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- Jan 30th 2014, 06:55 AM #1

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## Help please

Hi all,

I am struggling with the following:

an investor is considering a call option on the shares of XYZ. the strike price is 510p and the option can only be exercised in exactly 2 months time. at the moment the share price of XYZ is 500p.

in 2 months time the value of the option = Max[shareprice-510,0]

-during the first month the investor believes that the probability the share increases by5% is 0.35, the probability that it increases by 2% is 0.5 and the probability the share falls by 4% is 0.15.

- In The second month the investor believes that the probability the share increases by 4% is 0.3, the probability that it increases by 1% is 0.45 and the probability the share falls by 3% is 0.25

Calculate the price the investor is willing to pay for the option assuming they want to make 3% expected return over the period.

What I did is... I calculate the using a tree graph the expected return that is 11.177 and that is a return of 2.2%.

My problem here is that I need to get the fair price, knowing the expected return... so I need to do exactly the opposite.

What is the formula to do that? and also Can anyone explain how to do that?

Thanks

- Jan 30th 2014, 08:53 AM #2

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- Jan 30th 2014, 09:19 AM #3

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## Re: Help please

Hi Romsek,

I am not so sure about what you are saying. The question is "Calculate the price the investor is willing to pay for the option assuming they want to make 3% expected return over the period."

So it's the option price not the share price. What I did is in the picture

If you multiply all the value options by the probabilities (second column from the right hand side of the picture) and sum them all up you get 11.1769. (In some cases the option value is 0 as the price is lower than the strike price)

Also the investor can buy the option exactly after 2 months and not before.

So I was thinking that I need to do:

11.1769/(1-0.03)=10.8513

What do you think?Am I completely wrong?

Thanks for your help

- Jan 30th 2014, 09:38 AM #4

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