cars that we we discount at appropriate years? THanks
Hi Steve, Sorry to dig up an old post. I attempted (iii) of this equation and this was the formula that I came up with: 10000(1.10)^3 = 8000(1 + rate)*0.05 + 6000(1 + rate)^2*0.95*0.05 + 4000(1 + rate)^3 * 0.95^2(0.05) + 10,000(1 + rate)^3*0.95^3 Can't understand why they use the 10% for discounting the car value after defaulting? Thanks, Aaron
I see what you mean. Your formula is close, but it doesn't allow for the fact that the 10% might not be earned for the full three years. Default in the first year means that the bank should only expect to earn one year's rate. That's why the solution discounts each of the RHS terms for different lengths of time.
