17. (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 +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/d1|a=o, the Sks can be found recursively by an equation of the form Sk-1 =-akPk+bkSk, while the Pks are found by the running method. Find ak and bk. 17. (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 +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/d1|a=o, the Sks can be found recursively by an equation of the form Sk-1 =-akPk+bkSk, while the Pks are found by the running method. Find ak and bk