Lognormal assumption
Definition · Level 5 · Greeks & volatility
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Model premise that log-returns are normally distributed, so prices stay positive — but it badly understates how often large moves (fat tails) occur.
Example
A 1987-sized one-day crash is essentially impossible under it.
Where Tradecraft teaches it
Level 5 · Greeks & volatility, in the lesson “Black–Scholes, skew & the vol surface”: The model’s inputs and blind spots, parity as a hard constraint, and how desks quote skew.
Related terms
- Black–ScholesEuropean option-pricing model using spot, strike, time, rates, dividends and volatility; assumes lognormal prices, constant vol, no jumps and…
- Butterfly (vol quote)Smile-curvature quote: average of the 25Δ call and 25Δ put IVs minus ATM IV — how rich the wings are relative to the money.
- Jump riskExposure to a sudden price gap (earnings, news, overnight) that can’t be hedged along the way — a key place real markets break the model.
- Risk reversal (25-delta)Long an OTM call and short an OTM put (or the reverse), typically at 25Δ.
- Volatility skewImplied vol varying by strike. In equity indices, OTM puts trade above equally distant OTM calls (a downward “smirk”), driven by crash risk and…
- Volatility smileA U-shaped IV curve across strikes, with both OTM puts and OTM calls richer than at the money; common in FX pairs (often tilted to one side) and…