An Embedded option is a component of a financial bond

Bond (finance)

In finance, a bond is a debt security, in which the authorized issuer owes the holders a debt and, depending on the terms of the bond, is obliged to pay interest to use and/or to repay the principal at a later date, termed maturity...

 or other security, and usually provides the bondholder or the issuer the right to take some action against the other party. There are several types of options that can be embedded into a bond. Some common types of bonds with embedded options include callable bond

Callable bond

A callable bond is a type of bond that allows the issuer of the bond to retain the privilege of redeeming the bond at some point before the bond reaches the date of maturity. In other words, on the call date, the issuer has the right, but not the obligation, to buy back the bonds from the bond...

, puttable bond

Puttable bond

Puttable bond is a bond with an embedded put option. The holder of the puttable bond has the right, but not the obligation, to demand early repayment of the principal...

, convertible bond

Convertible bond

In finance, a convertible note is a type of bond that the holder can convert into shares of common stock in the issuing company or cash of equal value, at an agreed-upon price. It is a hybrid security with debt- and equity-like features...

, extendible bond

Extendible bond

Extendible bond is a complex bond with the embedded option for a holder to extend its maturity date by a number of years. Such a bond may be considered as a portfolio of a straight, shorter-term bond and a call option to buy a longer-term bond. This relatively rare type of bond works to the...

, and exchangeable bond

Exchangeable bond

Exchangeable bond is a type of hybrid security consisting of a straight bond and an embedded option to exchange the bond for the stock of a company other than the issuer at some future date and under prescribed conditions. An exchangeable bond is different from a convertible bond...

. A bond may have several options embedded if they are not mutually exclusive

Mutually exclusive

In layman's terms, two events are mutually exclusive if they cannot occur at the same time. An example is tossing a coin once, which can result in either heads or tails, but not both....

.

Securities

Security (finance)

A security is generally a fungible, negotiable financial instrument representing financial value. Securities are broadly categorized into:* debt securities ,* equity securities, e.g., common stocks; and,...

 other than bonds that may have embedded options include senior equity, convertible preferred stock

Preferred stock

Preferred stock, also called preferred shares, preference shares, or simply preferreds, is a special equity security that has properties of both an equity and a debt instrument and is generally considered a hybrid instrument...

 and exchangeable preferred stock. See Convertible security

Convertible security

A convertible security is a security that can be converted into another security. Most convertible securities are bonds or preferred stocks that pay regular quarterly interest and can be converted into shares of common stock if the stock price appreciates to a predetermined...

.

The valuation

Valuation (finance)

In finance, valuation is the process of estimating what something is worth. Items that are usually valued are a financial asset or liability. Valuations can be done on assets or on liabilities...

 of these securities combines Bond-

Bond valuation

Bond valuation is the determination of the fair price of a bond. As with any security or capital investment, the theoretical fair value of a bond is the present value of the stream of cash flows it is expected to generate. Hence, the value of a bond is obtained by discounting the bond's expected...

 or Equity-valuation, as appropriate, with option pricing. For bonds here, there are two main approaches: (1) Depending on the type of option, the option price, as calculated using Black Scholes, is either added to or subtracted from the price of the "straight" bond (i.e. as if it had no optionality) and this total is then the value of the bond. (2) A bespoke "tree" (usually a lattice based

Lattice model (finance)

In finance, a lattice model can be used to find the fair value of a stock option; variants also exist for interest rate derivatives.The model divides time between now and the option's expiration into N discrete periods...

 short rate model

Short rate model

In the context of interest rate derivatives, a short-rate model is a mathematical model that describes the future evolution of interest rates by describing the future evolution of the short rate, usually written r_t \,.-The short rate:...

) may be constructed where the option's effect is incorporated at each node in the tree, impacting either the bond price or the option price as specified; see further under Bond option

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. These instruments are typically traded OTC....

. Once the price has been calculated, the various yields can then be calculated for the security. Other securities with embedded derivatives are priced similarly.