I am currently revising for my computational finance exam in a computer science course and got stuck on this question:
Let S be the price of a share with the yearly drift rate μ = 0.25 and the yearly volatility σ = 0.5. Suppose that the share is worth S0 = 80p now. Calculate the probability that the share will go down by 10p or more in a year: express it through N, the distribution function for φ (0, 1) and calculate it numerically.
I know how normal distribution works but I don't know how this version of it works.
I was given the equation below to help me find my answer but I don't know how to apply it.
Stochastic differential equation: lnST – lnS0 ~ φ [(μ – σ^2/2) T, σ^2T]
I plugged in the numbers and came out with:
lnS1 ~ φ [4.50703, 0.25]
I also tried:
mean price = 80
σ = 0.5
below price = 70
X ~ N(80, 0.5)
Z = (70 – 80)/0.5 = -20
P(X ≤ 70) = P(Z ≤ = -20)
But I couldn't find data for 20 standard deviations in the normal distribution table. Anyone know how this works? Also, is there a way to calculate this on MATLAB?
