Topic: Binomial Tree

I can’t figure out how they computed the up move factor (1.2) and down move factor (0.8)?

Thank you so much

Question:

A risk manager from bank XYZ, Mark is considering writing a 6 month American put option on a non dividend paying stock ABC, The current stock price is USD 50 and the strike price of the option is USD 52. In order to find the no arbitrage price of the option, Mark uses a two-step binomial tree model. The stock price can go up or down by 20% each period, Mark’s view is that the stock price has an 80% probability of going up each period and a 20% probability of going down. The risk free rate is 12% per annum with continious compounding.

What is the risk neutral probability of the price going up in a single step?

a. 34.5%

b 57.6%

c 65.5%

d 80.0%

Explanantion:

b is correct

P(up) = (e^(rt) - d)/(u-d) = (e^(0.12*3/12) - 0.8)/(1.2 - 0.8) - 57.61%

you are surely joking right? It is clearly giving you the information and I quote “The stock price can go up or down by 20% each period”. which means up= (1+0.2) and down=(1-0.2).

Kaveh,

Thank you for clearing this.

no I wasn’t joking. i guess i got confused with the 80% and 20% probabilty. I am guessing it was a distractor?

your welcome. But no this is not a distractor. You are usually never given the probabilities, as you are expected to calculate them. It is often more likely that you are given any of the following:

• Prices after one up or down movement

• The volatility

• or simply in the form of the above question

I highly doubt that they will give you the inputs of the formula and ask you to calculate it. That would be way too easy.