Path Dependent Options: "Buy at the Low, Sell at the High"
Path Dependent Options: "Buy at the Low, Sell at the High"
复制标题
DOI：
10.1111/j.1540-6261.1979.tb00059.x
复制
发表时间：
1979-12
影响因子：
8
通讯作者：
M. Goldman;Howard B. Sosin;M. A. Gatto
中科院分区：
文献类型：
--
作者：
M. Goldman;Howard B. Sosin;M. A. Gatto
行使价完全取决于相关股票的最终价格的分布。本文研究了欧式期权的性质，其执行价格是股票的已实现样本路径的函数。具体地说，普通股东“在低位买入”，在高位卖出”的愿望可以通过一个看涨期权和一个看跌期权的组合来满足，看涨期权的执行价格等于mino. TS（r），看跌期权的执行价格等于maxo. TS（T），其中S是股票价格，T是期权的期限。严格地说，在无摩擦的情况下创造这些新的选择不会扩大投资者的机会。然而，在现实的市场环境中，这种新的选择很可能获得相当大的普及。这一呼吁有三个方面：（1）期权将保证投资者在低位买入并在高位卖出的幻想，（2）期权将在某种松散的直觉意义上将后悔减到最小，（3）期权将允许投资者在范围上有特殊信息（但可能没有关于最终股票价格的特殊信息）直接利用这些信息。在本文中，我们分析了这些期权的套期保值，定价和经济特性。只要有可能，我们就会将这些选项与传统选项进行比较和对比。在第二节中，我们建立了这些期权可以套期保值，并存在封闭形式的估值方程。这里特别强调的是当股票处于极值时这些期权的套期保值能力（即，等于其当前最大值或最小值）。第三部分通过分析和模拟，建立了这些期权的性质，并与传统期权进行了比较。特别是，我们研究：（1）这些期权关于两个状态变量--股票价格和到期时间的函数依赖性;（2）这些期权相对于股票和传统期权在开始时的定价。由于第二节中给出的一般定价关系的笨拙性，我们发现在第三节中，对于股票的调整后几何平均收益率的对数为零的特别直观的情况，我们可以方便地对这些期权的性质进行详细的分析和明确的推导。然后，我们通过模拟说明，定性地，我们的具体例子的结果结转到一般情况下。我们在第四节结束时对路径依赖期权进行了一般性讨论。
exercise prices is solely dependent on the distribution of the terminal price of the underlying stock. This paper examines the properties of European options with exercise prices that are functions of the realized sample path of the stock. In particular, the commonplace shareholder desire to "buy at the low" and sell at the high" can be satisfied with a combination of a call on the stock with an exercise price equal to mino.T S(r) and a put with exercise price equal to maxo,TS(T) where S is the stock price and T is the term of the option.' Strictly speaking, the creation of these new options in a frictionless context would not expand the investor's opportunity set. However, in a realistic market setting such new options might very well acquire substantial popularity. The appeal would be threefold: (1) the options would guarantee the investor's fantasy of buying at the low and selling at the high, (2) the options would, in some loose intuitive sense, minimize regret, and (3) the options would allow investors with special information on the range (but possibly without special information on the terminal stock price) to directly take advantage of such information. In this paper we analyze the hedging, pricing, and economic properties of these options. Wherever possible we compare and contrast these options with their traditional counterparts. In section two we establish that these options can be hedged and that closed-form valuation equations exist. Particular emphasis here centers on the hedgeability of these options when the stock is at an extremum (i.e., equal to its current maximum or minimum). In section three, by analysis and simulation, we establish the properties of these options and contrast them with those of their traditional counterparts. In particular we examine: (1) the functional dependence of these options with respect to two state variables-stock price and time to expiration, and (2) the pricing of these options relative to the stock and traditional options at the time of inception. Due to the ungainliness of the general pricing relations developed in section two, we found it convenient throughout section three to provide detailed analyses and explicit derivations of the properties of these options for the particularly intuitive case where the logarithm of the adjusted geometric mean return of the stock is zero. We then illustrate by simulation that, qualitatively, the results of our specific example carry over to the general case. We conclude in section four with a general discussion of path-dependent options.