2LectureTSf

2LectureTSf - Term Structure Explaining TS Determinants of...

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1 Term Structure Explaining TS Determinants of Interest Rate

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2 Definition of TS Relationship between the YTM on ZCB and time to maturity Uses Pricing bond, loan, mortgage… Forecasting interest rate, inflation, exchange rates, default rate. ..
3 Plot of the TS Need ZCBs 0 1 Par B 0 r 1 ? B = Par 1+ 0 r 1 0 r 1 = (Par/B) -1 0 1 2 Par B B = Par (1+ 0 r 2 ) 2 0 r 2 = (Par/B) 1/2 -1 0 r T = (Par/B) 1/T -1 0 r 1 , 0 r 2 ,…… 0 r T YTM on ZCB ►Spot Rate 0 r 2 ?

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4 Plot the spot rates Increasing Decreasing flat humped
5 2. Explaining TS First, we need to explain the concept of forward rate Forward rate= an implicit rate for future periods 2-year ZCB 0 1 2 0 r 2 Equivalent to two 1-year ZCB 0 r 1 1 f 2 (1+ 0 r 2 ) 2 = (1+ 0 r 1 ) (1+ 1 f 2 ) 1 f 2 = (1+ 0 r 2 ) 2 (1+ 0 r 1 ) - 1 0 1 2 0 r 2

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6 Note Spot rate is a geometric mean of the forward rates (1+ 0 r 2 )2 = (1+ 0 r 1 ) (1+ 1 f 2 ) 0 r 2 = √(1+ 0 r 1 ) (1+ 1 f 2 ) - 1 0 r T = √(1+ 0 r 1 ) (1+ 1 f 2 )(1+ 2 f 3 )…(1+ T-1 f T ) - 1 T Spot rate is determined by future rates► If forward rate goes up Spot rate increases
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This note was uploaded on 02/28/2012 for the course FINE 442 taught by Professor Larbihammami during the Spring '12 term at McGill.

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2LectureTSf - Term Structure Explaining TS Determinants of...

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