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Q: A stock has a current price 40. The continuous annual risk free rate is 2%. An investor wishes to create a purchased collar using options with maturity T = 0.25. Which of the following strike prices cannot be used for the put in the collar?

A) 38.37
B) 39.93
C) 40.01
D) 40.20
E) 41

A: E) 41

Reason: Put price in the collar must be less or equal to the forward priceof 40*exp(0.02*0.25)=40.2005

为什么啊？不明白他的解释？

或者谁有别的办法做这个题？

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关键词：urgent Continuous following purchase Investor continuous following investor current forward

The expected stock price in t=0.25 should be 40*exp(0.02*0.25)=40.2005,   Purchased put is the insurance against the decrease in the price in the future t=0.25.  If u set the strike price lower than 40.2005, u r actually buying an negative payoff 40.2005-41= -0.7995.

COLLAR的最极端就是当C和P的strike price是一样的时候。

然后参考公式：C-P=PV(FV-exercise price)

求出了FV是40.2左右，如果exercise price大于40.2，那等式就是负数了，就起不到collar的作用了~不成立~纯粹个人理解~~~

collar是買的, net financing cost>=0
最少是當FV=K
如果K>FV, C-P<0, 即是你的cost是負數了

thanks all. get it.