An embedded option is a component of a
financial bond or other security, which 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; common types of bonds with embedded options include
callable bond,
puttable bond,
convertible bond,
extendible bond Extendible bond (or extendable 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 ...
,
exchangeable bond, and capped
floating rate note. A bond may have several options embedded if they are not
mutually exclusive.
Securities
A security is a tradable financial asset. The term commonly refers to any form of financial instrument, but its legal definition varies by jurisdiction. In some countries and languages people commonly use the term "security" to refer to any fo ...
other than bonds that may have embedded options include senior equity,
convertible
A convertible or cabriolet () is a passenger car that can be driven with or without a roof in place. The methods of retracting and storing the roof vary among eras and manufacturers.
A convertible car's design allows an open-air driving ex ...
preferred stock
Preferred stock (also called preferred shares, preference shares, or simply preferreds) is a component of share capital that may have any combination of features not possessed by common stock, including properties of both an equity and a debt ins ...
and
exchangeable preferred stock. See
Convertible security.
The
valuation of these securities couples
bond- or
equity-valuation, as appropriate, with
option pricing. For bonds here, there are two main approaches, as follows.
''Pricing Interest Rate-dependent Financial Claims with Option Features''
Ch11 in: Richard Rendleman (2002). Applied Derivatives: Options, Futures, and Swaps (1st ed.). Wiley-Blackwell. . (Other securities with embedded derivatives are priced similarly.) Once the price has been calculated, the various yields can then be calculated for the security.
# Depending on the type of option, the option price
In finance, a price (premium) is paid or received for purchasing or selling options. This article discusses the calculation of this premium in general. For further detail, see: for discussion of the mathematics; Financial engineering for the impl ...
, as calculated using the Black–Scholes ( or other) model, 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.
# A bespoke "tree
In botany, a tree is a perennial plant with an elongated stem, or trunk, usually supporting branches and leaves. In some usages, the definition of a tree may be narrower, including only woody plants with secondary growth, plants that are ...
" (usually a lattice-based short-rate model) 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.
Calculating rate-sensitivities on these instruments is complicated: the embedded features make measures such as duration and convexity (and DV01
In finance, the duration of a financial asset that consists of fixed cash flows, such as a bond, is the weighted average of the times until those fixed cash flows are received.
When the price of an asset is considered as a function of yield, ...
) less meaningful; and analysts instead use effective duration and effective convexity.
References
Fixed income analysis
Commercial bonds
Bond valuation
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