This article introduces Bond Options, and provides pricing spreadsheets which use the the Black (1976) and Schaefer & Schwartz (1987) models.
A European bond option gives the holder the right (but not the obligation) to trade a bond at a predetermined date at a predetermined price (the strike price). The bond option is in-the-money if the trade is profitable. If not, the holder does not have to trade the bond and only loses the initial premium.
American options can be exercised at or before expiry. This greater flexibility means that American bond options are more expensive than their European counterparts.
A callable bond allows the bond issuer to buy back the bonds before maturity. The purchaser essentially buys an interest-bearing bond and sells a European option to the issuer. If interest rates fall, the issuer has the privilege of exercising the option. The issuer then refinances and reissues the bonds at a lower interest rates.
A puttable bond consists of an interest-bearing bond and an associated put option. Puttable bonds allows the holder to force the issuer to buy the bond back. These are often exercised if interest rates rises; the holder forces the issuer to repurchase the bonds, and then buys a bond with a higher coupon.
Bond Option Pricing in Excel
The Schaefer & Schwartz (1987) method uses a one-factor duration model to generate bond volatilities. It assumes that a longer bond results in greater price volatility.
The Black (1976) model is commonly employed to price European short-term bond options. Because of the assumptions used to derive the model, the option duration should be less than 20% of the time to maturity of the bond itself.
The pricing equations used in the spreadsheets were taken from “The Complete Guide to Option Pricing” by Espen Haug.