550_445_2010 TA 03 - 550.445 Modeling and Analysis of...

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Unformatted text preview: 550.445 Modeling and Analysis of Securities and Financial Markets II, Spring 2010 TA Section 03 Peter C.L. Lin peter.lin@jhu.edu 1 Homework Review 29.11 To calculate the convexity adjustment for the five-year rate define the price of a five year bond, as a function of its yield as G ( y ) = e- 5 y G prime ( y ) =- 5 e- 5 y G primeprime ( y ) = 25 e- 5 y . The convexity adjustment is . 5 . 08 2 . 25 2 4 = . 004 . Similarly for the two year rate the convexity adjustment is . 5 . 08 2 . 25 2 4 2 = . 0016 . We can therefore value the derivative by assuming that the five year rate is 8 . 4% and the two-year rate is 8 . 16%. The value of the derivative is . 24 e- . 08 4 = . 174 . If the payo ff occurs in five years rather than four years it is necessary to make a timing adjustment. From equation (29.4) this involves multiplying the forward rate by exp parenleftBigg- 1 . 25 . 25 . 08 4 1 1 . 08 parenrightBigg = . 98165 ....
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This note was uploaded on 03/19/2010 for the course EOE 342 taught by Professor Jooe during the Spring '10 term at Albany College of Pharmacy and Health Sciences.

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550_445_2010 TA 03 - 550.445 Modeling and Analysis of...

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