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September 25th, 2008, 10:28 AM   #1
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Probability task - please help me

U're a shop assistant and U sell the gold. I wanna buy from U 100 kilograms of gold, but I don't have to do it.
I know, that the price can change after one day. So I would like U to establish/agree on the price now. I will go to U tomorrow and I'll buy gold for today's established price.
It's true, that I always can profit from this operation.
So u said that I should pay today some amount of money. Let's mark the var X as amount of that money. X will be the expected value of the profit made by me.
I pay for U today X money and I agree on with U the price I'll buy gold tomorrow.
If I come tomorrow, U will give me the gold for the price, we agreeded on. If I don't come, U will give me nothing (U don't give me back the X money too).

We know, that today the price of gold is 80$
The price could decrease to 60$ tommorow (with probability 1/2) or it could increase to 120$ (with probability 1/2)
WE agree on, that tomorrow, U will sell the gold for me for 82$.
How much should be the X value?

Answer: X=19

Could U explain me why the correct answer is 19?

If U don't understand my translation of task, please write here, i'll try rewrite it
Thanks in the advance
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September 25th, 2008, 01:49 PM   #2
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Re: Probability task - please help me

Quote:
Originally Posted by Powermonster
U're a shop assistant and U sell the gold. I wanna buy from U 100 kilograms of gold, but I don't have to do it.
I know, that the price can change after one day. So I would like U to establish/agree on the price now. I will go to U tomorrow and I'll buy gold for today's established price.
It's true, that I always can profit from this operation.
So u said that I should pay today some amount of money. Let's mark the var X as amount of that money. X will be the expected value of the profit made by me.
I pay for U today X money and I agree on with U the price I'll buy gold tomorrow.
If I come tomorrow, U will give me the gold for the price, we agreeded on. If I don't come, U will give me nothing (U don't give me back the X money too).

We know, that today the price of gold is 80$
The price could decrease to 60$ tommorow (with probability 1/2) or it could increase to 120$ (with probability 1/2)
WE agree on, that tomorrow, U will sell the gold for me for 82$.

Answer: X=19

Could U explain me why the correct answer is 19?

If U don't understand my translation of task, please write here, i'll try rewrite it
Thanks in the advance
120-82=38. You have a prob. of 1/2 to make 38. By putting up 19, you have prob. of 1/2 of making an extra 19. You have a prob. of 1/2 of losing 19. Thus it is like an even money bet.

To put it another way you are betting 19. If you win you get 38. If you lose you get 0.
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September 25th, 2008, 03:41 PM   #3
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Re: Probability task - please help me

19 is not quite right because of the time value of money

the answer is the present value of 19 (which at a 1-day interval is very close)
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September 26th, 2008, 04:07 AM   #4
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Re: Probability task - please help me

ok, now i understand the part of this solution. I know what should I do when the probability of increasing and decreasing is the same (1/2).
But what should I do with this task:

We know, that today the price of gold is A
The price could decrease to B tommorow (with probability 1-P) or it could increase to C (with probability P)
WE agree on, that after D days, you will sell the gold for me for Q
How can i answer this?
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September 26th, 2008, 06:18 AM   #5
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Re: Probability task - please help me

what you are describing is a call option

The value of the option is the present value of the expecation at the maturity of the contract

This might be helpful:

http://en.wikipedia.org/wiki/Option_(finance)
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September 26th, 2008, 08:18 AM   #6
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Re: Probability task - please help me

my english isn't so good to understand whole text. Thanks for a link, but I only understand the part of all.
Could U write how can I calcutale my data in my task?
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