In this problem all interest rates are compounded continuously, all bonds mature and pay

In this problem all interest rates are compounded
continuously, all bonds mature and pay their coupons annually on the first of
January and the date of trade is January 1st 2015 just after thr. coupon. Here
are the market prices for the bonds, assume no bid/ask spread for the purpose
of this question.
BOND DATA
maturity 1/1/16 1/1/17 1/1/18 1/1/19 1/1/20
Coupon 5.5 8.25 2 7
Price 105 114.5 98 87.5 101.5
I. Compute the discount factors implied by the market to
each maturity date.

2. Plot the term structure of interest rates implied by the
market. Comment on the 51-cape of this curve and give two explanations for why
this particular shape might happen.
3. Fit a quadratic line of best fit through the rates as a.
function of matii0t7–
(T) ao ±alT-Fa2T2 to minimize ordinary least squares on the
rates 1fri fi(Ti))2•

4. Fit another
quadratic line of best fit to the rates to minimize the absolute deviation in
bond prices implied by the curve from the true prices ENi !Pi — Here Pi is the
bond price implied by the rates curve I- (IT) and is the true market price.
Hint – you may want to tu_-e Excel solver.
5 Plot the curves found in (3) and (4) and give an
interpretation of each. Which one do you think is more appropriate for trading
and why?

6. I have a new zero-coupon
bond with maturity 1/1/2034 and I need to find a. price for its first trade.
How could you attempt to price this bond? What price does your method suggest?
What would you do in practice? Comment briefly.