320-ps8 - FM320 Quantitative Finance The London School of...

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FM320 Quantitative Finance St´ ephane Guibaud The London School of Economics 2009/2010 Problem Set # 8 1. The price of a 1-year zero-coupon with final payoff $100 is $95 . 24. A 2-year bond with face value $100, annual coupon rate 8% and annual coupon payment has yield-to-maturity y = 6 . 92% (expressed as an annual rate with annual compounding). a) Find y 1 and y 2 the zero-rates at respective maturity 1 year and 2 year (express those rates as annual rates with annual compounding). b) A 2-year bond with face value $100, annual coupon rate 6 . 93% and annual coupon payment is just being introduced. At what price should this bond trade? c) Compute the 1-year forward rate in one year (expressed as an annual rate with annual compounding). d) Suppose the one-year zero rate prevailing after one year is 9 . 04%. What return would you have realized by investing in a 2-year zero coupon bond over one year? What return would you have realized over 2 years by saving at the one-year rate and rolling over? (express
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