2 step binomial

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

2 step binomial

Postby d2syh » Wed Nov 07, 2012 3:32 pm

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%.
Choose one answer.
a. $5.42
b. $4.93
c. $4.37
d. $3.97
The correct answer is $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

Postby swarnendupathak » Wed Nov 07, 2012 3:36 pm

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

Postby d2syh » Thu Nov 08, 2012 7:04 am

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

Postby swarnendupathak » Thu Nov 08, 2012 9:58 am

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

Postby naresh.thkr » Thu Nov 08, 2012 1:16 pm

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.


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