# 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 risk-neutral probabilities of ups and downs are all 1/2.

1. What is the price now of a discount bond with face of \$100 maturing one year from now?
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2. What is the price now of a discount bond with face of \$100 maturing two years from now?
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3. What is the price today of a two-year collar with a cap price of 5% and a floor price of 3%? The underlying notional is \$1,000.
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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 risk-neutral probabilities of ups and downs are 1/2.

1. What is the price now of a discount bond with face of \$100 maturing one year from now?
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2. What is the price now of a discount bond with face of \$100 maturing two years from now?
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3. 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%).
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