00:02
We have to calculate the value of a european good option.
00:07
So you can use the binomial option pricing model.
00:10
So given the parameters initial stock price that is s0 is equal to dollar 60.
00:27
Strike price k is equal to dollar 65.
00:38
Time to expiration denoted as t is equal to 2 years number of time steps that is n is equal to 2 upward stock price movement u is equal to 20 % that is 1 .20 downward stock price movement that is d is equal to 20 % 0 .80 and risk -free interest rate r is equal to 5 % per annum that is 0 .05.
01:55
So now we can calculate the following first.
01:59
We need to calculate the risk neutral probability of an upward movement that is p and downward movement that is one subtracted from p using the risk -free rate and the up -down factors.
02:11
So p is equal to e to the power r multiplied by change in time subtracted from d.
02:25
Divided by u subtracted from d.
02:29
Where change in time is equal to d divided by n is equal to 2 divided by 2 which is equal to 1 year.
02:40
So p is equal to e to the power 0 .05 multiplied by 1 subtracted from 0 .80 divided by 1 .20 subtracted from 0 .80 0 which is equal to 1 .051271096 subtracted from 0 .80 divided by 0 .40 which is equal to we get 0 .06267774 then one subtracted from p is equal to 0 .93732226 now secondly, we have to create a binomial price tree to calculate the option values at each node.
03:31
So start at the final node that is t is equal to 2 years.
03:35
So at t is equal to 2 years.
03:37
There are two possible stock prices.
03:42
First is s2 that is up is equal to $60 multiplied by 1 .20 is equal to $72 s2 that is upward movement and s2 that is down is equal to $60 multiplied by 0 .80 is equal to $48 that is downward movement...