On option pricing in binomial market with transaction costs

Option replication is studied in a discrete-time framework with proportional transaction costs. The model represents an extension of the Cox-Ross-Rubinstein binomial option-pricing model to cover the case of proportional transaction costs for one risky asset with different interest rates on bank credit and deposit. Contingent claims are supposed to be 2-dimensional random variables. Explicit formulas for self-financing strategies are obtained for this case.Received: March 2004, Mathematics Subject Classification (2000): 62P05JEL Classification: G11, G13The authors are grateful to an anonymous referee for numerous helpful comments and to Yulia Romaniuk for final corrections. The paper was partially supported by grant NSERC 264186.     

A geometric approach to portfolio optimization in models with transaction costs

We consider a continuous-time stochastic optimization problem with infinite horizon, linear dynamics, and cone constraints which includes as a particular case portfolio selection problems under transaction costs for models of stock and currency markets. Using an appropriate geometric formalism we show that the Bellman function is the unique viscosity solution of a HJB equation.Mathematics Subject Classification (1991): 60G44JEL Classification: G13, G11This research was done at Munich University of Technology supported by a Mercator Guest Professorship of the German Science Foundation (Deutsche Forschungsgemeinschaft). The authors also express their thanks to Mark Davis, Steve Shreve, and Michael Taksar for useful discussions concerning the principle of dynamic programming.     

Portfolio optimisation with strictly positive transaction costs and impulse control

One crucial assumption in modern portfolio theory of continuous-time models is the no transaction cost assumption. This assumption normally leads to trading strategies with infinite variation. However, following such a strategy in the presence of transaction costs will lead to immediate ruin. We present an impulse control approach where the investor can change his portfolio only finitely often in finite time intervals. Further, we consider transaction costs including a fixed and a proportional cost component. For the solution of the resulting control problems we present a formal optimal stopping approach and an approach using quasi-variational inequalities. As an application we derive a nontrivial asymptotically optimal solution for the problem of exponential utility maximisation.     

A note on transaction costs and the interpretation of dividend drop‐off ratios

In a recent edition of this Journal, Bartholdy and Brown (1999) presented an analysis of the ex‐dividend share price behaviour of shares listed on the New Zealand Stock Exchange. The authors conclude that their results are consistent with the tax clientele effect (driven by long‐term investors) and that there is little or no support for the short‐term trading hypothesis. Our purpose is to highlight the importance of transaction costs in analyses such as Bartholdy and Brown's. We argue that their results have an alternative interpretation because their analysis excludes the impact of transaction costs. We extend their model to include transaction costs and show that their results are not necessarily inconsistent with the short‐term trading hypothesis. A critical point of our analysis is that, in the presence of transaction costs, the equilibrium drop‐off ratio for dividend strip traders will be less than one, and, in some cases, can be less than the equilibrium drop‐off ratio for long‐term investors.