Do you need to compute $N(d)$ yourself when solving option pricing problems?

Conditions

• The context is standard exams or practice problems for option pricing.
• The problem requires evaluating the Black-Scholes-Merton formula.

Reasoning, step by step

1. Recall the Black-Scholes-Merton formula, which requires evaluating $N(d_1)$ and $N(d_2)$.
2. Check the problem statement to see if the values of $N(d_1)$ and $N(d_2)$ are explicitly given.
3. If the values are not given, determine if you are permitted to leave the answer in terms of $N(d_1)$ and $N(d_2)$.
4. If neither is true, use a standard normal distribution table to look up the values after rounding $d_1$ and $d_2$ to two decimal places.
5. Substitute the obtained or provided $N(d)$ values into the main formula to calculate the final option price.

Example

The instructor notes that $N(d_1)$ and $N(d_2)$ represent the cumulative probabilities of the standard normal distribution, and emphasizes that in typical exams, these values are usually provided directly, or candidates are allowed to write only the expression containing $N(d)$ without computing the final numerical value.

Common misconceptions

• Assuming you must manually integrate the standard normal probability density function to find $N(d)$.
• Believing that failing to compute the exact numerical value of $N(d)$ means the problem is unsolvable.
• Forgetting that $d_1$ and $d_2$ must be rounded to two decimal places if a table lookup is actually required.

Watch the explanation

Explore next

• How do we apply the Black-Scholes-Merton formula to compute $d_1$ and $d_2$ for a specific set of parameters?
• Why is the derivation of the Black-Scholes-Merton formula not required in this segment?