Example Derivatives Questions

  1. Derive delta
  2. Close to maturity
  3. Forward skew
  4. American vs European options
  5. Pin risk
  6. Diagram - Short straddle
  1. Black Scholes model
  2. Greeks
  3. Implied volatility
  4. Option Theory
  5. Pay-off diagram

Derive delta

How do you derive the delta of an option from the Black Scholes model?


Take a look at the lesson on ‘The Black Scholes Model and Implied Volatility’.


First, compute d_1.

(1)   \begin{equation*} d_1 = \frac{ln(\frac{S_t}{K})+(r+0.5 \sigma^2)(T-t)}{\sigma \sqrt{T-t}} \end{equation*}

Finally, look up N(d_1) in the z-statistic table. This value is the value of delta.