Exam 2 – Binomial Trees

[Anonymous]

Sitting exam 2 end of Feb and I just cannot get to grips with this question. When calculating the risk probability – I just can’t follow how to calc the “d” and “u” ?

Example of questions that stump me are as follows –

A 2-step binomial tree is used to value an American put option with strike 105 given that the underlying price is currently 100. At each step the underlying price can move up or down by 10 and the risk neutral probability is 0.6. There are no dividents paid on the underlying and the continuously compounded risk free interest rate over each step is 1%. What is the value of the option in this model?

Another example –

In a 2 step binomial at eachstep the underlying price can move up by a factor of u=1.1 and down by a factor of d=1/u. Continuously compounded risk free interest rate over each time step is 1% and there are no dividends on the underlying. Use the Cox Ross Rubinstein parameterisation to find the risk neutral probability and hence find the value of a European put option with strike 102 given that the underlying price is 100.

Can anybody please please help – a link to a tutorial or just some guidance, the more I look up you tube & notes – the more confused I am getting.

Thanks in advance

[Anonymous]

u and d are simply factors or multiples.

In your first example, I am assuming ‘up or down by 10’ means $10.

Which would mean if the current price is $100 it can go up to $110 or down to $90

The up factor here would be = 110/100 = 1.1
The down factor here would be = 90/100 = 0.9

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