A new computational tool for analysing dynamic hedging under transaction costs

This paper highlights a framework for analysing dynamic hedging strategies under transaction costs. First, self-financing portfolio dynamics under transaction costs are modelled as being portfolio affine. An algorithm for computing the moments of the hedging error on a lattice under portfolio affine dynamics is then presented. In a number of circumstances, this provides an efficient approach to analysing the performance of hedging strategies under transaction costs through moments. As an example, this approach is applied to the hedging of a European call option with a Black–Scholes delta hedge and Leland's adjustment for transaction costs. Results are presented that demonstrate the range of analysis possible within the presented framework.     

Equilibrium returns with transaction costs

We study how trading costs are reflected in equilibrium returns. To this end, we develop a tractable continuous-time risk-sharing model, where heterogeneous mean–variance investors trade subject to a quadratic transaction cost. The corresponding equilibrium is characterized as the unique solution of a system of coupled but linear forward–backward stochastic differential equations. Explicit solutions are obtained in a number of concrete settings. The sluggishness of the frictional portfolios makes the corresponding equilibrium returns mean-reverting. Compared to the frictionless case, expected returns are higher if the more risk-averse agents are net sellers or if the asset supply expands over time.     

A multi-asset investment and consumption problem with transaction costs

Finance and Stochastics - In this article, we study a multi-asset version of the Merton investment and consumption problem with CRRA utility and proportional transaction costs. We specialise to a...     

A comparison of transaction costs on Xetra and on Nasdaq

Abstract

In today's financial world, providing high quality of order execution at low transaction costs is vitally important to the competitiveness of trading platforms; thus the stock market's microstructure has become a subject of fierce debate and models for computing transaction costs have been needed for quite a while. Capital market synergetics is appropriate to investigate the market microstructure's effectiveness and is implemented in the computer program KapSyn.

In this paper we compare transaction costs for small, medium-size and block-size orders on each exchange, examining different market scenarios. By investigating the peculiarities of Xetra and of Nasdaq we point out their comparative advantages: calculation results clearly show the high operating efficiency of Nasdaq's small-order execution system and Xetra's favourable execution of medium-size and block-size orders. Investors' trading decisions may benefit from taking these results into account. For policy makers and academics these findings contribute to the debate about the optimal design of a market microstructure by highlighting the areas of high performance.     

Asymptotic arbitrage with small transaction costs

We give characterizations of asymptotic arbitrage of the first and second kind and of strong asymptotic arbitrage for a sequence of financial markets with small proportional transaction costs λ _n on market n, in terms of contiguity properties of sequences of equivalent probability measures induced by λ _n -consistent price systems. These results are analogous to the frictionless case; compare (Kabanov and Kramkov in Finance Stoch. 2:143–172, 1998; Klein and Schachermayer in Theory Probab. Appl. 41:927–934, 1996). Our setting is simple, each market n contains two assets. The proofs use quantitative versions of the Halmos–Savage theorem (see Klein and Schachermayer in Ann. Probab. 24:867–881, 1996) and a monotone convergence result for nonnegative local martingales. Moreover, we study examples of models which admit a strong asymptotic arbitrage without transaction costs, but with transaction costs λ _n >0 on market n; there does not exist any form of asymptotic arbitrage. In one case, (λ _n ) can even converge to 0, but not too fast.     

Robust hedging with proportional transaction costs

A duality for robust hedging with proportional transaction costs of path-dependent European options is obtained in a discrete-time financial market with one risky asset. The investor’s portfolio consists of a dynamically traded stock and a static position in vanilla options, which can be exercised at maturity. Trading of both options and stock is subject to proportional transaction costs. The main theorem is a duality between hedging and a Monge–Kantorovich-type optimization problem. In this dual transport problem, the optimization is over all probability measures that satisfy an approximate martingale condition related to consistent price systems, in addition to an approximate marginal constraint.     

A counter-example to an option pricing formula under transaction costs

In the paper by Melnikov and Petrachenko (Finance Stoch. 9: 141–149, 2005), a procedure is put forward for pricing and replicating an arbitrary European contingent claim in the binomial model with bid-ask spreads. We present a counter-example to show that the option pricing formula stated in that paper can in fact lead to arbitrage. This is related to the fact that under transaction costs a superreplicating strategy may be less expensive to set up than a strictly replicating one.     

A profitable trading and risk management strategy despite transaction costs

We present a new profitable trading and risk management strategy with transaction cost for an adaptive equally weighted portfolio. Moreover, we implement a rule-based expert system for the daily financial decision-making process using the power of spectral analysis. We use several key components such as principal component analysis, partitioning, memory in stock markets, percentile for relative standing, the first four normalized central moments, learning algorithm, and switching among several investment positions consisting of short stock market, long stock market and money market with real risk-free rates. We find that it is possible to beat the proxy for the equity market without short selling for 168 S&P 500-listed stocks during the 1998–2008 period and 213 Russell 2000-listed stocks during the 1995–2007 period. Our Monte Carlo simulation for both the various set of stocks and the interval of time confirms our findings.     

Dynamics of financial markets and transaction costs: A graph-based study

In financial markets, trading patterns influence the behaviour of arbitrage, surveillance, risk management and pricing returns. The analysis of these patterns is important for defining policies in financial regulation as well as portfolios of international assets. Using financialization as a conceptual framework to understand the current trading patterns of financial markets, this work employs a market graph model for studying the stock indexes of geographically separated financial markets. By using an edge creation condition based on a transaction cost threshold, the resulting market graph features a strong connectivity, some traces of a power law in the degree distribution and an intensive presence of cliques. Furthermore, an inverse relation between transaction costs and maximal clique size is noticed. The market graph model also indicates that infrastructure, sustainability and commodity indexes from APEC, EU and NAFTA affect the behaviour of markets. As a result, the graph approach shows a consistent set of outcomes that mostly explain the financialization dynamics of markets.     

International equity portfolio allocations and transaction costs

In spite of the critical role of transaction cost, there are not many papers that explicitly examine its influence on international equity portfolio allocation decisions. Using bilateral cross-country equity portfolio investment data and three direct measures of transaction costs for 36 countries, we provide evidence that markets where transaction costs are lower attract greater equity portfolio investments. The results imply that future research on international equity portfolio diversification cannot afford to ignore the role of transaction costs, and policy makers, especially in emerging markets, will have to reduce transaction costs to attract higher levels of foreign equity portfolio investments.     

Multivariate utility maximization with proportional transaction costs

We present an optimal investment theorem for a currency exchange model with random and possibly discontinuous proportional transaction costs. The investor’s preferences are represented by a multivariate utility function, allowing for simultaneous consumption of any prescribed selection of the currencies at a given terminal date. We prove the existence of an optimal portfolio process under the assumption of asymptotic satiability of the value function. Sufficient conditions for this include reasonable asymptotic elasticity of the utility function, or a growth condition on its dual function. We show that the portfolio optimization problem can be reformulated in terms of maximization of a terminal liquidation utility function, and that both problems have a common optimizer.     

Risk sensitive asset management with transaction costs

This paper develops a continuous time risk-sensitive portfolio optimization model with a general transaction cost structure and where the individual securities or asset categories are explicitly affected by underlying economic factors. The security prices and factors follow diffusion processes with the drift and diffusion coefficients for the securities being functions of the factor levels. We develop methods of risk sensitive impulsive control theory in order to maximize an infinite horizon objective that is natural and features the long run expected growth rate, the asymptotic variance, and a single risk aversion parameter. The optimal trading strategy has a simple characterization in terms of the security prices and the factor levels. Moreover, it can be computed by solving a {\it risk sensitive quasi-variational inequality}. The Kelly criterion case is also studied, and the various results are related to the recent work by Morton and Pliska. Mansucript received: July 1998; final version received: January 1999     

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.     

Speculative trading,prospect theory and transaction costs

A speculative agent with prospect theory preference chooses the optimal time to purchase and then to sell an indivisible risky asset to maximise the expected utility of the round-trip profit net of transaction costs. The optimisation problem is formulated as a sequential optimal stopping problem, and we provide a complete characterisation of the solution. Depending on the preference and market parameters, the optimal strategy can be “buy and hold”, “buy low, sell high”, “buy high, sell higher” or “no trading”. Behavioural preference and market friction interact in a subtle way which yields surprising implications on the agent’s trading patterns. For example, increasing the market entry fee does not necessarily curb speculative trading, but instead may induce a higher reference point under which the agent becomes more risk-seeking and in turn is more likely to trade.

     

Trends and determinants of Australian managed fund transaction costs

The present paper examines the often-overlooked managed fund fee that is incurred when investors enter and exit managed fund products. The present paper documents that transaction costs for investors, measured by the application-redemption spread, are above stock market brokerage rates although they have declined since 1995. The study analyses the relationship between this transaction fee and several variables. In summary, retail fund transaction costs are positively related to retail funds’ assets under management, whilst this relationship is negative for larger wholesale funds, consistent with economies of scale. Direct entry and exit fees and initial commissions are positively related to transaction costs which raises the possibility that the commissions are used to levy soft-dollar payments. The paper also documents a relationship between transaction costs and fund flows which differs between retail and wholesale funds. Overall, the findings are consistent with the proposition that the various fees are used by managers as interchangeable and the different fee regimes reflect different products and markets.