22.11 Yield vols vs price vols The change in forward bond price is related to the change in forward bond yield by δB SB ≈-DδyOr B B where D is the(modified)duration of the forward bond at option maturity Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull
Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 22.11 Yield Vols vs Price Vols The change in forward bond price is related to the change in forward bond yield by where D is the (modified) duration of the forward bond at option maturity y y Dy B B D y B B − − or
22.12 Yield vols vs price vols continued This relationship implies the following approximation o=DOo where o, is the yield volatility and o is the price volatility, yo is todays forward yield Often o, is quoted with the understanding that this relationship will be used to calculate Options, Futures, and other Derivatives, 5th edition 2002 by John C. Hull
Options, Futures, and Other Derivatives, 5th edition © 2002 by John C. Hull 22.12 Yield Vols vs Price Vols continued • This relationship implies the following approximation where sy is the yield volatility and s is the price volatility, y0 is today’s forward yield • Often sy is quoted with the understanding that this relationship will be used to calculate s s = Dy0 sy