15. (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, +) 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 P, be the present value as seen at time k and S = dP/dx=o, the S's can be found recursively by an equation of the form S-1 = -a P + b S. while the P's are found by the running method Find a and by