sl_1_spotyieldcurve - The zero coupon yield curve Ajay Shah...

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The zero coupon yield curve Ajay Shah http://www.mayin.org/˜ajayshah The zero coupon yield curve – p. 1/45
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Product definitions The zero coupon yield curve – p. 2/45
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Coupon versus zero-coupon bonds In the olden days, bonds came with attached “coupons”. You had to cut off the coupon and mail it in, to get interest. A bond that had no coupons, but only paid back Rs.100 at expiration, was a “zero coupon bond”. The zero coupon yield curve – p. 3/45
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Cashflows A hypothetical two-year 12% coupon bond, and a hypothetical two-year zero coupon bond: t 0.500 1.000 1.500 2.000 Coupon bond: 6 6 6 106 Zero coupon bond: 100 We use the notation ( c 1 , t 1 ) , ( c 2 , t 2 ) , . . . , ( c N , t N ) to denote a bond with N cashflows. The zero coupon yield curve – p. 4/45
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Strips You buy this coupon bond: t 0.500 1.000 1.500 2.000 Coupon bond: 6 6 6 106 You issue four zero-coupon bonds out of the four cashflows. Legal engineering so that your bankruptcy doesn’t affect the buyers of your zero coupon bonds. A way of allowing RBI to continue to issue coupon bonds, but trading can then be done in zero coupon bonds. The zero coupon yield curve – p. 5/45
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Key intuition A coupon bond is a portfolio of zero coupon bonds. The zero coupon yield curve – p. 6/45
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Elementary compound interest The zero coupon yield curve – p. 7/45
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Compound interest PV = C (1 + r ) T r is a feature of the economy. The zero coupon yield curve – p. 8/45
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Continuous compounding In continuous time, it works out that: PV = e - rT C Very convenient, for things like: Z 0 e - rt c ( t ) dt Note : if s = log(1 + r ) then e s = (1 + r ) . The zero coupon yield curve – p. 9/45
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A simple world - one r , one formula Suppose there are cashflows ( c 1 , t 1 ) , . . . , ( c N , t N ) . The economy tells us r , and then: PV = N X i =1 c i (1 + r ) t i The zero coupon yield curve – p. 10/45
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The yield curve The zero coupon yield curve – p. 11/45
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Unfortunately, We have an entire yield curve , with different r for different t . We can’t discount all future cashflows at the same rate. PV = C (1 + z ( T )) T The economy tells us all interest rates, i.e. the function z ( T ) . The zero coupon yield curve – p. 12/45
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Example – 2 August 2001 0 2 4 6 8 10 12 0 2 4 6 8 10 12 14 16 Interest rate (percent) Time (years) The zero coupon yield curve – p. 13/45
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Pricing a set of cashflows If there are cashflows ( c 1 , t 1 ) , . . . , ( c N , t N ) , the economy tells us z ( t ) , and then: PV = N X i =1 c i (1 + z ( t i )) t i The zero coupon yield curve – p. 14/45
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“The yield curve” “Spot yield curve” “Zero coupon yield curve” “Zero curve” are all the same. The zero coupon yield curve – p. 15/45
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This note was uploaded on 11/20/2009 for the course MBA financial taught by Professor Ibraheem during the Spring '09 term at Dubai Aerospace Enterprise University.

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sl_1_spotyieldcurve - The zero coupon yield curve Ajay Shah...

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