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Pricing of New Securities in an Incomplete Market: the Catch 22 of No‐Arbitrage Pricing
Author(s) -
Boyle Phelim,
Wang Tan
Publication year - 2001
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/1467-9965.00115
Subject(s) - arbitrage , valuation (finance) , economics , risk neutral measure , arbitrage pricing theory , martingale (probability theory) , incomplete markets , rational pricing , security market , financial economics , mathematical economics , capital asset pricing model , microeconomics , finance , mathematics , statistics
There are two distinctly different approaches to the valuation of a new security in an incomplete market. The first approach takes the prices of the existing securities as fixed and uses no‐arbitrage arguments to derive the set of equivalent martingale measures that are consistent with the initial prices of the traded securities. The price of the new security is then obtained by appealing to certain criteria or on the basis of some preference assumption. The second method prices the new security within a general equilibrium framework. This paper clarifies the distinction between the two approaches and provides a simple proof that the introduction of the new security will typically change the prices of all the existing securities. We are left with the paradox that a genuinely new derivative security is not redundant, but the dominant pricing paradigm in derivative security pricing is the no‐arbitrage approach, which requires the redundancy of the security. Given the widespread practice of using the no‐arbitrage approach to price (or bound the price of) a new security, we also comment on some justifications for this approach.