# How to construct the binomial model for European option?

The annual interest rate is 5.3% and the annualized volatility of a non-dividend paying stock over the next six months will be 12.5% (annualized). i) Construct binomial trees of 5, 10 and 30 periods to calculate the value of a European-style 6-month call option with strike price 8.3% above today's spot price. ii)Calculate the corresponding Deltas in the three cases.

Well for the above problem, I stuck at how to construct the binomial tree model. For reference my knowledge of binomial tree model for stock option is the first 4 chapter of Shreve- Stochastic Calculus for finance.In his book, whenever he wants to construct a binomial model, he always have a up (u) factor, and down (d) factor for stock price, thus you can have the model pretty easily. In this problem, I am given the volatility, thus I have no idea how to start. Please help .

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In the case that volatility is given, you're very close. You can calculate $u$ and $d$ using volatility:
$$u = e^{\mbox{volatility}*\sqrt{T}}$$
$$d = \frac{1}{u} = e^{-\mbox{volatility}*\sqrt{T}}$$
I've edited your post to use $\LaTeX$. Please make sure it is correct. –  chrisaycock Nov 5 '13 at 17:35