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673_08_A_primer_on_coupon_bonds

# 673_08_A_primer_on_coupon_bonds - Coupon Bonds A Primer NBA...

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1 Coupon Bonds – A Primer NBA 673 February 16, 2006

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2 Arbitraging Forwards F(0, T) = S(0)*(1 + i l *T) [i l = actual rate, F = actual price] F (0, T) = S(0)*(1 + i s *T) [i s = theoretical rate, F = theoretical price] Assume that i l < i s . What do you do? Do you buy, or do you sell forwards? Time 0 Time T [Net Cash] [Net Cash] ----------------------------------------------------------------------------------------------------- Buy forward 0 S(T) – F(0,T) Sell stock short S(0) -S(T) Lend money from selling -S(0) S(0)/B(0,T) ------------------------------------------------------------------------------------------------------ 0 S(0)/B(0,T)-F(0,T) S(0)/B(0,T)-F(0,T) = F(0,T) – F(0,T) = S(0)*(1 + i s *T) – S(0)*(1 + i l *T) = = S(0)*(i s – i l )*T > 0 [We make money!]
Coupon Bonds Coupon bond = collection of zeros. Coupon is often quoted as a percent of principal. If P=1 and coupon is 5%, then each payment is \$.05. (Note: In practice, T=6 months, and coupons are given as per year payments. A “5% coupon” implies that c = \$.05/2 = \$.025. We will always make sure to state what convention we use.) Price = c*B(0,T) + c*B(0,2T) + c*B(0,3T) + P*B(0,T) Why is it that the price of the collection equal to the sum of the components’ price? A real coupon bond will consist of several such “unit” coupon bonds. The principal of the real coupon bond is the number of units of the “unit” coupon bonds that the real bond represents (it is also the amount of money that one gets at maturity over the regular coupon payment). T

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673_08_A_primer_on_coupon_bonds - Coupon Bonds A Primer NBA...

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