# Embedded option

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{{Short description|Contract feature giving the holder option-like rights within a host financial instrument}}
{{more citations needed|date=January 2021}}
An '''embedded option''' 
<ref>Adam Hayes (2021). [https://www.investopedia.com/terms/e/embeddedoption.asp "Embedded Options: Definition and Use Cases"], [Investopedia](/source/Investopedia)</ref>
is a component of a [financial bond](/source/bond_(finance)) 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](/source/callable_bond), [puttable bond](/source/puttable_bond), [convertible bond](/source/convertible_bond), [extendible bond](/source/extendible_bond), [exchangeable bond](/source/exchangeable_bond), and capped [floating rate note](/source/floating_rate_note). A bond may have several options embedded if they are not [mutually exclusive](/source/mutually_exclusive).

[Securities](/source/Security_(finance)) other than bonds that may have embedded options include senior equity, [convertible](/source/Preferred_stock) [preferred stock](/source/preferred_stock) and [exchangeable preferred stock](/source/Preferred_stock). See [Convertible security](/source/Convertible_security).{{Citation needed|date=January 2023}}

The [valuation](/source/valuation_(finance)) of these securities couples [bond-](/source/bond_valuation) or [equity-valuation](/source/equity_valuation), as appropriate, with [option pricing](/source/option_pricing). For bonds here, there are two main approaches, as follows.<ref>[https://web.archive.org/web/20160304073048/http://rendleman.com/ARNAVSHETH/CHAP11.pdf "Pricing Interest Rate-dependent Financial Claims with Option Features"], Ch11 in:  Richard Rendleman (2002). ''Applied Derivatives: Options, Futures, and Swaps'' (1st ed.). Wiley-Blackwell. {{ISBN|978-0-631-21590-5}}.</ref> Other securities with embedded derivatives are priced similarly.   
# Depending on the type of option, the [option price](/source/option_premium), as calculated using the [Black–Scholes](/source/Black%E2%80%93Scholes_model) ([or other](/source/Valuation_of_options)) model, is either added to or subtracted from the [price of the "straight" bond](/source/bond_valuation) (i.e. as if it had no optionality) and this total is then the value of the bond. 
# A bespoke "[tree](/source/BOPM)" (usually a [lattice-based](/source/Lattice_model_(finance)) [short-rate model](/source/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](/source/Bond_option) under [bond option](/source/bond_option).

Once the price has been calculated, [the various yields](/source/Bond_valuation) can then be calculated for the security.
Calculating [rate-sensitivities](/source/Bond_duration) on these instruments is complicated: the embedded features make measures such as [duration](/source/Bond_duration) and [convexity](/source/Bond_convexity) (and [DV01](/source/DV01)) less meaningful; and analysts instead use [effective duration](/source/effective_duration) and  [effective convexity](/source/effective_convexity).

==References==
{{reflist}}

{{Bond market}}

Category:Embedded options
Category:Fixed income analysis
Category:Commercial bonds
Category:Bond valuation

{{investment-stub}}

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Adapted from the Wikipedia article [Embedded option](https://en.wikipedia.org/wiki/Embedded_option) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Embedded_option?action=history)). Available under [Creative Commons Attribution-ShareAlike 4.0 International](https://creativecommons.org/licenses/by-sa/4.0/). Changes may have been made.