Questions from Corporate Finance

Q: Verify that ASaeγt satisfies the Black-Scholes PDE for

Verify that ASaeγt satisfies the Black-Scholes PDE for

Q: Verify that you earn the same profit and payoff by (a

Verify that you earn the same profit and payoff by (a) shorting the S&R index for $1000 and (b) selling a 1050-strike S&R call, buying a 1050-strike put, and borrowing $1029.41.

Q: Use a change of numeraire and measure to verify that the value

Use a change of numeraire and measure to verify that the value of a claim paying K if ST

Q: A barrier COD option is like a COD except that payment for

A barrier COD option is like a COD except that payment for the option occurs whenever a barrier is struck. Price a barrier COD put for the same values as in the previous problem, with a barrier of $95...

Q: Compute daily volatilities for 1991 through 2004 for IBM, Xerox,

Compute daily volatilities for 1991 through 2004 for IBM, Xerox, and the S&P 500 index. Annualize by multiplying by √252. How do your answers compare to those in Problem 24.1? Answer Problem 24.1 Her...

Q: Suppose that S1 and S2 follow geometric Brownian motion and pay continuous

Suppose that S1 and S2 follow geometric Brownian motion and pay continuous proportional dividends at the rates δ1 and δ2. Use the martingale argument to show that the value of a claim paying S1(T ) if...

Q: a. What is the 2-year forward price for a

a. What is the 2-year forward price for a 1-year bond? b. What is the price of a call option that expires in 2 years, giving you the right to pay $0.90 to buy a bond expiring in 1 year? c. What is the...

Q: Suppose you short the S&R index for $1000 and

Suppose you short the S&R index for $1000 and buy a 1050-strike call. Construct payoff and profit diagrams for this position. Verify that you obtain the same payoff and profit diagram by borrowing $10...

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

Suppose the firm issues a single zero-coupon bond with maturity value $100. a. Compute the yield, probability of default, and expected loss given default for times to maturity of 1, 2, 3, 4, 5, 10, an...

Q: Repeat the previous problem, but set φ = 0.05

Repeat the previous problem, but set φ = 0.05. Be sure that you simulate the risk neutral process, obtained by including the risk premium in the interest rate process. Repeat the previous problem Usi...