One and two step binomial valuation models

[noalv4]

Hi David,
I'm trying to answer the practice questions regarding the topic and I can't understand why my unswer is wrong (the spreadsheet that supose to be attached to these answers is not valid any more)

can help me with the solution path, for the following question, please? I followed the binomical tree from the end back.

1.3. A stock has a current price of $40 and a volatility of 20% per annum. We use a two-step binomial model to value a European put option with a strike price of $38; each step is one year such that the option has two years (T = 2.0) to expiration. The riskfree rate is 3% per annum. What is the value of the two-year European put option?

a) $2.37
b) $3.16
c) $4.25
d) $5.19

My answer is:
u=EXP(0.2*SQRT1)=1.2214
d=1/u=0.8187

P=EXP(0.03*1)-0.8187/1.2214-0.8187=0.5257
1-p=0.4743
Value of put option t2= (38-28.77)=9.224 (38=K, 28.77 is S2 as follow (40*.8787*.8187=28.77)
the value of put option at t1 is: ((0.5257*0)+(0.4743*$9.224))*EXP(-0.03*1)=$4.245
the value of put at t is: 4.245*0.4743*EXP(-0.03*1)=$1.953

Your answer is: a. $2.37

Where am I wrong?

Thanks,
Noa

 

[ShaktiRathore]

40*.8187*.8187=26.81 u made mistake here only be careful from next time and be careful before posting
Value of put option t2= (38-26.81)=11.19
value=pd*pd*value of put at t2*EXP(-0.03*2)
0.4743*0.4743*11.19*EXP(-0.03*2)=2.37

thnks

 

[David Harper CFA FRM]

Hi Noa,

Source question is here, with image and updated XLS link http://forum.bionicturtle.com/threads/p1-t4-1-one-and-two-step-binomial-valuation-models.4744/
I think your u,d, and p are correct.
But instead of 40*.8787*.8187=28.77, I have S[2,0] = 40*exp(-20%*1)^2 = $26.8128 which leads to the 2.37,
so looks like the difference is node[2,0]; i.e., T2 [dd] = 26.81 versus 28.77?

We will update the PDF to have correct links asap, thanks,

 

[David Harper CFA FRM]

ShaktiRathore thanks for awesome help!

 

[noalv4]

thank you both... it seems that i need some rest....

Noa.