Questions from Corporate Finance

Q: Verify that S(t)e−δ(T−

Verify that S(t)e−δ(T−t)N(d1) satisfies the Black-Scholes equation.

Q: Under the same assumptions as the previous problem, show that the

Under the same assumptions as the previous problem, show that the value of a claim paying
is
where σ2, δ1, and δ2 are defined as in the previous problem. In the next set of problems you will use Mo...

Q: Assume that S = $45, K = $40,

Assume that S = $45, K = $40, r = 0.05, δ = 0.02, and σ = 0.30. Using the up rebate formula (equation (23.21)), find the value of H that maximizes (H − K) × UR(S, σ, r , T , δ), for T = 1, 10, 100, 10...

Q: Using Monte Carlo, simulate the process dr = a(b

Using Monte Carlo, simulate the process dr = a(b − r)dt + σdZ, assuming that r = 6%, a = 0.2, b = 0.08, φ = 0, and σ = 0.02. Compute the prices of 1-, 2-, and 3-year zero-coupon bonds, and verify that...

Q: Consider production ratios of 2:1:1, 3:

Consider production ratios of 2:1:1, 3:2:1, and 5:3:2 for oil, gasoline, and heating oil. Assume that other costs are the same per gallon of processed oil. a. Which ratio maximizes the per-gallon prof...

Q: Replicate the GARCH(1,1) estimation in Example 24

Replicate the GARCH(1,1) estimation in Example 24.2, using daily returns from on IBM from January 1999 to December 2003. Compare your estimates with and without the four largest returns.

Q: Suppose you buy a 40–45 bull spread with 91 days

Suppose you buy a 40–45 bull spread with 91 days to expiration. If you delta-hedge this position, what investment is required? What is your overnight profit if the stock tomorrow is $39? What if the s...

Q: If XYZ does nothing to manage copper price risk, what is

If XYZ does nothing to manage copper price risk, what is its profit 1 year from now, per pound of copper? If on the other hand XYZ sells forward its expected copper production, what is its estimated p...

Q: Using the same information as the previous question, draw payoff and

Using the same information as the previous question, draw payoff and profit diagrams for a short position in the stock. Verify that profit is 0 at a price in 1 year of $55.

Q: Suppose the firm issues a single zero-coupon bond.

Suppose the firm issues a single zero-coupon bond. a. Suppose the maturity value of the bond is $80. Compute the yield and default probability for times to maturity of 1, 2, 3, 4, 5, 10, and 20 years....