Market Incompleteness and Super Value Additivity: Implications for Securitization

Abstract

In an incomplete market economy, all claims cannot be priced uniquely based on arbitrage. The prices of attainable claims (those that are spanned by traded claims) can be determined uniquely, whereas the prices of those that are unattainable can only be bounded. We first show that tighter price bounds can be determined by considering all possible portfolios of unattainable claims for which there are bid/offer prices. We provide an algorithm to establish these bounds. We then examine how a price-taking agent can “package” new assets in order to take advantage of the incompleteness since the market places a premium on claims that improve its spanning. In particular, we prove that a firm with a new investment opportunity can maximize its value by “stripping away” the maximal attainable portion of the cash flow, for which prices are determined uniquely, and selling the balance to investors at prices that preclude arbitrage. Our framework has several applications in financial economics to problems ranging from securitization to the valuation of real options.