One-period ITT

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6/29/14
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We have implied trinomial tree with information: S(0)=50, in period 1 share takes values 60, 40 and 30. Can we determine the price of call option if we are given the price of a put option? Strikes are 50 for call and 30 for put option. Interest rate is 10%.

Now this would be easy to solve if there would be 2 equal strikes with put-call parity equation. But there are two different strikes. Any ideas how to solve this? Thanks.
 
What are you really being given? I already know the price of a put option that never finishes in the money. So do you. And now hopefully you should see what the problem is really asking.
 
I see that the put option is worthless. Thanks, didn't notice that. But I still don't know how to solve this, since the put at 50 (or call) are not worhless? And I have similar exercise with information, S at time zero is again 50, at time one are possible prices: 10, 40 or 60. Same strikes and question. Is this even possible to solve?
 
Isn't the put only necessarily worthless if it expires after period 1? How do you know there isn't a "period 2" when it could fall below 30?
 
That is also true. But it doesn't matter anyway... The exercise says that you know one of the two prices. Let's say for this put with strike 30. How to determine the price for a call with strike 50?
 
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