calculation-reference
Black-Scholes on BA II Plus
How to structure Black-Scholes option inputs and what the BA II Plus can and cannot do directly.
TL;DR
The BA II Plus does not have a native Black-Scholes worksheet. Use it for exponentials, discounting, and arithmetic, then use supplied normal probabilities or a table for N(d1) and N(d2).
Formula Reference
Call option
c = S x N(d1) - X x e^(-rT) x N(d2)Use continuous compounding for the exercise price discount.
d1
d1 = [ln(S/X) + (r + sigma^2 / 2)T] / [sigma x sqrt(T)]d2 = d1 - sigma x sqrt(T).
BA II Plus Keystrokes
- Compute S / X.
- Use LN for ln(S/X).
- Compute sigma squared, divide by 2, add r, multiply by T.
- Add the numerator terms.
- Compute sigma x sqrt(T) and divide.
- Use a normal table or supplied values for N(d1) and N(d2).
Worked Example
- Problem: S = 50, X = 48, r = 4 percent, sigma = 25 percent, T = 0.5.
- Compute d1 and d2 on the calculator.
- Use the normal CDF values supplied by the question or a table.
- Discount X by e^(-rT), then apply the call formula.
Common Mistakes
- Expecting the BA II Plus to return N(d) directly.
- Using simple discounting when the formula calls for continuous compounding.
- Entering percentages inconsistently as 25 instead of 0.25 in d1.
Related Guides
- CFA Level I Derivatives Formula Sheet - Public formula sheet for forwards, futures, options, put-call parity, and Black-Scholes inputs.
- BA II Plus Calculator Shortcuts for CFA Level I - Fast BA II Plus workflows for clearing registers, storing values, changing signs, and avoiding exam-day calculator errors.
- Time Value of Money Calculations on the BA II Plus - CFA Level I TVM reference for present value, future value, annuities, perpetuities, and BA II Plus inputs.