option 是关于strike的凸函数，因此如果违背凸性即可套利。

K1<K2

0<a<1

C(a*K1+(1-a)*K2)>a*C(K1)+(1-a)*C(K2)

这个题里面a等于0.5（因为strike正好平分）

6=0.5*5+0.5*7,因此可以套利。

显然本来是小于现在是等于，因此左边高估，右边低估，所以short 高估，long低估。

因为option不能0.5份得买，因此你可以short 2份100的，long一份90＋long 一份110的。

构建了之后，现在你的这个portfolio的value是0

到期的时候无论什么情况发生value应该都为非负，因此实现了套利。

这种策略一般称为butterfly就是利用凸性。

best，

感谢！

xuexile

Note also that a call option is a decreasing function of the strike. Here, it is just the opposite, that is, the option with larger strike has larger value. Therefore, there are arbitrage opportunities.

For example, you can short one call option with the strike 110 and long one call option with the strike 90. You then receive 2$ now. Moreover, at maturity, you receive
(S-90)^+ - (S-110)^+ = max{90, min{S, 110}} - 90 >=0. That is, you can potentially get 20$ at the maturity, if S >= 110, but lose nothing.

thank you very much