关于barrier option

问题如下：

A trader writes the following 1-year European-style barrier options as protection against large movements in a non-dividend paying stock that is currently trading at EUR 40.96.

All of the options have the same strike price. Assuming the risk-free rate is 2% per annum, what is the common strike price of these options?

选项：

A.

EUR 39.00

B.

EUR 40.00

C.

EUR 41.00

D.

EUR 42.00

解释：

The sum of the price of an up-and-in barrier call and an up-and-out barrier call is the price of an otherwise equivalent European call. The price of the European call is EUR 3.52 + EUR 1.24 = EUR 4.76.

The sum of the price of a down-and-in barrier put and a down-and-out barrier put is the price of an otherwise equivalent European put. The price of the European put is EUR 2.00 + EUR 1.01 = EUR 3.01.

Using put-call parity, where C represents the price of a call option and P the price of a put option,

Hence, K = e^0.02 × (3.01+ 40.96 – 4.76) = 40.00