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Sep 2011, #3

M

MindFull

Ton up Member
Hi All,

I just wanted to verify the answer for the last part of this question. Since the investor has decided to write a call and buy a put, thus removing all risk, the investor will be earning the risk free rate on the investment. I'm a little unsure about this. Is there any other way to solve this? Any help?

Thanks.
 
You could value the components separately, but for [2] marks, you're not going to want to do that.

Between them, the call and put eliminate upside and downside variation, so the investor will get 100,000 no matter what. The PV of this has to be just 100,000 discounted at the risk-free rate.
 
Mike Lewry said:
You could value the components separately, but for [2] marks, you're not going to want to do that.

Between them, the call and put eliminate upside and downside variation, so the investor will get 100,000 no matter what. The PV of this has to be just 100,000 discounted at the risk-free rate.
Click to expand...


hmm.. if we were long in stock, put and short in call, then it'd be a 'collar'.. but if its just long put and short call, then

S<100'000
payoff from put (100'000 - St), payoff from call 0. total payoff is 100'000- St
s>100'000
payoff from put 0, payoff from call - (100'000 - St). total payoff is 100'000 - St.

So both outcomes are the same. but the amount at time it is still not certain but varies with St?
 
i'd therefore multiply by the probability Phi (-d2)?
 
Although it's maybe not 100% clear from the wording, the question says that the investor buys the share, as well as writing a call and buying the put. So, they are long the share and the put and short the call, ie +St + pt - ct.

Hence, if ST < 100, the overall payoff at T is:

+ST + (100 - ST) + 0 = 100

Whereas, if ST > 100, the overall payoff at T is:

+ST + 0 - (ST - 100) = 100

So, they get 100 whatever happens.
 
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