binomial model

Good Student
Posts: 29
Joined: Thu Oct 04, 2012 2:09 am

binomial model

A stock price is currently \$50. Each month for the next two months it is expected to increase by 9% or reduce by 11%. The risk-free interest rate is 6.5%. Use a two-step tree to calculate the value of a derivative that pays off max [(50 – ST), 0]2, where ST is the stock price in two months?
a. \$18.45
b. \$19.67
c. \$18.84
d. \$19.36

The risk neutral probability of an up move, p = (e1/12 *0.065 – 0.89) / (1.09 – 0.89) = .5772
Value of the option = [108.16 * (1-0.5772)2 + 2.25 * (1-0.5772) / 0.5772] e-0.065*2/12 = \$19.67

{Why dont we consider the payoff 2.25 twice here as we usually do while calculating values of options?}

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content.pristine
Finance Junkie
Posts: 356
Joined: Wed Apr 11, 2012 11:26 am

Re: binomial model

There seems to be something very wrong with the question.
They are basically asking us to value a 2 european put options with strike 50.

Lets work this out step by step
U=1.09
D=1-.11 = 0.89
using the formula, prob(up) = 0.58 and prob(down) = 1-0.58 = 0.42

The binomial tree looks like:
T=0 50
T=1 44.5 54.4
T=2 39.605 48.505 59.405
prob at T=2 0.18 0.49 0.33
the 2 put option payoff:
20.79 2.99 0
taking the weights as the probabilities, the payoff is 5.18.
This needs to be discounted by 2 months : 5.18*e^(-6.5%*2/12) = 5.12

What is the source of this question?

Good Student
Posts: 29
Joined: Thu Oct 04, 2012 2:09 am

Re: binomial model

FRM Level 1 Mock Test - II afternoon session
very good explanation. i understood the topic.
but in this question- The payoff is max[(50-St),0]^2. So i just hav a doubt in the portion i mentioned earlier.