Bond Options

Abstract

Abstract This article describes various types of options on bonds and presents the main approaches used for their modeling and valuation. We start with a brief description of bond option contracts and the closely related options on bond futures as well as options embedded in the bond contract itself. We then present some standard approaches for valuation restricting ourselves to options on default‐free bonds with a focus on European bond options. We start by describing the original approaches based on the Black–Scholes–Merton model where the quantity that is directly modeled is the bond's price or yield and discuss some of the inconsistencies related to this approach. This is followed by a presentation of the Black 1976 model. We also establish a relationship between the valuation of bond options and its relation to the standard valuation approach for vanilla interest rate derivatives such as caps, floors, and swaptions. We then turn to the valuation of bond options based on a full‐term structure model focusing on the special case of short term models. We present the Jamishidian decomposition, which allows for an explicit determination of the exercise boundary for European options on coupon bonds for a class of one‐factor short‐rate models satisfying a monotonicity condition. We conclude with a brief description of the approaches used for the pricing of Bermudan and American bond options.