NO.PZ2016031202000024
问题如下:
Assume the exercise price=$20, risk free rate=3%, the expiration=0.5, and the spot price of the underlying=$30, the minimum price of American call is:
选项:
A.
$10.29
B.
$10
C.
$0
解释:
A is correct. The minimum European call price was calculated as 10.29 in previous question, the exercise value of American call is Max(0,30-20)=10. The value of American call should be greater than European call, so the minimum value of the American call is 10.29
中文解析:
美式期权和欧式期权不同,美式期权任何时间都可以行权,欧式期权只能在到期日行权。所以美式期权的call option的价值要大于欧式期权的。
美式随时可行权,这里直接用30-20表示今天就行权的价值。而欧式只能到期的时候再行权,期权的最小价值就是到期日价值再折现到今天;即=(ST-X)/(1+Rf T)=S0-X/(1+Rf T)(ST折现到0时刻=S0),计算结果为10.29。
因为美式期权的call option的价值要大于欧式期权的,虽然用30-20算出来的是10,但是还是要取欧式期权的最小价值10.29。
ST-X)/(1+Rf T)=S0-X/(1+Rf T)(ST折现到0时刻=S0),计算结果为10.29。 这个具体是怎么带入数字得到的?