Derivatives · Core
Implied Volatility
Implied volatility is the σ you plug into Black-Scholes to match the market price — a quote of the option, not a forecast you must believe.
Definition
Invert the pricing model to get σ_imp. Each strike and tenor has its own. The smile and term structure are the market. Realized vol is what the spot path did; implied is what options cost.
Why it matters
You trade implied versus realized, versus other implieds, versus events. Directional stories that ignore IV are incomplete.
Case
VIX at 12 with a packed event calendar. Spot can be quiet and options still rich if the jump is in the smile. IV was the scare; realized was the shrug.
How to read it
Always say tenor and moneyness. ‘Vol is high’ without a point on the surface is not a number.
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