## Binomial Trees

kaushalya.narendran
Posts: 7
Joined: Sat Jan 11, 2014 2:11 pm

### Binomial Trees

(i) A 6 month American put option
(ii) So= 50
(iii) X=52
(iv) Volatility=20%
(v)The stock price has a 80% probability to go up each period and a 20% probability of going down each period
(vi) Risk free rate=12% p.a.

How do we calculate the up move factor (u) and the expected payoff (Pu) given the above details.

Kindly explain along with the steps to calculate.

Finance Junkie
Posts: 258
Joined: Thu Sep 20, 2012 3:42 pm

### Binomial Trees

We can calculate the up move factor by putting the values in this formula (e^σ√h)
e^.20√.5 = 1.1519
Now the expected payoff is :-
If there is two up move then the expected payoff is (50*1.8^2) = 162 =Payoff = 0
If there is one up and one down move then the payoff is (50*1.8*.20) = 52-18 = 34
If there is two down move, then the payoff is (50 * .2^2) = 52-2 = 50.

Hope the calculation is clear to you.

Finance Junkie
Posts: 258
Joined: Thu Sep 20, 2012 3:42 pm

### Binomial Trees

It is a graphical presentation basically. The intrinsic values are shown with probability of going down or up .The binomial tree is used for calculating option values or premiums .