Utility maximization in markets with bid–ask spreads

A one-period financial market model with transaction costs is considered in this paper. Redefining the risky asset price process in a suitable way, we obtain an explicit solution to the utility maximization problem when the risk preferences of the investor are based on the exponential utility function and a liability can be included in her portfolio. The arbitrage-free interval price for a general liability, as well as its replication price, is characterized in terms of expectations with respect to equivalent martingale measures. The indifference price is derived and its asymptotic limit when the risk aversion is going to infinity is analysed.     

Tick size and spreads: The case of Nasdaq’s decimalization

Recent studies by the Securities and Exchange Commission (SEC) and by academics have provided empirical evidence that Nasdaq trade execution costs are still higher than, for instance, on the NYSE. Introducing decimal pricing is one concrete plan to enhance Nasdaq’s competitiveness. However, effects of tick size changes are difficult to predict. For that reason models have been required for quite a while. Capital market synergetics is appropriate to investigate the effects of market microstructure changes.In this paper, we examine the impact of a variation in Nasdaq’s minimum price increment on quoted spreads. First, our findings confirm the numerical value of the decline in the average quoted spread in 1997 as an immediate effect of reducing the tick size from $1/8 to $1/16. This strongly affirms the reliability of our calculation results. Second, by applying the same research design again, we investigate the impact of a further reduction in the tick size to $1/100. No such study is available at the moment. The expected changes in the average quoted spreads due to the reduction in the tick size from $1/16 to $1/100, the change through decimalization, range from an increase of 2.82% to a decrease of 15.51%. Derived by applying the same method again, the figures embody a reliable forecast of the real effects and are therefore of eminent importance to academics and to practitioners as well.     

Computing arbitrage upper bounds on basket options in the presence of bid–ask spreads

We study the problem of computing the sharpest static-arbitrage upper bound on the price of a European basket option, given the bid–ask prices of vanilla call options in the underlying securities. We show that this semi-infinite problem can be recast as a linear program whose size is linear in the input data size. These developments advance previous related results, and enhance the practical value of static-arbitrage bounds as a pricing technique by taking into account the presence of bid–ask spreads. We illustrate our results by computing upper bounds on the price of a DJX basket option. The MATLAB code used to compute these bounds is available online at www.andrew.cmu.edu/user/jfp/arbitragebounds.html.     

Classification of spreads ofPG(3, 4)∖PG(3, 2)

We show that the 800 spreads ofPG(3, 4)PG(3, 2) fall into three orbits of sizes 120, 120 and 560, under the action of its automorphism group.