Financial Structure and Market Equilibrium in a Vertically Differentiated Industry

This paper examines the effects of uncertainty and the choice of financial structure in a vertically differentiated duopoly. In the market model consumers are located along a continuum of taste parameters and prefer unanimously higher to lower qualities when quality prices are set at average variable cost. In such a model only two firms can survive with a positive market share. We introduce uncertainty in demand by varying the range of the consumer taste parameter and consider a simultaneous game of sequential choices of quality, financial structure and product price, with varying order of decision-making and revelation of information. We consider both restricted and free entry. It is shown that financial structure affects market equilibrium, which is also heavily dependent on the order of choice of structure and quality, as well as on whether uncertainty exists in the lower or the upper limit of the taste parameter. In all cases leverage increases the lower quality and in most cases it also increases the lower quality price. There are also welfare implications, with the use of leverage when it is optimal improving both total and consumer surplus.Vertical differentiation; uncertainty; financial structure; leverage; quality; sequential choice

Option Pricing and Replication with Transaction Costs and Dividends

This paper derives optimal perfect hedging portfolios in the presence of transaction costs within the binomial model of stock returns, for a market maker that establishes bid and ask prices for American call options on stocks paying dividends prior to expiration. It is shown that, while the option holder's optimal exercise policy at the ex-dividend date varies according to the stock price, there are intervals of values for such a price where the optimal policy would depend on the holder's preferences. Nonetheless, the perfect hedging assumption still allows the derivation of optimal hedging portfolios for both long and short positions of a market maker on the option.Pricing; Transaction costs; American options; Dividends

Stochastic Dominance Bounds on Derivative Prices in a Multiperiod Economy with Proportional Transaction Costs

By applying stochastic dominance arguments, upper bounds on the reservation write price of European calls and puts and lower bounds on the reservation purchase price of these derivatives are derived in the presence of proportional transaction costs incurred in trading the underlying security. The primary contribution is the derivation of bounds when intermediate trading in the underlying security is allowed over the life of the option. A tight upper bound is derived on the reservation write price of a call and a tight lower bound is derived on the reservation purchase price of a put. These results jointly impose tight upper and lower bounds on the implied volatility.

Différenciation verticale et structure du marché

L’objectif de ce travail est de faire un survol des progrès récents sur la structure des marchés où se retrouvent plusieurs qualités du même produit. L’accent est mis sur les cas où les consommateurs demeurent unanimes quant au classement des produits, si ces derniers sont offerts à des prix reflétant les augmentations du coût moyen nécessaires pour l’amélioration de leur qualité. Les considérations stratégiques du choix des qualités sous des hypothèses alternatives, quant à la nature du coût fixe ainsi qu’en présence de firmes à plusieurs produits, sont aussi examinées.In this paper, we review the literature on vertical product differentiation in connection with its impact on market structure. Two types of vertical differentiation are identified according to whether consumer unanimity over product ranking is maintained at prices reflecting average cost increments necessary to produce higher qualities. If this is the case, the finiteness property prevents market fragmentation by imposing an upper bound on the number of firms even when the fixed cost approaches zero. This situation yields absolute product differentiation advantages to the high quality producers. We focus on the implications of quality choices on entry barriers and market structure under two different assumptions on the nature of the fixed cost. Research on multiproduct firms is also reviewed

Différenciation verticale et structure du marché

In this paper, we review the literature on vertical product differentiation in connection with its impact on market structure. Two types of vertical differentiation are identified according to whether consumer unanimity over product ranking is maintained at prices reflecting average cost increments necessary to produce higher qualities. If this is the case, the finiteness property prevents market fragmentation by imposing an upper bound on the number of firms even when the fixed cost approaches zero. This situation yields absolute product differentiation advantages to the high quality producers. We focus on the implications of quality choices on entry barriers and market structure under two different assumptions on the nature of the fixed cost. Research on multiproduct firms is also reviewed. L’objectif de ce travail est de faire un survol des progrès récents sur la structure des marchés où se retrouvent plusieurs qualités du même produit. L’accent est mis sur les cas où les consommateurs demeurent unanimes quant au classement des produits, si ces derniers sont offerts à des prix reflétant les augmentations du coût moyen nécessaires pour l’amélioration de leur qualité. Les considérations stratégiques du choix des qualités sous des hypothèses alternatives, quant à la nature du coût fixe ainsi qu’en présence de firmes à plusieurs produits, sont aussi examinées.

Mispricing of S&P 500 Index Options

We document widespread violations of stochastic dominance in the one-month S&P 500 index options market over the period 1986-2002. These violations imply that a trader can improve her expected utility by engaging in a zero-net-cost trade. We allow the market to be incomplete and also imperfect by introducing transactions costs and bid-ask spreads. There is higher incidence of violations by OTM than by ITM calls, contradicting the common inference drawn from the observed implied volatility smile that the problem lies with the left-hand tail of the index return distribution. Even though pre-crash option prices conform to the BSM model reasonably well, they are incorrectly priced. Over 1997-2002, many options, particularly OTM calls, are overpriced irrespective of which time period is used to determine the index return distribution. These results do not support the hypothesis that the options market is becoming more rational over time. Finally, our results dispel another common misconception, that the observed smile is too steep after the crash: most of the violations by post-crash options are due to the options being either underpriced over 1988-1995, or overpriced over 1997-2002.Derivative pricing; volatility smile, incomplete markets, transactions costs, index options, stochastic dominance bounds

Option Pricing: Real and Risk-Neutral Distributions

The central premise of the Black and Scholes [Black, F., Scholes, M. (1973). The pricing of options and corporate liabilities. Journal of Political Economy 81, 637–659] and Merton [Merton, R. (1973). Theory of rational option pricing. Bell Journal of Economics and Management Science 4, 141–184] option pricing theory is that there exists a self-financing dynamic trading policy of the stock and risk free accounts that renders the market dynamically complete. This requires that the market be complete and perfect. In this essay, we are concerned with cases in which dynamic trading breaks down either because the market is incomplete or because it is imperfect due to the presence of trading costs, or both. Market incompleteness renders the risk-neutral probability measure non unique and allows us to determine the option price only within a range. Recognition of trading costs requires a refinement in the definition and usage of the concept of a risk-neutral probability measure. Under these market conditions, a replicating dynamic trading policy does not exist. Nevertheless, we are able to impose restrictions on the pricing kernel and derive testable restrictions on the prices of options.We illustrate the theory in a series of market setups, beginning with the single period model, the two-period model and, finally, the general multiperiod model, with or without transaction costs.We also review related empirical results that document widespread violations of these restrictions.Option; Pricing

Are Options on Index Futures Profitable for Risk Averse Investors? Empirical Evidence

American call and put options on the S&P 500 index futures that violate the stochastic dominance bounds of Constantinides and Perrakis (2007) over 1983-2006 are identified as potentially profitable investment opportunities. Call bid prices more frequently violate their upper bound than put bid prices do, while evidence of underpriced calls and puts over this period is scant. In out-of-sample tests, the inclusion of short positions in such overpriced calls, puts, and, particularly, straddles in the market portfolio is shown to increase the expected utility of any risk averse investor and also increase the Sharpe ratio, net of transaction costs and bid-ask spreads. The results are strongly supportive of mispricing. (JEL G11, G13, G14)