Lookback options and diffusion hitting times: A spectral expansion approach

Lookback options have payoffs dependent on the maximum and/or minimum of the underlying price attained during the options lifetime. Based on the relationship between diffusion maximum and minimum and hitting times and the spectral decomposition of diffusion hitting times, this paper gives an analytical characterization of lookback option prices in terms of spectral expansions. In particular, analytical solutions for lookback options under the constant elasticity of variance (CEV) diffusion are obtained.Received: 1 October 2003, Mathematics Subject Classification: 60J35, 60J60, 60G70JEL Classification: G13The author thanks Phelim Boyle for bringing the problem of pricing lookback options under the CEV process to his attention and for useful discussions and Viatcheslav Gorovoi for computational assistance. This research was supported by the U.S. National Science Foundation under grants DMI-0200429 and DMS-0223354.     

Understanding the Implied Volatility Surface for Options on a Diversified Index

This paper describes a two-factor model for a diversified index that attempts to explain both the leverage effect and the implied volatility skews that are characteristic of index options. Our formulation is based on an analysis of the growth optimal portfolio and a corresponding random market activity time where the discounted growth optimal portfolio is expressed as a time transformed squared Bessel process of dimension four. It turns out that for this index model an equivalent risk neutral martingale measure does not exist because the corresponding Radon-Nikodym derivative process is a strict local martingale. However, a consistent pricing and hedging framework is established by using the benchmark approach. The proposed model, which includes a random initial condition for market activity, generates implied volatility surfaces for European call and put options that are typically observed in real markets. The paper also examines the price differences of binary options for the proposed model and their Black-Scholes counterparts. Mathematics Subject Classification: primary 90A12; secondary 60G30; 62P20 JEL Classification: G10, G13     

The Walk‐down to Beatable Analyst Forecasts: The Role of Equity Issuance and Insider Trading Incentives*

It has been alleged that firms and analysts engage in an "earnings‐guidance game" where analysts first issue optimistic earnings forecasts and then "walk down" their estimates to a level that firms can beat at the official earnings announcement. We examine whether the walk‐down to beatable targets is associated with managerial incentives to sell stock after earnings announcements on the firm's behalf (through new equity issuance) or from their personal accounts (through option exercises and stock sales). Consistent with these hypotheses, we find that the walk‐down to beatable targets is most pronounced when firms or insiders are net sellers of stock after an earnings announcement. These findings provide new insights on the impact of capital‐market incentives on communications between managers and analysts.     

A Note on the Joint Distribution of α, β-Percentiles and Its Application to the Option Pricing

In this paper, using Laplace transform, we will calculate the joint density of twopercentiles of stock prices in the Black–Sholes model and make the price of exchange options of such twopercentiles.     

商业银行股权激励的特殊意义与现实问题分析

银行业普遍存在的管制,使银行面临着有限的控制权市场和接管威胁,从而大大降低了市场约束银行管理者的能力,因此对银行而言,通过股权激励机制协调股东和管理者的利益、降低代理成本显得尤为重要.我国商业银行实施股权激励不应盲目照搬西方国家的范例,应慎重选择股权激励的实施范围,目前最好只局限在高级管理人员,通过对股权激励机制的合理设计来充分发挥其长期激励效应,切不可盲目扩大激励范围,将股权激励演变成一种新的福利措施.应尽快建立起以经济资本为核心的业绩考核体系,在经济资本的约束下实现业务发展模式和盈利模式的转变.股权激励机制的有效实施离不开完善的银行治理结构.     

Stickiness of Rental Rates and Developers’ Option Exercise Strategies

In this study we incorporate sticky rents into a real options model to rationalize the widely documented overbuilding puzzle in real estate markets. Given the assumption that developers’ objective function is to maximize total revenue by selecting an optimal occupancy level, our model provides a better explanation of the phenomena we observed in the real world than the traditional market-clearance based real options models. We also show that developers’ exercise strategies can be affected by the size and the type of property markets. In other words, developers’ exercise strategies could differ among markets and under different conditions. Submitted to Cambridge—Maastricht 2005 Symposium.     

Sequential American Exchange Property Options

Property development activities often occur in stages, which are appropriately modeled as sequential American exchange property options, where there are interim expenditures required in order to keep the property development options “alive”. Normally American exchange options require a numerical solution, but herein there is a new closed-form approximate solution, which is computationally efficient and accurate. This method combines repeats of Margrabe European exchange and Geske compound option solutions with tight upper boundaries of either American perpetuities or European exchange options with a high volatility. Illustrations are provided of the sensitivity of the real sequential options and optimal timing to changes in several parameters, which provide a framework for property policy (tax, subsidy and regulatory) guidelines and for property development strategy evaluation. There are several plausible applications of these real option models in commercial and residential property development, within commercial property leases, with regard to switching tenants, and agricultural alternatives.     

Investment decisions in the wireless industry applying real options

The wireless industry is one of the most capital intensive high-technology industries. This paper applies real options techniques to estimate investments under uncertainty in two new ventures: (a) deferral of the expansion from 2.5G to 3G networks; and (b) expansion of a 2.5G network using Wi-Fi as an alternative technology. The cases are examined and analyzed both qualitatively and quantitatively, using realistic assumptions and parameters. Investment cost, number of subscribers, pricing of services, and risk are at the core of investment decision processing. In both cases, sensitivity analysis of the value of the (real) option considering the above key parameters was conducted, to extrapolate useful findings that should be taken into consideration by the decision makers in wireless companies.     

Optimal investment and production decisions and the value of the firm

We explore the effects of uncertainty on a firm that can respond by modifying its investment or production schedule (or both simultaneously) to variations in output price. Investment may increase capacity and/or reduce costs. We consider a firm with finite resources.Our model uses option theory instead of the more traditional net present value framework. One of the early papers using this approach is Brennan and Schwartz (1985) in which an investment project to extract a finite natural resource is valued. In that paper, the value of the firm is a function of two state variables, the finite resource to be extracted (output to be produced in the future) and the commodity spot price. In order to maximize firm value, the manager can respond by modifying one control variable, the production level. In our model we handle instead three state variables (spot price, resources, accumulated investment) and two control variables (production rate and investment rate), and solve numerically.We obtain both the value and the optimal policy of a firm that has investment projects that increase capacity and/or reduce costs and illustrate optimal policies as resources and available investments decrease over the life of the firm. Firms may start by only investing, then invest and produce, to end only producing.We thank Scott Wo, the referee and the editor for their comments and suggestions. Cortázar and Lowener acknowledge the financial support from FONDECYT and FONDER.     

The effects of newly listed derivatives in a thin stock market

This study examines the informational feedback effects associated to the listing and trading of derivatives in Switzerland. The observed changes in the price and higher moments of stock returns are representative of a thin stock market. The listing of stock options and index futures generated positive abnormal returns for large stocks and for the index while small stocks essentially benefited from the launching of index options. While reducing the variance of blue chips and of the index, their variance's stochasticity increased (decreased) at index options' (futures) listings. Finally, we detect significant stock and index derivatives' price leads which do not however generate arbitrage opportunities.