B
barbados
Member
Hi,
I came upon the following question:
Stock price is currently 50. Its expected return and volatility are 12% and 30%, respectively. What is the probability that the stock price will be greater than 80 in 2 years.
Obviously, the answer can be obtained by calculating P[S_2 > 80] = P[ln S_2 > ln80] = ... = 1 - Phi(0.7542)
However, why is the following reasoning not working:
We know that the change in the stock price is given by:
dS = mu S dt + sigma S dz -> dS ~ N(mu S dt, sigma^2 S^2 dt)
So given the question above, I need to calculate P[dS > 80 - 50] =
P[ N(0,1) > (30 - 0.12 x 50 x 2)/(0.30 x 50 x sqrt(2))] = 1 - Phi(0.8485)
This is not equal to the first method. Where am I going wrong in the second method.
PS - the second method I took from Hull Q12.12 which is a similar question.
Thanks,
Barbados.
I came upon the following question:
Stock price is currently 50. Its expected return and volatility are 12% and 30%, respectively. What is the probability that the stock price will be greater than 80 in 2 years.
Obviously, the answer can be obtained by calculating P[S_2 > 80] = P[ln S_2 > ln80] = ... = 1 - Phi(0.7542)
However, why is the following reasoning not working:
We know that the change in the stock price is given by:
dS = mu S dt + sigma S dz -> dS ~ N(mu S dt, sigma^2 S^2 dt)
So given the question above, I need to calculate P[dS > 80 - 50] =
P[ N(0,1) > (30 - 0.12 x 50 x 2)/(0.30 x 50 x sqrt(2))] = 1 - Phi(0.8485)
This is not equal to the first method. Where am I going wrong in the second method.
PS - the second method I took from Hull Q12.12 which is a similar question.
Thanks,
Barbados.