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.     

On the Existence of Linear Equilibria in Models of Market Making

We derive necessary and sufficient conditions for a linear equilibrium in three types of competitive market making models: Kyle type models (when market makers only observe aggregate net order flow), Glosten–Milgrom and Easley–O'Hara type models (when market makers observe and trade one order at a time), and call markets models (individual order models when market makers observe a number of orders before pricing and executing any of them). We study two cases: when privately informed (strategic) traders are symmetrically informed and when they have differential information. We derive necessary and sufficient conditions on the distributions of the random variables for a linear equilibrium. We also explore those features of the equilibrium that depend on linearity as opposed to the particular distributional assumptions and we provide a large number of examples of linear equilibria for each of the models.     

证券市场交易机制的国际发展趋势研究

证券市场的两种主要交易机制是竞价方式和做市商制度.文章在综合分析国际上有代表性的相关研究文献后,发现在交易机制与股票买卖价差的关系方面,采用竞价方式的股票其买卖价差较小,采用做市商机制的股票其买卖价差较大;在股票交易成本方面,采用竞价交易机制的股票交易成本较低,而做市商机制的股票交易成本较高.从国际上证券交易机制的发展趋势看,以一种方式为主,多种方式为辅的"混合交易"机制是最有优势的机制,是证券交易机制的未来发展模式.     

隐性交易成本与资产定价——基于上证180指数成份股票交易数据的实证研究

文章利用上证180指数成份股票的高频数据计算隐性交易成本,探讨其与资产定价的关系。发现:(1)隐性交易成本与换手率、规模和收益率都存在着明显的线性负相关关系。在股票收益率下降时期,隐性交易成本通过流动性深度成本间接影响股票收益率。(2)较之隐性交易成本,规模因素与换手率因素对收益率的影响有着更好的测度性。很可能是因为这两个因素与流动性深度成本也有着显著相关性。(3)隐性交易成本与规模因素整体上呈线性负相关关系,分段上的关系则很可能是凹函数与凸函数的组合。     

Fallout from the Mutual Fund Trading Scandal

In September 2003, several prominent mutual fund companies came under investigation for illegal trading practices. Allegations suggested these funds allowed certain investors to profit from short-term trading schemes at the expense of other investors. Surprisingly, regulatory authorities have known for more than two decades of the potential for such abuses, yet have taken limited steps to correct the problem. We explore investor reaction to the scandal by measuring assets under management, stock returns, and performance. Mutual funds managed by investigated firms show a substantial decline in post-announcement assets under management. These firms also experienced significantly negative announcement-period returns. Finally, we discuss several policy suggestions to prevent future trading abuses and provide direction for future research.     

Robustness of the Black and Scholes Formula

Consider an option on a stock whose volatility is unknown and stochastic. An agent assumes this volatility to be a specific function of time and the stock price, knowing that this assumption may result in a misspecification of the volatility. However, if the misspecified volatility dominates the true volatility, then the misspecified price of the option dominates its true price. Moreover, the option hedging strategy computed under the assumption of the misspecified volatility provides an almost sure one-sided hedge for the option under the true volatility. Analogous results hold if the true volatility dominates the misspecified volatility. These comparisons can fail, however, if the misspecified volatility is not assumed to be a function of time and the stock price. The positive results, which apply to both European and American options, are used to obtain a bound and hedge for Asian options.     

中国碳交易市场的现状、问题及对策建议

在世界碳交易市场迅速发展的背景下,中国也逐步建立了碳排放权交易市场,以各试点地区的碳排放交易所数据为基础分析了中国碳交易市场的发展状况。研究认为,中国碳交易市场发展尚未成熟,存在碳排放权交易的法律法规不健全,市场分割问题,据此提出积极培育碳金融市场主体,完善相关法律法规,建立全国统一的碳交易市场的措施建议。     

WIENER CHAOS: A NEW APPROACH TO OPTION HEDGING

This paper addresses the problem of estimating and analyzing the residual risk that is not hedged by a discrete hedging strategy. the use of die chaotic representation allows an elegant decomposition of the residual risk to be hedged by adequate assets. Alternative strategies to the classical delta hedging and optimization under the risk-neutral and historical probabilities are discussed.     

关于培育套期保值市场的思考

1999年是我国商品期货市场整顿与规范的一年。在这种条件下 ,培育套期保值市场是当前我国期货市场发展战略的首要选择。套期保值在期货市场发展中起着支柱的作用 ,当前我国套期保值市场不发达 ,其原因是多方面的。应采取措施培育期货保值市场 ,发展期货市场     

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.     

Trading Portfolios Electronically – An Experimental Approach

This paper focuses on a simple axiom – investors prefer to hold diversified combinations of assets. Arguing that pooling vehicles like mutual funds offer approximate solutions, we propose a portfolio trading mechanism that allows individuals to trade diverse combinations of assets through a single order. Given the complexity of the market mechanism, we construct a prototype of this trading system and test it through a series of laboratory experiments with student subjects. We address the quality of the price discovery process, quality of allocations, and efficiency of the market mechanism. Results from a set of laboratory experiments indicate that the performance of such systems is sensitive to design aspects as well as relative experience of participants.     

Multidimensional Variance‐Optimal Hedging in Discrete‐Time Model—A General Approach

One of the well‐known approaches to the problem of option pricing is a minimization of the global risk, considered as the expected quadratic net loss. In the paper, a multidimensional variant of the problem is studied. To obtain the existence of the variance‐optimal hedging strategy in a model without transaction costs, we can apply the result of Monat and Stricker. Another possibility is a generalization of the nondegeneracy condition that appeared in a paper of Schweizer, in which a one‐dimensional problem is solved. The relationship between the two approaches is shown. A more difficult problem is the existence of an optimal solution in the model with transaction costs. A sufficient condition in a multidimensional case is formulated.     

Robust Hedging of Barrier Options

This article considers the pricing and hedging of barrier options in a market in which call options are liquidly traded and can be used as hedging instruments. This use of call options means that market preferences and beliefs about the future behavior of the underlying assets are in some sense incorporated into the hedge and do not need to be specified exogenously. Thus we are able to find prices for exotic derivatives which are independent of any model for the underlying asset. For example we do not need to assume that the underlying assets follow an exponential Brownian motion.
We find model-independent upper and lower bounds on the prices of knock-in and knock-out puts and calls. If the market prices the barrier options outside these limits then we give simple strategies for generating profits at zero risk. Examples illustrate that the bounds we give can be fairly tight.