1. A security sells for $40. A 3-month call with a strike of $42 has a premium of $2.49. The risk-free rate is 3 percent. What is the value of the put according to put-call parity?
2. Which of the following statements regarding the Black-Scholes-Merton option-pricing model is TRUE?
A.As the number of periods in the binomial options-pricing model is increased toward infinity, it converges to the Black-Scholes-Merton option-pricing model.
B.The Black-Scholes-Merton option-pricing model is the discrete time equivalent of the binomial option-pricing model.
C.The Black-Scholes-Merton model is superior to the binomial option-pricing model in its ability to price options on assets with periodic cash flows.
D.As the periods in the binomial option-pricing model are lengthened, it converges to the Black-Scholes-Merton option-pricing model.
3. If we use four of the inputs into the Black-Scholes-Merton option-pricing model and solve for the asset price volatility that will make the model price equal to the
market price of the option, we have found the:
4. A stock that is currently trading at $50 and can either move to $55 or $45 over the next 6-month period. The continuously compounded risk-free rate is 2.25 percent.
What is the risk-neutral probability of an up movement?
5. Given the following ratings transition matrix, calculate the two-period cumulative probability of default for a B credit.
1. Correct answer:B
p = c + X – S = 2.49 + 42 e –0.03 × 0.25 – 40 = $4.18
2. Correct answer: A
As the option period is divided into more/shorter periods in the binomial option-pricing model, we approach the limiting case of continuous time and the binomial model results converge to those of the continuous-time Black-Scholes-Merton option pricing model.
3. Correct answer:A
The question describes the process for finding the expected volatility implied by the market price of the option.
4. Correct answer:C:
The risk-neutral probability, p, can be calculated as . In this case, r = 0.0225, u = 1.1, d = 0.9, which makes p equal to [e[0.0225*(6/12)] - 0.9] / [1.1 - 0.9] = .5566
5. Correct answer: d
Scenario one: B can go into default the first year, with probability of 0.02.
Scenario two: B could go to A then D, with probability of 0.03 × 0.00 = 0.
Scenario three: B could go to B then D, with probability of 0.90 × 0.02 = 0.018. Scenario four: B could go to C then D, with probability of 0.05 × 0.14 = 0.007. The total is 0.045.