## 2 step binomial

d2syh
Good Student
Posts: 21
Joined: Fri Aug 17, 2012 3:27 pm

### 2 step binomial

Calculate the value of a 1-year European call option using two step binomial tree. The underlying asset is trading at \$50 and the strike price is \$48. The risk free interest rate is 8%. The asset has a volatility of 10% and a dividend yield of 5%.
a. \$5.42
b. \$4.93
c. \$4.37
d. \$3.97
u = 1.0732; d = 0.9317; p = 0.5895; f = e-2*0.08*0.5[0.5895(0.5895*9.588 +0.4105*2) + 0.5895*0.4105*2] = \$3.97

Pls explain how to get u=1.0732.

swarnendupathak
Finance Junkie
Posts: 119
Joined: Mon Sep 17, 2012 11:06 am

### Re: 2 step binomial

Hi,
U = e^(sigma*time^0.5), here the time factor is 6 months or 0.50 years as the total period is 1 year & we are into calculating two step binomial.

Swarnendu

d2syh
Good Student
Posts: 21
Joined: Fri Aug 17, 2012 3:27 pm

### Re: 2 step binomial

thanks..

How do we derive 9.588?
And the r/s of f=e-2*0.08*0.5[0.5895(0.5895*9.588 +0.4105*2) + 0.5895*0.4105*2] = \$3.97

swarnendupathak
Finance Junkie
Posts: 119
Joined: Mon Sep 17, 2012 11:06 am

### Re: 2 step binomial

Just simply try with binomial option pricing method ..you will get the exact answer.

Swarnendu

naresh.thkr
Good Student
Posts: 25
Joined: Sat Aug 11, 2012 7:02 pm

### Re: 2 step binomial

But while calculating prob of up move and down move here, should we consider time ( t ) = 0.5 or 1?
We can get 9.58 = 50*1.073^2-48

Naresh.