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Concept
Bond option
Summary
In finance, a bond option is an option to buy or sell a bond at a certain price on or before the option expiry date. These instruments are typically traded OTC.
A European bond option is an option to buy or sell a bond at a certain date in future for a predetermined price.
An American bond option is an option to buy or sell a bond on or before a certain date in future for a predetermined price.
Generally, one buys a call option on the bond if one believes that interest rates will fall, causing an increase in bond prices. Likewise, one buys the put option if one believes that interest rates will rise. One result of trading in a bond option, is that the price of the underlying bond is "locked in" for the term of the contract, thereby reducing the credit risk associated with fluctuations in the bond price.
Bonds, the underlyers in this case, exhibit what is known as pull-to-par: as the bond reaches its maturity date, all of the prices involved with the bond become known, thereby decreasing its volatility. On the other hand, the Black–Scholes model, which assumes constant volatility, does not reflect this process, and cannot therefore be applied here; see Black–Scholes model #Valuing bond options.
Addressing this, bond options are usually valued using the Black model or with a lattice-based short-rate model such as Black-Derman-Toy, Ho-Lee or Hull–White. The latter approach is theoretically more correct, , although in practice the Black Model is more widely used for reasons of simplicity and speed. For American- and Bermudan- styled options, where exercise is permitted prior to maturity, only the lattice-based approach is applicable.
Using the Black model, the spot price in the formula is not simply the market price of the underlying bond, rather it is the forward bond price. This forward price is calculated by first subtracting the present value of the coupons between the valuation date (i.e. today) and the exercise date from today's dirty price, and then forward valuing this amount to the exercise date.
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