The GARCH Option Pricing Model: A Modification of Lattice Approach

Ritchken and Trevor (1999) proposed a lattice approach for pricing American options under discrete time-varying volatility GARCH frameworks. Even though the lattice approach worked well for the pricing of the GARCH options, it was inappropriate when the option price was computed on the lattice using standard backward recursive procedures, even if the concepts of Cakici and Topyan (2000) were incorporated. This paper shows how to correct the deficiency and that with our adjustment, the lattice method performs properly for option pricing under the GARCH process. JEL Classification: C10, C32, C51, F37, G12     

On option pricing in binomial market with transaction costs

Option replication is studied in a discrete-time framework with proportional transaction costs. The model represents an extension of the Cox-Ross-Rubinstein binomial option-pricing model to cover the case of proportional transaction costs for one risky asset with different interest rates on bank credit and deposit. Contingent claims are supposed to be 2-dimensional random variables. Explicit formulas for self-financing strategies are obtained for this case.Received: March 2004, Mathematics Subject Classification (2000): 62P05JEL Classification: G11, G13The authors are grateful to an anonymous referee for numerous helpful comments and to Yulia Romaniuk for final corrections. The paper was partially supported by grant NSERC 264186.     

Fast accurate binomial pricing

We discuss here an alternative interpretation of the familiar binomial lattice approach to option pricing, illustrating it with reference to pricing of barrier options, one- and two-sided, with fixed, moving or partial barriers, and also the pricing of American put options. It has often been observed that if one tries to price a barrier option using a binomial lattice, then one can find slow convergence to the true price unless care is taken over the placing of the grid points in the lattice; see, for example, the work of Boyle & Lau [2]. The placing of grid points is critical whether one uses a dynamic programming approach, or a Monte Carlo approach, and this can make it difficult to compute hedge ratios, for example. The problems arise from translating a crossing of the barrier for the continuous diffusion process into an event for the binomial approximation. In this article, we show that it is not necessary to make clever choices of the grid positioning, and by interpreting the nature of the binomial approximation appropriately, we are able to derive very quick and accurate pricings of barrier options. The interpretation we give here is applicable much more widely, and helps to smooth out the ‘odd-even’ ripples in the option price as a function of time-to-go which are a common feature of binomial lattice pricing.     

文化距离、海外华人网络与中国企业对外直接投资区位选择

本文利用企业层面对外直接投资项目面板数据,采用负二项回归模型实证考察了文化距离与东道国华人网络对中国企业对外直接区位选择的影响。实证研究发现,东道国与中国文化距离的增加对中国企业对外直接投资有显著的抑制作用,但东道国华人网络对中国企业对外直接投资有显著的促进作用。文章最后对研究的理论价值和实践意义进行了讨论。     

活力度分级法在天津空港经济区行道树健康评价中的应用

树木活力度分级评价方法被作为主要评价方法,对天津空港经济区10种主要行道树的生长态势进行了分级和统计,结果显示:空港经济区主要行道树的活力度以4级为主,3级和5级次之,1级和2级较少,反映出该区域行道树生长态势总体情况较差。在此基础上,提出行道树养护管理建议,并对活力度分级评价方法的应用进行了展望,为将来的行道树分级和绿化管理提供了有益的参考。     

Using regression tree ensembles to model interaction effects: a graphical approach

Multiplicative interaction terms are widely used in economics to identify heterogeneous effects and to tailor policy recommendations. The execution of these models is often flawed due to specification and interpretation errors. This article introduces regression trees and regression tree ensembles to model and visualize interaction effects. Tree-based methods include interactions by construction and in a nonlinear manner. Visualizing nonlinear interaction effects in a way that can be easily read overcomes common interpretation errors. We apply the proposed approach to two different datasets to illustrate its usefulness.     

Martingales and Portfolio Decisions: A User’s Guide

This article gives an overview and introduction to the Martingale approach to multi-period (dynamic) portfolio decisions. While Martingale pricing techniques have long been used with considerable success in the pricing of derivatives and financial assets in general, their potential to improve the practice of dynamic portfolio decisions is not sufficiently recognized yet. This article shows that the approach is, in principle, not difficult to implement for readers equipped with standard option replication techniques if markets are sufficiently “complete” in order to provide investors with the relevant information about the pricing of financial risks. The article provides a practical guide to implement the basic features of the approach in a binomial framework.     

Efficient Calibration of Trinomial Trees for One-Factor Short Rate Models

In this paper we propose a computationally efficient implementation of general one factor short rate models with a trinomial tree. We improve the Hull–Whites procedure to calibrate the tree to bond prices by circumventing the forward rate induction and numerical root search algorithms. Our calibration procedure is based on forward measure changes and is as general as the Hull–White procedure, but it offers a more efficient and flexible method of constructing a trinomial term structure model. It can be easily implemented and calibrated to both prices and volatilities. JEL classification G13, C6