Example
  • Trade Date: 1 March 2003
  • Maturity Date: 6 March 2006
  • Option Buyer: Bank A
  • Underlying asset: FNMA Bond
  • Spot Price: $101
  • Strike Price: $102
  • On the Trade Date, Bank A enters into an option with Bank B to buy certain FNMA Bonds from Bank B for the Strike Price mentioned. Bank A pays a premium to Bank B which is the premium percentage multiplied by the face value of the bonds.
  • At the maturity of the option, Bank A either exercises the option and buys the bonds from Bank B at the predetermined strike price, or chooses not to exercise the option. In either case, Bank A has lost the premium to Bank B.

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.[1] These instruments are typically traded OTC.

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.[1] 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.

Valuation

Compare: Swaption § Valuation

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; [1] 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. [2] The latter approach is theoretically more correct, [3], 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.

Embedded options

The term "bond option" is also used for option-like features of some bonds ("embedded options"). These are an inherent part of the bond, rather than a separately traded product. These options are not mutually exclusive, so a bond may have several options embedded. [8] Bonds of this type include:

Callable and putable bonds can be valued using the lattice-based approach, as above, but additionally allowing that the effect of the embedded option is incorporated at each node in the tree, impacting the bond price and / or the option price as specified. [9] These bonds are also sometimes valued using Black–Scholes. Here, the bond is priced as a "straight bond" (i.e. as if it had no embedded features) and the option is valued using the Black Scholes formula. The option value is then added to the straight bond price if the optionality rests with the buyer of the bond; it is subtracted if the seller of the bond (i.e. the issuer) may choose to exercise. [10] [11] [12][permanent dead link] For convertible and exchangeable bonds, a more sophisticated approach is to model the instrument as a "coupled system" comprising an equity component and a debt component, each with different default risks; see Lattice model (finance)#Hybrid securities.

Relationship with caps and floors

European Put options on zero coupon bonds can be seen to be equivalent to suitable caplets, i.e. interest rate cap components, whereas call options can be seen to be equivalent to suitable floorlets, i.e. components of interest rate floors. See for example Brigo and Mercurio (2001), who also discuss bond options valuation with different models.

References

  1. ^ a b "Bond option".
Discussion

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