金融经济学4.pdf

金融经济学
利用期权完备化市场:简单介绍
2011-09-20
期权的定义
A call option is A put option is
an option to buy an option to sell
a certain asset a certain asset
by a certain date by a certain date
for a certain for a certain
price price
Options, Futures, and Other Derivatives, by John C. Hull
有关的名词
Underlying asset
Maturity(Expiration)
date
Exercise(Strike )price
European or American
options
Option writer
3
Payoff of Call option at exercise time. Payoff of Put option at exercise time.
4
有关的名词
Intrinsic Value
. At-the-money option
. In-the-money option
. Out-of-the-money option
5
Ways Derivatives are Used
 To hedge risks
 To speculate (take a view on the future
direction of the market)
 To lock in an arbitrage profit
 To change the nature of a liability
 To change the nature of an investment
without incurring the costs of selling
one portfolio and buying another
Options, Futures, and Other Derivatives, by John C. Hull
6
举例:看跌期权的保险功能
考察投资组合:一只股票和一份以该股票为标的的执行价格为K 的卖权;
S₁≤ K S₁≥ K
股票支付 S₁ S₁
期权支付 K-S₁ 0
投资组合的支付 K S₁
7
股票期权价格的几个性质
记号:
S :股票0期的价格; :股票1期的价格(支付);
c(S,K)(p(S,K)): 执行价格为 K 的欧式看涨(看跌)期权的价格;
:无风险利率;
性质1:S ≥ c(S,K) ≥ 0;
性质2: c(S,K)关于S 非降,关于 K 非增;
性质3: c(S,K) 是关于K 的凸函数;
性质4:以组合资产为标的的期权价格要小于以组合中的单个
证券为标的资产的相应期权的组合的价值,即
8
股票期权的几个性质
性质5 :欧式看涨期权价格的上下界:
性质6: Put-Call Parity,
9
完全市场中欧式期权定价:套利定价的典型例子
风险中性定价公式:
二叉树模型:假设市场中存在无风险证券及价格过程如下的
风险证券(u > d)
uS
p
S
1-p
dS
注:市场无套利⇒
10