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##### In this problem, all interest rates are compounded continuously,

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solution

**Question**

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 the coupon. Here are the market prices for the bonds, assume no bid/ask spread for the purpose of this question.;BOND DATA;Maturity | Coupon | Price;1/1/16 | 5.5 | 105;1/1/17 | 8.25 | 114.5;1/1/18 | 2 | 98;1/1/19 | 3.5 | 87.5;1/1/20 | 7 | 101.5;1. 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 shape of this curve and give two explanations for why this particular shape might happen.;3. Fit a quadratic line of best through the rates as a function of maturity;r(T) = a0 + a1*T + a2*(T^2);to minimize ordinary least squares on the rates: (See attached for formula);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 (see attachment) Here Pi is the bond price implied by the rates curve r(t) and Pi is the true market price. Hint - you may want to use excel solver.;5. Plot 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.;Attachment Preview;Finance.pdf;Additional Requirements;Level of Detail: Show all work;Other Requirements: If you can do some (but not all) parts, I am willing to adjust the price.

Paper#21582 | Written in 18-Jul-2015

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