题目
Consider a one-year barrier call option on a non-dividend-paying stock with a volatility of 30.0% per annum when the stock's price is $25.00 and the option's strike price is $20.00. The risk-free rate is 3.0%. The price of a regular call (i.e., without the barrier) in this case is $6.32. This barrier option has a barrier at $18.00 such that, if it is a knock-in (aka, down-and-in) its price is only $0.22. Each of the following statements is true (or at least plausible!) EXCEPT which statement must be false?
选项
A.The corresponding knock-out (aka, down-and-in) must have a price of about $6.10
B.If the barrier is increased to $22.00, then the price of this knock-in must be higher than $0.22
C.If the barrier is increased to $22.00, then the price of the corresponding knock-out must be lower than $6.10
D.If the barrier is increased to $28.00, then the price of this knock-in will be $6.32 and the price of the corresponding knock-out will be zero
答案
D
解析
When S = $25.00, K = $20.00 and H = $28.00, the up-and-in call option price is about $5.96 and the corresponding up-and-out call option price is $6.32 - $5.96 =$0.36.这道题实际上通过障碍线的变动，去分析期权的价值状态就可以，无需进行计算。答案中的向上敲入式看涨期权价格5.96实际上是通过计算得出来的（BSM模型的衍生），十分复杂，FRM考试中不考察此类计算。