Contingent claim

{{see|Financial economics #State prices}}

{{also|Arrow-Debreu security|Risk-neutral measure}}

In financial economics, contingent claim analysis is widely used as a framework both for developing pricing models, and for extending the theory. Thus, from its origins in option pricing and the valuation of corporate liabilities,Black, Fischer; Myron Scholes (1973). "The Pricing of Options and Corporate Liabilities". Journal of Political Economy. 81 (3): 637–654. doi:10.1086/260062. it has become a major approach to intertemporal equilibrium under uncertainty. 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

The general approach here is to define risky outcomes relative to states of the world, and to then use claims to represent and value state outcomes:

:$Price\; =\backslash sum\_\{s\}(q\_\{s\}X\_\{s\})/r$

::where $s$ are the states, $X$ are the claims (or cashflows), $q$ are the risk neutral probabilities, $r$ is the "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. Edwin H. Neave and Frank J. Fabozzi (2012). Introduction to Contingent Claims Analysis, in Encyclopedia of Financial Models, Frank Fabozzi ed. Wiley (2012)Mark Rubinstein. (2005). "Great Moments in Financial Economics: IV. The Fundamental Theorem (Part I)", Journal of Investment Management, Vol. 3, No. 4, Fourth Quarter 2005; ~ (2006). Part II, Vol. 4, No. 1, First Quarter 2006.

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... as well as options and futures on fixed income securities." David F. Babbel and Craig R. Merrill (1996). Valuation of Interest-Sensitive Financial Instruments (SOA Monograph M-FI96-1). Wiley. {{ISBN|978-1883249151}}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 Volume 4, Issue 3, May 1977, Pages 289-321

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

A recent development in corporate finance,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}} 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”. This contingent claim valuation, uses option pricing models 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. 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." See Real options valuation generally, and § Applicability of standard techniques there. (One major modification here is that these models often rely on a replicating portfolio as opposed to traditional risk neutral pricing.)

Typical corporate finance "project" valuations would include patents, undeveloped natural resource reserves, and contingent value rights – all of these exhibiting optionality. See {{sectionlink|Valuation (finance) #Specialised cases}}.

Funding dependent, corporate financial investments and special purpose entities also often inhere optionality and must then be modeled correspondingly.

Contingent claim valuation is also used to value specific balance sheet assets and liabilities which similarly exhibit option like characteristics.Kenneth D. Garbade (2001). Pricing Corporate Securities as Contingent Claims. MIT Press. {{ISBN|9780262072236}} Examples are employee stock options, warrants and other convertible securities, and investments with embedded options such as callable bonds or contingent convertible bonds.

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Category:Derivatives (finance)