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I have been to two different interviews for jobs related to option trading, and both time I have been asked a question, which is pretty basic, and still I could not answer it.

If you have an European call option, with :

  • Expiration : 1 year
  • Volatility : 10%
  • Strike : 100
  • Spot : 100 (at the money)
  • Risk free rates : 0

What is its price? I could not use the BS formula, because I have no calculator. I think I should probably have used a binomial tree, but I didn't find out how.

Thank you for your help

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  • $\begingroup$ possible duplicate of What are some useful approximations to the Black-Scholes formula? $\endgroup$
    – vonjd
    May 19, 2015 at 16:15
  • $\begingroup$ Well it might not be a duplicate, depending on the answer. I am not necessarily asking for an approximation formula, except if that's the only way of solving it. If there is another method to do that, it would not be a duplicate. $\endgroup$
    – Sithered
    May 20, 2015 at 7:12
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    $\begingroup$ So the answer to this question is (from @vonjd in link above) call = put = StockPrice * 0.4 * volatility * Sqrt( Time ) which is 100*0.4*0.1*1 = 4 and since we know the intrinsic value is zero, that's the time value. If the option was in the money then you could add the intrinsic value, and out of the money, well... take off some time value? $\endgroup$
    – rupweb
    May 20, 2015 at 13:49

2 Answers 2

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There is a good quick well-known approximation for at-the-money options: $$\textrm{Call,Put} = 0.4 S \sigma \sqrt{T}.$$ See further discussion at What are some useful approximations to the Black-Scholes formula?.

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I think that you can find the answer to this question here:

http://people.stern.nyu.edu/wsilber/chuang-silber%20approx%20option%20value.pdf

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