An Asymptotic Analysis of an Optimal Hedging Model for Option Pricing with Transaction Costs

Davis, Panas, and Zariphopoulou (1993) and Hodges and Neuberger (1989) have presented a very appealing model for pricing European options in the presence of rehedging transaction costs. In their papers the 'maximization of utility' leads to a hedging strategy and an option value. The latter is different from the Black–Scholes fair value and is given by the solution of a three–dimensional free boundary problem. This problem is computationally very time–consuming. In this paper we analyze this problem in the realistic case of small transaction costs, applying simple ideas of asymptotic analysis. The problem is then reduced to an inhomogeneous diffusion equation in only two independent variables, the asset price and time. The advantages of this approach are to increase the speed at which the optimal hedging strategy is calculated and to add insight generally. Indeed, we find a very simple analytical expression for the hedging strategy involving the option's gamma.     

消费者忠诚的经济学分析

消费者忠诚以其对企业经营绩效产生的巨大贡献而日益成为人们关注的焦点。借鉴美国经济学家赫希曼的“退出、呼吁与忠诚”理论对此进行经济学意义上的探讨，在简要分析消费者的退出与呼吁行为对企业的影响的基础上，辨析了“忠诚”在消费者做出退出或呼吁决策中作为一种制度性障碍作用的约束条件与实现功效。     

Local Vega Index and Variance Reduction Methods

In this article we discuss a generalization of the Greek called vega which is used to study the stability of option prices and hedging portfolios with respect to the volatility in various models. We call this generalization the local vega index. We compute through Monte Carlo simulations this index in the cases of Asian options under the classical Black-Scholes setup. Simulation methods using Malliavin calculus and kernel density estimation are compared. Variance reduction methods are discussed.     

Overstatement of Implied Variance in the Dollar/Yen Currency Option Market

This paper investigates the predictive power of implied variancesextracted from the dollar/yen option prices. Implied variances areestimated from transaction prices of currency options traded on PHLXusing the option pricing model of Garman and Kohlhagen (1983). Incontrast to recent findings on stock and stock index options, theout-of-sample tests indicate that the implied variance is an upwardbiased estimator of future variance; and that the variance forecastsfrom GARCH and historical models do not contain significantincremental information in predicting future variance. Tradingstrategies are also developed to exploit the observed overstatementof variance in the dollar/yen option market. Traders that can executethe delta-neutral trading strategies at the observed markettransaction prices could lock in a significant profits during theperiod examined. However, for investors that facing highertransaction costs, the magnitude of the profits is generally notlarge enough to allow for abnormal risk-adjusted profits.     

Valuation of Callable Warrants

A simple valuation model for callable warrants is derived and tested. The model is expressed in closed form except for one term which can be evaluated numerically. Predictions of 78 warrant prices are compared to market prices and the average error is -.224 percent. By contrast, the Black-Scholes model applied to the same warrants produces an average error of 31.44 percent. Thus the callability feature cannot safely be ignored in determining warrant values.     

Window Double Barrier Options

This paper examines a path-dependent contingent claim called the window double barrier option, including standard but also more exotic features such as combinations of single and double barriers. Price properties and hedging issues are discussed, as well as financial applications.Explicit formulae are provided, along with simple techniques for theirimplementation. Numerical results show that they compare very favourablywith alternative pricing approaches in terms of accuracy and efficiency.     

浅析我国股票期权激励制度的税收方案

股票期权制度作为一种有效的激励机制,它把经理人的利益和其对企业在未来发展中的贡献紧密地联系在一起,因此我国越来越多的企业采用这种制度。本文从我国推行股票期权制度过程中遇到的税收法律问题作了分析,并提出有效的对策建议。     

Quadratic term structure models in discrete time

This paper extends the results on quadratic term structure models in continuous time to the discrete time setting. The continuous time setting can be seen as a special case of the discrete time one. Discrete time quadratic models have advantages over their continuous time counterparts as well as over discrete time affine models. Recursive closed form solutions for zero coupon bonds are provided even in the presence of multiple correlated underlying factors, time-dependent parameters, regime changes and “jumps” in the underlying factors. In particular regime changes and “jumps” cannot so easily be accommodated in continuous time quadratic models. Pricing bond options requires simple integration and model estimation does not require a restrictive choice of the market price of risk.     

‘Entry Thresholds and Actual Entry and Exit in Local Markets’

Bresnahan and Reiss (1991) derive entry thresholds for local markets but do not investigate actual entry and exit flows. This paper investigates for thirteen Belgian retail and consumer service industries whether markets with actual numbers of firms higher (lower) than the thresholds display exit (entry) in subsequent periods. The results confirm that over a three-year period the rate of (net) entry is positively affected by the presence of ‘market room’. The exit rate, however, does not show a negative relation with ‘market room’.      

Pricing Stock Options in a Jump‐Diffusion Model with Stochastic Volatility and Interest Rates: Applications of Fourier Inversion Methods

Fast closed form solutions for prices on European stock options are developed in a jump‐diffusion model with stochastic volatility and stochastic interest rates. The probability functions in the solutions are computed by using the Fourier inversion formula for distribution functions. The model is calibrated for the S and P 500 and is used to analyze several effects on option prices, including interest rate variability, the negative correlation between stock returns and volatility, and the negative correlation between stock returns and interest rates.