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.     

Optimal hedging in an extended binomial market under transaction costs

We develop an approach to optimal hedging of a contingent claim under proportional transaction costs in a discrete time financial market model which extends the binomial market model with transaction costs. Our model relaxes the binomial assumption on the stock price ratios to the case where the stock price ratio distribution has bounded support. Non-self-financing hedging strategies are studied to construct an optimal hedge for an investor who takes a short position in a European contingent claim settled by delivery. We develop the theoretical basis for our optimal hedging approach, extending results obtained in our previous work. Specifically, we derive a no-arbitrage option price interval and establish properties of the non-self-financing strategies and their residuals. Based on the theoretical foundation, we develop a computational algorithm for optimizing an investor relevant criterion over the set of admissible non-self-financing hedging strategies. We demonstrate the applicability of our approach using both simulated data and real market data.     

Optimal dividend problems for Sparre Andersen risk model with bounded dividend rates

ABSTRACT

This paper concerns the optimal dividend problem with bounded dividend rate for Sparre Andersen risk model. The analytic characterizations of admissible strategies and Markov strategies are given. We use the measure-valued generator theory to derive a measure-valued dynamic programming equation. The value function is proved to be of locally finite variation along the path, which belongs to the domain of the measure-valued generator. The verification theorem is proved without additional assumptions on the regularity of the value function. Actually, the value function may have jumps. Under certain conditions, the optimal strategy is presented as a Markov strategy with space-time band structure. We present an iterative algorithm to approximate the optimal value function and the optimal dividend strategy. As applications, some numerical examples are given.     

No-arbitrage criteria for financial markets with transaction costs and incomplete information

This note deals with criteria of absence of arbitrage opportunities for an investor acting in a market with frictions and having a limited access to the information flow. We develop a mathematical scheme covering major models of financial markets with transaction costs and prove several results including a criterion for the robust no-arbitrage property and a hedging theorem.      

Hedging errors with Leland's option model in the presence of transaction costs

Nonzero transaction costs invalidate the Black–Scholes [1973. Journal of Political Economy 81, 637–654] arbitrage argument based on continuous trading. Leland [1985. Journal of Finance 40, 1283–1301] developed a hedging strategy which modifies the Black–Scholes hedging strategy with a volatility adjusted by the length of the rebalance interval and the rate of the proportional transaction cost. Kabanov and Safarian [1997. Finance and Stochastics 1, 239–250] calculated the limiting hedging error of the Leland strategy and pointed out that it is nonzero for the approximate pricing of an European call option, in contradiction to Leland's claim. As a further contribution, we first identify the mathematical flaw in the argument of Leland's claim and then quantify the expected percentage of hedging losses in terms of the hedging frequency and the level of the option strike price.     

Optimal portfolios and Heston's stochastic volatility model: an explicit solution for power utility

Given an investor maximizing utility from terminal wealth with respect to a power utility function, we present a verification result for portfolio problems with stochastic volatility. Applying this result, we solve the portfolio problem for Heston's stochastic volatility model. We find that only under a specific condition on the model parameters does the problem possess a unique solution leading to a partial equilibrium. Finally, it is demonstrated that the results critically hinge upon the specification of the market price of risk. We conclude that, in applications, one has to be very careful when exogenously specifying the form of the market price of risk.     

Optimal taxation and redistribution in an OLG model with unemployment

This paper concerns redistribution via nonlinear income taxation in an overlapping generations model with two ability-types. We assume that the wage rates are determined by bargaining between unions and firms, meaning that the equilibrium is characterized by involuntary unemployment. We show that the policy instruments that are used to calculate the marginal labor income tax rate for each ability-type give rise to intertemporal tax base effects. In addition, since the relationship between the employment and the capital stock implies intertemporal production inefficiency at the second best optimum, imperfect competition in the labor market may itself justify capital income taxation.      

A market model with medium/long-term effects due to an insider

In this article, we consider a modification of the Karatzas–Pikovsky model of insider trading. Specifically, we suppose that the insider agent influences the long/medium-term evolution of Black–Scholes type model through the drift of the stochastic differential equation. We say that the insider agent is using a portfolio leading to a partial equilibrium if the following three properties are satisfied: (a) the portfolio used by the insider leads to a stock price which is a semimartingale under his/her own filtration and his/her own filtration enlarged with the final price; (b) the portfolio used by the insider is optimal in the sense that it maximises the logarithmic utility for the insider when his/her filtration is fixed; and (c) the optimal logarithmic utility in (b) is finite. We give sufficient conditions for the existence of a partial equilibrium and show in some explicit models how to apply these general results.     

Robust optimal excess-of-loss reinsurance and investment strategy for an insurer in a model with jumps

This paper considers a robust optimal excess-of-loss reinsurance-investment problem in a model with jumps for an ambiguity-averse insurer (AAI), who worries about ambiguity and aims to develop a robust optimal reinsurance-investment strategy. The AAI’s surplus process is assumed to follow a diffusion model, which is an approximation of the classical risk model. The AAI is allowed to purchase excess-of-loss reinsurance and invest her surplus in a risk-free asset and a risky asset whose price is described by a jump-diffusion model. Under the criterion for maximizing the expected exponential utility of terminal wealth, optimal strategy and optimal value function are derived by applying the stochastic dynamic programming approach. Our model and results extend some of the existing results in the literature, and the economic implications of our findings are illustrated. Numerical examples show that considering ambiguity and reinsurance brings utility enhancements.