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.     

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.     

The Demand for Hedging and the Value of Hedging Opportunities

Hedging strategies typically assume that hedging is costless and that only one futures market exists. When these assumptions are dropped, the demand for hedging is shown to depend on basis risk, price risk, and the hedger's risk preference. The marginal and incremental value of hedging opportunities are computed for the general cases of one and two markets and applied to the specific case of Pennsylvania dairy input hedging.     

A Comparison of Two Quadratic Approaches to Hedging in Incomplete Markets

This paper provides comparative theoretical and numerical results on risks, values, and hedging strategies for local risk-minimization versus mean-variance hedging in a class of stochastic volatility models. We explain the theory for both hedging approaches in a general framework, specialize to a Markovian situation, and analyze in detail variants of the well-known Heston (1993) and Stein and Stein (1991) stochastic volatility models. Numerical results are obtained mainly by PDE and simulation methods. In addition, we take special care to check that all of our examples do satisfy the conditions required by the general theory.     

A Futures Duration-Convexity Hedging Method

A duration-based hedge ratio is the conventional method to hedge against price changes of a fixed-income instrument. However, the relationship between bond prices and interest rates is nonlinear, creating a convexity effect. Moreover, term structure changes often are nonparallel in nature, which causes imperfect hedges for the duration-based hedging model. One solution to these problems is to dynamically change the duration-based hedge ratio; however, this procedure is costly and is not effective when jumps in prices occur. A superior solution is to develop a two-instrument hedge ratio that simultaneously hedges both duration and convexity effects. This paper first presents such a two-instrument hedge ratio and then we examine its effectiveness. The simulation results show that this duration-convexity hedge ratio is vastly superior to alternative hedge ratio methods for both simple and complex changes in the term structure.     

利用交叉套期保值防范价格风险

在目前我国期货市场交易品种有限的情况下,一方面,期货市场应加快推出新品种的进程以满足众多企业的套期保值需求,另一方面,广大企业应当积极利用交叉套期保值,并采用实例分析,确定风险最小化的最佳套期比.     

公共财政框架下政府审计的拓展与政府会计的完善

政府审计是加强预算管理的一个重要工具。中国在建立公共财政的过程中，进行了一系列预算管理制度的改革，政府审计必须适应现行的预算管理制度，在审计内容上、方法上积极拓展。本文主要论述了当前公共财政框架下政府审计需要拓展的方面。另外，为保证预算管理制度改革顺利实施，政府会计等其他制度建设也需相应追行改革和完善。     

英语学术论文中模糊限制语的使用对比研究

通过对比英语本族语者与二语学习者英语学术论文中模糊限制语的使用情况,探讨了影响英语学习者英语学术写作中模糊限制语使用差异的因素,指出,在英语学术论文的写作中应尽可能避免文化思维差异及母语迁移对学术论文写作的影响,使学术论文写作符合国际规范,达到国际学术交流的目的。     

OPTIMAL CONTINUOUS-TIME HEDGING WITH LEPTOKURTIC RETURNS

We examine the behavior of optimal mean–variance hedging strategies at high rebalancing frequencies in a model where stock prices follow a discretely sampled exponential Lévy process and one hedges a European call option to maturity. Using elementary methods we show that all the attributes of a discretely rebalanced optimal hedge, i.e., the mean value, the hedge ratio, and the expected squared hedging error, converge pointwise in the state space as the rebalancing interval goes to zero. The limiting formulae represent 1-D and 2-D generalized Fourier transforms, which can be evaluated much faster than backward recursion schemes, with the same degree of accuracy. In the special case of a compound Poisson process we demonstrate that the convergence results hold true if instead of using an infinitely divisible distribution from the outset one models log returns by multinomial approximations thereof. This result represents an important extension of Cox, Ross, and Rubinstein to markets with leptokurtic returns.