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All interest rates are annual interest rates with semi-annual compounding. All coupon rates are annual rates paid semi-annually. All bonds have a $100 face value
Assume that forward rates for the next year are given by r(0.5)=6% and r(1)=7% and consider an 8% coupon bond maturing 1 year from now.
a) Find the bond price. Keep at least 6 decimal digits while doing calculations and reporting the answer.
b) Assume at t=0.5 the half-year spot rate will be exactly 7%. Find the price of the bond at t=0.5.
c) Assume at t=0.5 the half-year spot rate can be either 5% or 9% with equal probabilities. Find the expected price of the bond at t=0.5.
d) Assume at t=0.5 the half-year spot rate can be either (7-x)% or (7+x)% with equal probabilities, where 0<x<7. Write the expected price of the bond P(x) at t=0.5 as a function of x. Using Excel, draw the expected bond price P(x) for 0<x<7. Make sure to use the appropriate scale so that the shape of the expected bond price function is clearly visible.
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