基于几何布朗运动欧式的保护性看跌期权对冲策略及研究.pdf

Study on European Protective
Put Option Hedging Strategies Based on
the Geometric Brownian Motion



A Thesis Submitted to Chongqing University
in Partial Fulfillment of the Requirement for the
Master’s Degree of Science
By
Dongmei Li

Supervised by Ass. Prof. Guanghui Huang
Specialty: Probability and Statistics



College of Mathematics and Statistics of Chongqing
University, Chongqing, China
May, 2014
重庆大学硕士学位论文` 中文摘要

摘要

本文主要研究了利用欧式看跌期权减小股票市场风险造成的损失的对冲策略
问题。
文中假设股票价格变动符合几何布朗运动模型,假设可选的用来对冲风险的
欧式期权的到期日相同,而敲定价格不同。文章主要介绍了两种不同的欧式保护
性看跌期权对冲策略:含有欧式看跌期权到期必然执行和对冲预算资金全部用来
购买看跌期权这两个假设条件的 ABRW 策略和在放松 ABRW 策略中两个假设条件
基础上构造的 UNB 策略。在考虑了期权买卖价差不存在和存在两种情况下,分别
得到了两种 EPPO 投资策略的损失值超过给定最大风险值(𝑉𝑎𝑅)的概率计算的积
分表达式。在置信水平和各种参数值已知时,利用该概率计算公式可以推导出选
择每个欧式看跌期权对冲时投资者的最大风险值,进而比较所有结果,选择使得
最大风险值最小的对冲策略为最优的策略。
通过模拟参数变动实验,得到了四组因素的 7 个参数影响下 ABRW 策略和
UNB 策略的最小𝑉𝑎𝑅和实际对冲花费。由模拟实验结果图表推出:放松两个假设
条件构造的 UNB 策略更符合实际情况,可以减少投资者的损失值,更有利于投资
者对冲股票风险。

关键词:风险管理,欧式保护性看跌期权对冲策略,流动性风险,买卖价差,几
何布朗运动

I
重庆大学硕士学位论文英文摘要

ABSTRACT

The problem of hedging strategies is studied in this paper, where an European put
option is used to reduce the lose for the market risk of stock.
It is assumed that the mathematical model of stock price is chosen to be a
geometric Brown motion and the available European options which are used to hedge
risk are specified by the same maturity time and the different strike price in this paper.
Two different European protective put option hedging strategies are introduced, one is
ABRW strategy, which contains that the European put option is supposed to always
finished-in-the-money at maturity and all the hedge budget funds is supposed to buy put
options, the else is UNB strategy which bases on the former strategy and relaxes the two
assumptions in it. With and without the consideration of the bid-ask spread, the Integral
expressions of the probability that the loss exceeds a given maximu