(Short rate sensitivity) Gavin Jones sometimes has flashes of brilliance. He asked his instructor if duration would measure the sensitivity of price to a parallel shift in the short rate curve. (That is, rk → rk+1.) His instructor smiled and told him to work it out. He was unsuccessful at first because his formulas became very complicated. Finally he discovered a simple solution based on the running present value method. Specifically, letting Pk be the present value as seen at time k and Sk =dPk/d2]1=0, the Sk's can be found recursively by an equation of the form Sk–1 =-a«Pk+bkSk, while the Pr’s are found by the running method. Find ak and bk.
(Short rate sensitivity) Gavin Jones sometimes has flashes of brilliance. He asked his instructor if duration would measure the sensitivity of price to a parallel shift in the short rate curve. (That is, rk → rk+1.) His instructor smiled and told him to work it out. He was unsuccessful at first because his formulas became very complicated. Finally he discovered a simple solution based on the running present value method. Specifically, letting Pk be the present value as seen at time k and Sk =dPk/d2]1=0, the Sk's can be found recursively by an equation of the form Sk–1 =-a«Pk+bkSk, while the Pr’s are found by the running method. Find ak and bk.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:(Short rate sensitivity)
instructor if duration would measure the sensitivity of price to a parallel shift in the short
rate curve. (That is, r → ri +2.) His instructor smiled and told him to work it out. He was
unsuccessful at first because his formulas became very complicated. Finally he discovered
a simple solution based on the running present value method. Specifically, letting Pk be
the present value as seen at time k and Sk =dPk/d\x=0, the Sk's can be found recursively
by an equation of the form Sk-1=-a¢Pk+b¢Sk, while the P's are found by the running
method. Find ak and bg.
Gavin Jones sometimes has flashes of brilliance. He asked his
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