Final Exam Practice: fixed income
A. Binomial Option Pricing 30 points
Assume that the interest rate starts at 4% and in each period
and either increases by 2% or decreases by 2% (from 4% up to 6% or
down to 2% would be the first move). The riskneutral probabilities
of ups and downs are all 1/2.

What is the price now of a discount bond with face of $100
maturing one year from now?

What is the price now of a discount bond with face of $100
maturing two years from now?

What is the price today of a twoyear collar with a cap
price of 5% and a floor price of 3%? The underlying
notional is $1,000.
B. Binomial Option Pricing 30 points
Assume that the interest rate starts at 6% and in each period
and either increases by 2% or decreases by 2% (from 6% up to 8% or
down to 4%). The riskneutral probabilities of ups and downs are
1/2.

What is the price now of a discount bond with face of $100
maturing one year from now?

What is the price now of a discount bond with face of $100
maturing two years from now?

What is the price today of an interest rate floor with a
strike of 7% and two periods to maturity? The underlying
notional is $100 (so the cash flow is 2 if the rate is 5%).