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