5_immunization

5_immunization - ISyE 6673 Financial Optimization Models...

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Unformatted text preview: ISyE 6673 Financial Optimization Models Shabbir Ahmed E-mail: sahmed@isye.gatech.edu Homepage: www.isye.gatech.edu/~sahmed Topic: Immunization Interest rate terminology Spot rate : s t is the (annual) interest rate on money held from time 0 until time t , i.e., 1 dollar held for t years grows to (1 + s t ) t dollars. Discount rate : d t = 1 /s t . Forward rate : Interest rate for money to be borrowed between two dates in the future but under terms agreed upon today. Given years i and j (with i < j ) and spot rates s i and s j , the forward rate f ij satisfies (1 + s j ) j = (1 + s i ) i (1 + f ij ) j- i , hence f ij = h (1 + s j ) j (1 + s i ) i i 1 / ( j- 1)- 1 . Short rate : forward rate spanning a single period, i.e, r t = f t,t +1 . Note that (1 + s t ) t = (1 + r )(1 + r 1 ) .. (1 + t t- 1 ) . 1 Review: The Dedication Model Data: P i ,C it , and T i , are price, cashflows, and maturity of bond i ; and r ,r 1 ,. .. ,r T- 1 are the short-rates from the term structure...
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5_immunization - ISyE 6673 Financial Optimization Models...

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