For the CFA Level II exam, should I just memorize the BSM formula or actually understand the derivation?
I have maybe 80 hours of study time left before the exam and I am trying to decide where to spend it. Is it enough to memorize $c = S_0 \cdot e^{-qT} \cdot N(d_1) - K \cdot e^{-rT} \cdot N(d_2)$ and the $d_1/d_2$ expressions, or do I need to understand the replication argument too?
Memorise the formula AND understand the replication argument. They are not substitutes — they answer different exam questions.
What memorisation buys you: the ability to plug numbers into a price calculation when the exam gives you , , , , , and the relevant values. That is maybe 30-40% of the BSM-related questions.
What understanding buys you: the ability to answer conceptual questions that the formula alone cannot answer:
- "If the expected return of the stock doubles, what happens to the call price?" (Answer: nothing — the expected return is not in the formula and replication explains why.)
- "If implied volatility doubles overnight while spot stays the same, what happens?" (The call price rises; vega is positive.)
- "If a stock pays a sudden dividend, the call price drops because…" (Holders of the call do not collect the dividend.)
- "Delta hedging breaks down when…" (When markets gap, transaction costs are large, or vol is stochastic.)
These conceptual questions are where the points pile up because they require multi-step reasoning.
My recommended split of your 80 hours:
That allocation produces an exam answer faster and more correctly than pure memorisation. The replication argument is also a transferable skill — it shows up in fixed-income (binomial trees), currency forwards, and even some corporate-finance questions.
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