Bond option

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.

• 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.^[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

• Using the Black model, the
  Girsanov's theorem. The volatility used, is typically "read-off" an Implied volatility surface
  .

• The lattice-based model entails a tree of short rates – a zeroeth step – consistent with today's
  Trinomial: the logic is as described, although there are then three nodes in question at each point.) See Lattice model (finance) § Interest rate derivatives
  .

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 bond: allows the issuer to buy back the bond at a predetermined price at a certain time in future. The holder of such a bond has, in effect, sold a call option to the issuer. Callable bonds cannot be called for the first few years of their life. This period is known as the lock out period.
• Puttable bond: allows the holder to demand early redemption at a predetermined price at a certain time in future. The holder of such a bond has, in effect, purchased a put option on the bond.
• Convertible bond: allows the holder to demand conversion of bonds into the stock of the issuer at a predetermined price at a certain time period in future.
• Extendible bond: allows the holder to extend the bond maturity date by a number of years.
• Exchangeable bond: allows the holder to demand conversion of bonds into the stock of a different company, usually a public subsidiary of the issuer, at a predetermined price at certain time period in future.

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

• Toy, W. (January–February 1990). "A One-Factor Model of Interest Rates and Its Application to Treasury Bond Options" (PDF). Financial Analysts Journal: 24–32. Archived from the original
  (PDF) on 2008-09-10.
• ISBN 978-3-540-22149-4
  .
• ISBN 0-471-41488-3., Chapter 33: Valuing Fixed Income Securities
• ISBN 978-1-883249-25-0
  .
• R. Stafford Johnson (2010). Bond Evaluation, Selection, and Management (2nd ed.).
  ISBN 978-0470478356
  .
• David F. Babbel (1996). Valuation of Interest-Sensitive Financial Instruments: SOA Monograph M-FI96-1 (1st ed.). John Wiley & Sons.
  ISBN 978-1883249151
  .

• Bond Options, Caps and the Black Model, Milica Cudina, University of Texas at Austin
• Valuing Bonds with Embedded Options^{[permanent dead link]}, Frank J. Fabozzi
• Valuing Convertible Bonds as Derivatives, Goldman Sachs (authors include Emanuel Derman and Piotr Karasinski)
• The Valuation and Calibration of Convertible Bonds, Sanveer Hariparsad, University of Pretoria
• Martingales and Measures: Black's Model, Jacqueline Henn-Overbeck, University of Basel
• Binomial Interest Rate Trees and the Valuation of Bonds with Embedded Options, Stafford Johnson, Xavier University
• The Problem with Black, Scholes et al., Andrew Kalotay
• Methods of Pricing Convertible Bonds, Ariel Zadikov, University of Cape Town

Online tools

• Black Bond Option Model, Dr.
  Thomas Ho
  , thomasho.com
• Bond Option Pricing using the Black Model Dr. Shing Hing Man, Thomson-Reuters' Risk Management
• Pricing A Bond Using the BDT Model Dr. Shing Hing Man, Thomson-Reuters' Risk Management
• 'Greeks' Calculator using the Black model, Dr. Razvan Pascalau,
  SUNY Plattsburgh
• Pricing Bond Option using G2++ model, pricing-option.com