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Stock price is $15 today. In a year, it has 50%-50% chances of going up or down. If it goes up, then 80% probability of the price being $25. If it goes down, then there is a 40% probability of price being $5 and a 60% probability of it being $0. Find the price of a call option at strike $25.

My approach:

I think I should, first of all, find the value of the stock on the up branch of the tree that happens with a probability of 0.2. I don't know though how to find such value.

I thought to include in the reasoning the formulas of $p,u,d$ of the tree, but it doesn't seem to help.

This is the tree I am talking about. Nevertheless, in this problem, the tree should have only one node so $n=1$, and since the maturity is 1 year, t should also be 1, $t=1$

D Stanley
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Mining
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1 Answers1

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If this is a theoretical homework problem then I have no clue what the answer is. In the real world, option pricing is based on six option pricing variables:

  • stock price

  • strike price

  • time remaining until expiration

  • dividend, if any

  • carry cost

  • volatility

In your example, the first five are known values today. Volatility is the wild card. Without it, you can't accurately price the option using an option pricing model to calculate fair value.

Bob Baerker
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