The Theory of Good-Deal Pricing in Financial Markets

The term ‘no-good-deal pricing’ in this paper encompasses pricing techniques based on the absence of attractive investment opportunities – good deals – in equilibrium. We borrowed the term from [8] who pioneered the calculation of price bands conditional on the absence of high Sharpe Ratios. Alternative methodologies for calculating tighter-than-no-arbitrage price bounds have been suggested by [4], [6], [12]. The theory presented here shows that any of these techniques can be seen as a generalization of no-arbitrage pricing. The common structure is provided by the Extension and Pricing Theorems, already well known from no-arbitrage pricing, see [15]. We derive these theorems in no-good-deal framework and establish general properties of no-good-deal prices. These abstract results are then applied to no-good-deal bounds determined by von Neumann-Morgenstern preferences in a ...nite state model1 . One important result is that no-good-deal bounds generated by an unbounded utility function are always strictly tighter than the no-arbitrage bounds. The same is not true for bounded utility functions. For smooth utility functions we show that one will obtain the no-arbitrage and the representative agent equilibrium as the two opposite ends of a spectrum of no-good-deal equilibrium restrictions indexed by the maximum attainable certainty equivalent gains. A sizeable part of ...nance theory is concerned with the valuation of risky income streams. In many cases this valuation is performed against the backdrop of a frictionless market of basis assets. Whenever the payo¤ of the focus asset can be synthesized from the payo¤s of basis assets the value of the focus asset is uniquely determined and this valuation process is preference-free – any other price of the focus asset would lead to an arbitrage opportunity. In reality, however, the perfect replication is an unattainable ideal, partly due to market frictions and partly due to genuine sources of unhedgeable risk presenting themselves, for example, as stochastic volatility. When perfect replication is