Black-Scholes Model
Black-Scholes is the European option formula under lognormal spot, constant vol, and continuous hedging — a quoting convention more than a belief about the world.
Definition
A closed form for C and P given S, K, T, r, q, and σ. The market inverts it to implied vol. Real markets have smiles, jumps, and stochastic rates. The hedge still starts from these Greeks.
Why it matters
Every listed option is an implied-vol number in this metric. You can disagree with the assumptions and still need the language.
Case
1987 showed the smile; 2008 showed jumps. The formula stayed the quotation grid. Local and stochastic vol grew up around it.
How to read it
Treat σ as a quote. Then ask which assumption (lognormal, continuous hedge, no jump) is the one that will hurt this position.
Key papers
Landmark references with real publisher or arXiv links — not token-overlap noise.
- The Pricing of Options and Corporate LiabilitiesBlack, Scholes · 1973 · Journal of Political EconomyThe European call formula.