Question $3$

Consider a corporate bond rated $"A",$ with $7$ years to maturity, face value $$1,000,$ annual coupon

rate of $5\mathrm{.}5\%,$ and semi$-$annual coupon payments. The default probability is constant over the bond's

life, and equal to $0\mathrm{.}166\%$ per semester. When the corporation defaults, bondholders receive $$400$ at

the time of default. The fair interest rate to discount the bond's cash flows is $3\%$ per semester.

a$)$ What is the fair price of the corporate bond?

b$)$ What is the fair yield$-$to$-$maturity of the corporate bond?

c$)$ What is the expected fair price one semester in the future? And what is the expected coupon

payment one semester in the future?

d$)$ What is the expected holding period for buying the bond for its fair price today and selling it

for its expected fair price one semester ahead?