Should Stochastic Volatility Matter to the Cost-Constrained Investor?

Significant strides have been made in the development of continuous-time portfolio optimization models since Merton (1969) . Two independent advances have been the incorporation of transaction costs and time-varying volatility into the investor's optimization problem. Transaction costs generally inhibit investors from trading too often. Time-varying volatility, on the other hand, encourages trading activity, as it can result in an evolving optimal allocation of resources. We examine the two-asset portfolio optimization problem when both elements are present. We show that a transaction cost framework can be extended to include a stochastic volatility process. We then specify a transaction cost model with stochastic volatility and show that when the risk premium is linear in variance, the optimal strategy for the investor is independent of the level of volatility in the risky asset. We call this the Variance Invariance Principle.     

Dynamic Optimization of Long-Term Growth Rate for a Portfolio with Transaction Costs and Logarithmic Utility

We study the optimal investment policy for an investor who has available one bank account and n risky assets modeled by log-normal diffusions. The objective is to maximize the long-run average growth of wealth for a logarithmic utility function in the presence of proportional transaction costs. This problem is formulated as an ergodic singular stochastic control problem and interpreted as the limit of a discounted control problem for vanishing discount factor. The variational inequalities for the discounted control problem and the limiting ergodic problem are established in the viscosity sense. The ergodic variational inequality is solved by using a numerical algorithm based on policy iterations and multigrid methods. A numerical example is displayed for two risky assets.     

OPTIMAL LOT SOLUTION TO CARDINALITY CONSTRAINED MEAN–VARIANCE FORMULATION FOR PORTFOLIO SELECTION

The pioneering work of the mean–variance formulation proposed by Markowitz in the 1950s has provided a scientific foundation for modern portfolio selection. Although the trade practice often confines portfolio selection with certain discrete features, the existing theory and solution methodologies of portfolio selection have been primarily developed for the continuous solution of the portfolio policy that could be far away from the real integer optimum. We consider in this paper an exact solution algorithm in obtaining an optimal lot solution to cardinality constrained mean–variance formulation for portfolio selection under concave transaction costs. Specifically, a convergent Lagrangian and contour-domain cut method is proposed for solving this class of discrete-feature constrained portfolio selection problems by exploiting some prominent features of the mean–variance formulation and the portfolio model under consideration. Computational results are reported using data from the Hong Kong stock market.     

A NOTE ON THE EFFECTS OF TAXES ON OPTIMAL INVESTMENT

We integrate two approaches to portfolio management problems: that of Morton and Pliska (1995) for a portfolio with risky and riskless assets under transaction costs, and that of Cadenillas and Pliska (1999) for a portfolio with a risky asset under taxes and transaction costs. In particular, we show that the two surprising results of the latter paper, results shown for a taxable market consisting of only a single security, extend to a financial market with one risky asset and one bond: it can be optimal to realize not only losses but also gains, and sometimes the investor prefers a positive tax rate.     

HEDGING AND PORTFOLIO OPTIMIZATION UNDER TRANSACTION COSTS: A MARTINGALE APPROACH12

We derive a formula for the minimal initial wealth needed to hedge an arbitrary contingent claim in a continuous-time model with proportional transaction costs; the expression obtained can be interpreted as the supremum of expected discounted values of the claim, over all (pairs of) probability measures under which the “wealth process” is a supermartingale. Next, we prove the existence of an optimal solution to the portfolio optimization problem of maximizing utility from terminal wealth in the same model, we also characterize this solution via a transformation to a hedging problem: the optimal portfolio is the one that hedges the inverse of marginal utility evaluated at the shadow state-price density solving the corresponding dual problem, if such exists. We can then use the optimal shadow state-price density for pricing contingent claims in this market. the mathematical tools are those of continuous-time martingales, convex analysis, functional analysis, and duality theory.     

人民币汇率改革下企业如何规避汇率风险

人民币汇率改革使企业直接暴露在汇率风险之下,企业面临的汇率风险控制成为迫在眉睫的问题。企业在签订交易合同过程中,除了应注意选择货币的问题之外,还要充分利用金融工具避险,这已经成为一种在技术上解决汇率风险的主要方法。企业应多向银行咨询,利用其研究力量来帮助自己分析前景,合理在外汇市场上运用各种外汇衍生工具来规避风险。企业只有采用多种方式,才能使汇率风险化解到最小值。     

基于交易费用视角的中国体制转型绩效研究

交易费用的变动可作为衡量中国体制转型绩效的一个重要尺度。通过借鉴已有研究成果,构建MIMIC模型,测算中国自改革开放以来交易部门的交易费用和非市场交易费用及其变动趋势。结果显示,改革开放以来,中国的交易服务水平并未显著提高,且非市场交易费用居高不下。应将推动服务业发展作为产业结构优化升级的战略重点,加快建立法治政府和服务型政府,积极推进"十二五"期间的经济转型升级。     

Option Pricing in Discrete‐Time Incomplete Market Models

Various aspects of pricing of contingent claims in discrete time for incomplete market models are studied. Formulas for prices with proportional transaction costs are obtained. Some results concerning pricing with concave transaction costs are shown. Pricing by the expected utility of terminal wealth is also considered.     

从相对交易成本视角分析战略联盟

科斯强调节约交易成本是企业形成的一个重要因素,但忽略了组织能力也是制度选择中的重要变量,笔者在此基础上,将组织能力和节约交易成本相结合,从相对交易成本的变化尝试解释战略联盟。     

Leland's Approach to Option Pricing: The Evolution of a Discontinuity

A claim of Leland (1985) states that in the presence of transaction costs a call option on a stock S , described by geometric Brownian motion, can be perfectly hedged using Black–Scholes delta hedging with a modified volatility. Recently Kabanov and Safarian (1997) disproved this claim, giving an explicit (up to an integral) expression of the limiting hedging error, which appears to be strictly negative and depends on the path of the stock price only via the stock price at expiry S _T . We prove in this paper that the limiting hedging error, considered as a function of S _T , exhibits a removable discontinuity at the exercise price. Furthermore, we provide a quantitative result describing the evolution of the discontinuity: Hedging errors, plotted over the price at expiry, show a peak near the exercise price. We determine the rate at which that peak becomes narrower (producing the discontinuity in the limit) as the lengths of the revision intervals shrink.     

现行汇率制度下我国企业的外汇交易风险防范

在新的汇率制度下,我国企业面临着比以前更大的外汇交易风险。本文通过对外汇交易风险防范的目标和原则,以及我国企业在防范外汇交易风险中的问题进行分析,并结合我国汇率制度和金融市场的实际情况,总结了一些防范企业外汇交易风险的措施。