Pricing of New Securities in an Incomplete Market: the Catch 22 of No-Arbitrage Pricing

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.