AN EQUILIBRIUM GUIDE TO DESIGNING AFFINE PRICING MODELS

The paper examines equilibrium models based on Epstein–Zin preferences in a framework in which exogenous state variables follow affine jump diffusion processes. A main insight is that the equilibrium asset prices can be computed using a standard machinery of affine asset pricing theory by imposing parametric restrictions on market prices of risk, determined inside the model by preference and model parameters. An appealing characteristic of the general equilibrium setup is that the state variables have an intuitive and testable interpretation as driving the consumption and dividend dynamics. We present a detailed example where large shocks (jumps) in consumption volatility translate into negative jumps in equilibrium prices of the assets as agents demand a higher premium to compensate for higher risks. This endogenous “leverage effect,” which is purely an equilibrium outcome in the economy, leads to significant premiums for out‐of‐the‐money put options. Our model is thus able to produce an equilibrium “volatility smirk,” which realistically mimics that observed for index options.     

运用期权定价模型评估公司价值

本着把期权思想应用于公司价值评估,分别运用二叉树模型和Black-Scholes模型计算公司价值,并对这一方法的应用价值及局限性进行一定的探讨。     

A Nonstandard Approach to Option Pricing

Nonstandard probability theory and stochastic analysis, as developed by Loeb, Anderson, and Keisler, has the attractive feature that it allows one to exploit combinatorial aspects of a well-understood discrete theory in a continuous setting. We illustrate this with an example taken from financial economics: a nonstandard construction of the well-known Black-Scholes option pricing model allows us to view the resulting object at the same time as both (the hyperfinite version of) the binomial Cox-Ross-Rubinstein model (that is, a hyperfinite geometric random walk) and the continuous model introduced by Black and Scholes (a geometric Brownian motion). Nonstandard methods provide a means of moving freely back and forth between the discrete and continuous points of view. This enables us to give an elementary derivation of the Black-Scholes option pricing formula from the corresponding formula for the binomial model. We also devise an intuitive but rigorous method for constructing self-financing hedge portfolios for various contingent claims, again using the explicit constructions available in the hyperfinite binomial model, to give the portfolio appropriate to the Black-Scholes model. Thus, nonstandard analysis provides a rigorous basis for the economists' intuitive notion that the Black-Scholes model contains a built-in version of the Cox-Ross-Rubinstein model.     

存款保险的期权定价模型构造及实证研究

存款保险定价是存款保险制度建设中的核心内容,保险定价效率直接影响制度的功效。碍于现金流贴现估价模型的局限性,从期权的角度阐述了存款保险与期权的关系,指出存款保险合同实质上就是一份看跌期权,从理论和实证两方面论述了如何运用Black-Schole期权定价模型确定存款保险价格的问题,对实践中存款保险的合理定价和制度建设具有重要的指导意义。     

投资决策理论新发展——实物期权理论研究综述

投资决策,即公司资源最优配置的选择问题,欧美等国理论研究者、实务工作者已开始将实物期权理论(即实际投资机会)引入到投资决策的实践中,并取得了一定的成果。本文详细介绍了国外经济学者在基于实物期权理论的投资决策等领域的研究进展,包括实物期权的理论基础及定价、该理论与传统投资决策理论的比较研究等,以期为国内后续的相关研究和实践提供借鉴。     

二叉树方法在风险投资决策中的应用

在过去的20年中,许多学者开始应用期权定价方法去估计实物资产价值,并在此基础上对公司的最优投资决策进行了大量研究。利用二叉树方法,通过对一个欧式期权与一个美式期权构成的复合期权进行定价,完成对风险投资问题的估价。主要有两个方面的内容:用实例说明怎样用二叉树方法对投资期权进行估价;把从期权模型获得的价值与用净现值方法得到的价值相关联,从而获得风险投资的最终的价值。     

企业投资决策的实物期权方法分析

在现代市场经济条件下,传统的投资决策方法已经不能适应于环境不确定而产生的动态投资管理的需要,因而,一种全新的投资决策分析工具———实物期权方法应运而生,在面对较大的环境不确定性情况下,实物期权方法则显得更为有效和科学。     

基于实物期权理论的风险投资项目评价

期权理论在金融领域的应用十分广泛,实物期权理论也被用于企业投资项目评价之中。针对风险投资项目的特殊性,以期权理论为基础,阐述风险投资项目的期权特征,进而以实例分析Black—Scholes期权定价模型在风险投资项目评价中的应用,并与NPV法所得出的结果进行对比,从而达到对投资和管理进行决策的目的。     

Generic Existence and Robust Nonexistence of Numéraires in Finite Dimensional Securities Markets

A numéraire is a portfolio that, if prices and dividends are denominated in its units, admits an equivalent martingale measure that transforms all gains processes into martingales. We first supply a necessary and sufficient condition for the generic existence of numéraires in a finite dimensional setting. We then characterize the arbitrage‐free prices and dividends for which the absence of numéraires survives any small perturbation preserving no arbitrage. Finally, we identify the cases when any small, but otherwise arbitrary, perturbation of prices and dividends preserves either the existence of numéraires, or their nonexistence under no arbitrage.     

Option Pricing in ARCH-type Models

ARCH models have become popular for modeling financial time series. They seem, at first, however, to be incompatible with the option pricing approach of Black, Scholes, Merton et al., because they are discrete-time models and possess too much variability. We show that completeness of the market holds for a broad class of ARCH-type models defined in a suitable continuous-time fashion. As an example we focus on the GARCH(1,1)-M model and obtain, through our method, the same pricing formula as Duan, who applied equilibrium-type arguments.     

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.     

THE RANGE OF TRADED OPTION PRICES

Suppose we are given a set of prices of European call options over a finite range of strike prices and exercise times, written on a financial asset with deterministic dividends which is traded in a frictionless market with no interest rate volatility. We ask: when is there an arbitrage opportunity? We give conditions for the prices to be consistent with an arbitrage-free model (in which case the model can be realized on a finite probability space). We also give conditions for there to exist an arbitrage opportunity which can be locked in at time zero. There is also a third boundary case in which prices are recognizably misspecified, but the ability to take advantage of an arbitrage opportunity depends upon knowledge of the null sets of the model.     

论政府价格规制中的公众参与

在政府价格规制中引入公众参与机制有利于价格规制政策的制定。本文基于规制经济理论的分析框架,运用博弈论模拟了公众参与价格规制的讨价还价过程。政府在价格规制中引入公众参与机制,其形式取决于政策质量和公众接受程度两者的权衡。在此基础上对当前我国公用事业价格规制中存在的问题进行分析,并提出政策建议。     

ANALYTICAL COMPARISONS OF OPTION PRICES IN STOCHASTIC VOLATILITY MODELS

This paper gives an ordering on option prices under various well-known martingale measures in an incomplete stochastic volatility model. Our central result is a comparison theorem that proves convex option prices are decreasing in the market price of volatility risk, the parameter governing the choice of pricing measure. The theorem is applied to order option prices under q -optimal pricing measures. In doing so, we correct orderings demonstrated numerically in Heath, Platen, and Schweizer ( Mathematical Finance , 11(4), 2001) in the special case of the Heston model.     

Feeder Cattle Options: Where’s the Beef?

Feeder cattle is one of the most important commodities in the livestock industry worldwide. Nonetheless, beef production is subject to many uncertainties; therefore, the risk management tools that agents use must be efficient. This article discusses the financial options available in the Brazilian futures market to feeder cattle producers and describes the best risk pricing model to determine the option premium. Our results consider several option pricing models and different types of volatility. The best pricing is obtained with the model of Bjerksund and Stensland with the implied volatility.     

美式封顶看涨期权的变分不等方程模型

期权及其定价理论是目前金融工程的前沿问题。美式看涨期权的出售者具有无限制的义务,承担着巨大的风险,而美式封顶看涨期权可以使出售者承担有限责任,降低了风险。本文在假定无风险利率r不大于连续红利q时,基于Black-Scholes模型推导出有红利的美式封顶看涨期权定价模型-变分不等方程模型,并且用有限差分格式给出了模型的数值解法。     

THE EARLY EXERCISE PREMIUM REPRESENTATION OF FOREIGN MARKET AMERICAN OPTIONS1

The note deals with the pricing of American options related to foreign market equities. the form of the early exercise premium representation of the American option's price in a stochastic interest rate economy is established. Subsequently, the American fixed exchange rate foreign equity option and the American equity-linked foreign exchange option are studied in detail.