# Contingent claim

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{{Short description|Derivative whose payoff depends on an underlying asset or uncertain future event}}
In [finance](/source/finance), a '''contingent claim''' is a [derivative](/source/derivative_(finance)) whose future payoff depends on the value of another “[underlying](/source/underlying)” asset,<ref name="gray">Dale F. Gray, [Robert C. Merton](/source/Robert_C._Merton) and [Zvi Bodie](/source/Zvi_Bodie). (2007).  Contingent Claims Approach to Measuring and Managing Sovereign Credit Risk.  ''Journal of Investment Management'', Vol. 5, No. 4, (2007), pp. 5–28</ref><ref name= "Brennan">[M. J. Brennan](/source/Michael_Brennan_(finance)) (1979). The Pricing of Contingent Claims in Discrete Time Models. ''The Journal of Finance''.  Vol. 34, No. 1 (Mar., 1979), pp. 53-68</ref> or more generally, that is dependent on the realization of some uncertain future event.<ref name ="Ross">Sean Ross. [https://www.investopedia.com/ask/answers/052715/what-kinds-derivatives-are-types-contingent-claims.asp#ixzz58ZjispbB  What kinds of derivatives are types of contingent claims?]. [Investopedia](/source/Investopedia)</ref> 
These are so named, since there is only a payoff under certain contingencies.<ref name="Damodaran">"Approaches to valuation", Ch2.  in [Aswath Damodaran](/source/Aswath_Damodaran) (2012). ''Investment Valuation: Tools and Techniques for Determining the Value of any Asset''. John Wiley & Sons. {{ISBN|9781118206591}}</ref> 
Any derivative instrument that is not a contingent claim is called a '''forward commitment'''.<ref name="Ross"/>  

The prototypical contingent claim is an [option](/source/option_(finance)),<ref name="gray"/> the right to buy or sell the underlying asset at a specified exercise price by a certain expiration date;  whereas ([vanilla](/source/vanilla_option)) [swaps](/source/swap_(finance)), [forwards](/source/forward_(finance)), and [futures](/source/future_(finance)) are forward commitments, since these grant no such optionality.<ref name="Ross"/> 

Contingent claims are applied under [financial economics](/source/financial_economics) in developing models and theory, and in [corporate finance](/source/corporate_finance) as a [valuation framework](/source/Valuation_(finance)).
This approach originates with [Robert C. Merton](/source/Robert_C._Merton),
<ref>Zvi Bodie (2020). [https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3314385 Robert C. Merton and the Science of Finance]. ''Annual Review of Financial Economics'', Vol. 12, pp. 19-38, 2020</ref>  
decomposing the value of a corporate into a set of options in his "[Merton model](/source/Merton_model)" of credit risk.

==Financial economics==
{{see|Financial economics #State prices}}
{{also|Arrow-Debreu security|Risk-neutral measure}}
In [financial economics](/source/financial_economics), '''contingent claim analysis''' is widely used  as a framework both for developing pricing models, and for extending the theory.<ref name="Neave_Fabozzi"/> Thus, from its origins in option pricing and the valuation of corporate liabilities,<ref>Black, Fischer; Myron Scholes (1973). "The Pricing of Options and Corporate Liabilities". Journal of Political Economy. 81 (3): 637–654. doi:10.1086/260062.</ref> it has become a major approach to [intertemporal equilibrium under uncertainty](/source/Intertemporal_equilibrium).<Ref Name="Babbs_Selby"> Simon Babbs and Michael Selby (1992). [https://warwick.ac.uk/fac/soc/wbs/subjects/finance/research/wpaperseries/1993/93-38.pdf  Contingent Claims Analysis], in The New Paigrave Dictionary of Money and Finance, eds J Eatwell, M Milgate and P Newman, Macmillan (1992), pp 437-440</ref>

The general approach here is to define risky outcomes relative to [states of the world](/source/state_price), and to then use claims to represent and value state outcomes:
:<math display=inline>Price =\sum_{s}(q_{s}X_{s})/r</math>
::where <math>s</math> are the states, <math>X</math> are the claims (or cashflows), <math>q</math> are the [risk neutral probabilities](/source/Risk-neutral_measure), <math>r</math> is the "[risk-free rate](/source/risk-free_rate)".
Thus given a definition of risky states, all financial instruments and arrangements can be represented as combinations of contingent claims on those states.<ref name="Neave_Fabozzi"> Edwin H. Neave and  [Frank J. Fabozzi](/source/Frank_Fabozzi) (2012).  Introduction to Contingent Claims Analysis, in Encyclopedia of Financial Models, Frank  Fabozzi ed. Wiley (2012)</ref><ref>[Mark Rubinstein](/source/Mark_Rubinstein). (2005). "Great Moments in Financial Economics: IV. The Fundamental Theorem (Part I)", ''[Journal of Investment Management](/source/Journal_of_Investment_Management)'', Vol. 3, No. 4, Fourth Quarter 2005; ~ (2006). Part II, Vol. 4, No. 1, First Quarter 2006.</ref>

This framework is therefore “broader than ‘option pricing’ because it encompasses the full gamut of valuation approaches directed toward the pricing of contingent claims.” This would include "the full range of models designed to price government, corporate, and [mortgage-backed securities](/source/mortgage-backed_securities)... as well as options and futures on [fixed income securities](/source/fixed_income_securities)."<Ref Name="Babbel_Merrill"> David F. Babbel and Craig R. Merrill  (1996). Valuation of Interest-Sensitive Financial Instruments (SOA Monograph M-FI96-1). Wiley. {{ISBN|978-1883249151}}</ref><ref>See for example: Jonathan E. Ingersoll (1977). [http://faculty.som.yale.edu/jonathaningersoll/downloads/1977_ConvertibleSecurities.pdf A contingent-claims valuation of convertible securities]. ''[Journal of Financial Economics](/source/Journal_of_Financial_Economics)'' Volume 4, Issue 3, May 1977, Pages 289-321</ref>

==Corporate finance==
{{see|Corporate finance #Valuing flexibility|Business valuation #Option pricing approaches|Valuation (finance) #Valuation overview}}

A recent development in [corporate finance](/source/corporate_finance),<ref name="Damodaran"/><ref name="Larrabee_Voss">David T. Larrabee, Jason A. Voss (2012).  ''Valuation Techniques: Discounted Cash Flow, Earnings Quality, Measures of Value Added, and Real Options''. John Wiley & Sons, 2012. {{ISBN|978-1-118-39743-5}}</ref> is “the acceptance, at least in some cases, that the value of an asset may be greater than the present value of expected cash flows, if the cash flows are contingent on the occurrence or non-occurrence of an event”.<ref name ="Damodaran"/>   This '''contingent claim valuation''', uses  [option pricing models](/source/List_of_finance_topics) to measure the value of assets that share option-like characteristics.

While these models were initially used to value traded options, there has been an attempt in recent years to extend the reach of these models into [more traditional valuation](/source/valuation_(finance)). The fundamental premise here, is that “discounted cash flow models tend to understate the value of assets that provide payoffs that are contingent on the occurrence of an event."<ref name ="Damodaran"/>  See [Real options valuation](/source/Real_options_valuation) generally, and [§ Applicability of standard techniques](/source/Real_options_valuation) there.  (One major modification here is that these models often rely on a [replicating portfolio](/source/Rational_pricing) as opposed to traditional risk neutral pricing.)

Typical [corporate finance "project" valuations](/source/Corporate_finance) would include [patents](/source/Patent_valuation), [undeveloped natural resource reserves](/source/Valuation_(finance)), and ["suffering companies"](/source/Valuation_(finance)) –  all of these exhibiting optionality.  See {{sectionlink|Valuation (finance) #Specialised cases}}.
Funding dependent, corporate financial investments and [special purpose entities](/source/special_purpose_entities) also often inhere optionality and must then be modeled correspondingly.

Contingent claim valuation is also used to value specific [balance sheet](/source/balance_sheet) [assets](/source/assets) and [liabilities](/source/Liability_(financial_accounting)) which similarly exhibit option-like characteristics.<ref name="Garbade">Kenneth D. Garbade (2001). ''Pricing Corporate Securities as Contingent Claims.'' [MIT Press](/source/MIT_Press). {{ISBN|9780262072236}}</ref>  Examples are  [employee stock option](/source/employee_stock_option)s, [contingent value rights](/source/contingent_value_rights), [warrants](/source/Warrant_(finance)) and other [convertible securities](/source/convertible_security), and [investment](/source/investment)s with [embedded option](/source/embedded_option)s such as [callable bond](/source/callable_bond)s or [contingent convertible bond](/source/contingent_convertible_bond)s.

==References==
{{Reflist|30em}}

Category:Derivatives (finance)

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