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.     

我国汇率制度改革与银行间外汇市场发展分析

2005年7月21日,我国宣布开始实行以市场供求为基础,参考一篮子货币进行调节、有管理的浮动汇率。在这种新形势下,银行间外汇市场要改变过去依附于结售汇制度的框架,确立新的发展战略取向。本文将从外汇市场组织结构改革、交易清算方式改进、交易品种的引进的转变三个方面为切入点对此进行分析。     

EVALUATING HEDGING ERRORS: AN ASYMPTOTIC APPROACH

We propose a methodology for evaluating the hedging errors of derivative securities due to the discreteness of trading times or the observation times of market prices, or both. Utilizing a weak convergence approach, we derive the asymptotic distributions of the hedging errors as the discreteness disappears in several situations. First, we examine the hedging error due to discrete-time trading when the true strategy is known, which generalizes the result of Bertsimas, Kogan, and Lo (2000) to continuous Itô processes. Then we consider a data-driven strategy, when the true strategy is unknown. This strategy is free of parametric model assumptions, therefore it is expected to serve as a benchmark for the evaluation of parametric strategies. Finally, we consider a case study of the Black-Scholes delta-hedging strategy when the volatility is unknown in the proposed framework. The results obtained give us a prospect for further developments of the framework under which various parametric strategies could be compared in a unified manner.     

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.     

中国民航业金融衍生工具现状及其发展

随着20世纪70年代布雷顿森林体系的瓦解,“双挂钩”的国际货币体系成为历史,金融衍生工具应运而生。为了降低经济活动的不确定性和风险,金融衍生工具在国际民航行业迅速发展。相比而言,国内民航企业对金融衍生工具认识范围不全面、风险管控不到位、操作程序不规范、内部审批不严格,致使金融衍生品在中国民航业的交易规模极为有限,且无法充分发挥套期保值作用。本文就金融衍生工具在国内民航业的现状、存在的问题进行分析,并提出相应的缓解措施,以促进形成具有中国特色和符合中国国情的航空金融衍生品市场。     

DISCRETE TIME HEDGING OF THE AMERICAN OPTION

In a complete financial market we consider the discrete time hedging of the American option with a convex payoff. It is well known that for the perfect hedging the writer of the option must trade continuously in time, which is impossible in practice. In reality, the writer hedges only at some discrete time instants. The perfect hedging requires the knowledge of the partial derivative of the value function of the American option in the underlying asset, the explicit form of which is unknown in most cases of practical importance. Several approximation methods have been developed for the calculation of the value function of the American option. We claim in this paper that having at hand any uniform approximation of the American option value function at equidistant discrete rebalancing times it is possible to construct a discrete time hedging portfolio, the value process of which uniformly approximates the value process of the continuous time perfect delta‐hedging portfolio. We are able to estimate the corresponding discrete time hedging error that leads to a complete justification of our hedging method for nonincreasing convex payoff functions including the important case of the American put. This method is essentially based on a new type square integral estimate for the derivative of an arbitrary convex function recently found by Shashiashvili.     

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.     

外汇交易市场的汇率协整分析

本文通过单位根检验,确定汇率的价格序列具有一阶差分平稳性,在此基础上对外汇交易市场几种汇率之间的协整关系进行实证分析,研究发现他们存在着长期的稳定关系,这将有助于投资者制定决策并有效地规避风险。     

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     

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.     

The Chinese RMB: Its Value,Its Peg,and Its Future

The valuation of the Chinese renminbi (RMB) has drawn lots of attention lately and a great deal of pressure on the part of developed nations for revaluation. In addressing the issue of valuation, this paper develops a new purchasing power parity (PPP) index of China’s exchange rate and finds that the while undervalued, the undervaluation is neither unusual nor bad policy. Moreover, China’s overall external trade balance does not seem to be that far out of equilibrium. China’s desire to join the G-7 club is likely to result in abandoning its peg, however, despite the increased risk to its economic development.JEL Classification F310     

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.     

HEDGING BY SEQUENTIAL REGRESSIONS REVISITED

Almost 20 years ago Föllmer and Schweizer (1989) suggested a simple and influential scheme for the computation of hedging strategies in an incomplete market. Their approach of  local  risk minimization results in a sequence of one-period least squares regressions running recursively backward in time. In the meantime, there have been significant developments in the  global  risk minimization theory for semimartingale price processes. In this paper we revisit hedging by sequential regression in the context of global risk minimization, in the light of recent results obtained by Černý and Kallsen (2007) . A number of illustrative numerical examples are given.     

THE COST OF ILLIQUIDITY AND ITS EFFECTS ON HEDGING

Though liquidity is commonly believed to be a major effect in financial markets, there appears to be no consensus definition of what it is or how it is to be measured. In this paper, we understand liquidity as a nonlinear transaction cost incurred as a function of rate of change of portfolio. Using this definition, we obtain the optimal hedging policy for the hedging of a call option in a Black‐Scholes model. This is a more challenging question than the more common studies of optimal strategy for liquidating an initial position, because our goal requires us to match a random final value. The solution we obtain reduces in the case of quadratic loss to the solution of three partial differential equations of Black‐Scholes type, one of them nonlinear.     

我国外汇储备快速增长的原因、利弊及对策研究

我国外汇储备的快速增长增强了我国的综合国力,提高了我国的国际地位,加速了我国国民经济的发展,同时可以增强中央银行干预外汇市场、支持本币的能力,并可能最终实现人民币的可自由兑换;但外汇储备高速增长给人民币升值和通货膨胀带来压力,同时增加了储备资产管理的难度和风险。