1A. The Black-Scholes-Merton model for European puts, obtained by applying put-call parity to the Black-Scholes-Merton model for European calls, is customarily expressed by which of the following:

a. P=Xe^-rcTN(-d₂)-S₀N(-d₁) b. P=X(1+r)^-TN(-d₂)-S₀N(-d₁) c. P=X(1+r)^-TN(-d₁)-S₀N(-d₂)

d. P=Xe^-rcTN(-d₁)-S₀N(-d₂) e. none of the above

1B. Find the upcoming net payment in a plain vanilla interest rate swap in which the fixed party pays 10 percent and the floating rate for the upcoming payment is 9.5 percent. The notional amount is $20 million and payments are based on the assumption of 180 days in the payment period and 360 days in a year.

a. fixed payer pays $1,950,000 b. fixed payer pays $950.000 c. floating payer pays $1 million d. floating payer pays $50,000 e. fixed payer pays $50,000

1C. If the stock price is 44, the exercise price is 40, the put price is 1.54, and the Black-Scholes-Merton price using 0.28 as the volatility is 1.11, the implied volatility will be

a. higher than 0.28 b. lower than 0.28 c. 0.28 d. lower than the risk-free rate

e. none of the above

1D. Consider a binomial world in which the current stock price of 80 can either go up by 10 percent or down by 8 percent. The risk-free rate is 4 percent. Assume a one-period world. The call has an exercise price of 80.

What would be the calls price if the stock goes up?

a. 3.60 b. 8.00 c. 5.71 d. 4.39 e. none of the above