Options
Calls and puts confer asymmetric rights whose quoted prices imply the volatility surface the rest of quant finance builds on.
An option is a right without an obligation: a call lets its holder buy the underlying at the strike, a put lets them sell. Payoffs are asymmetric by construction: the buyer risks only the premium while keeping exposure to favorable moves, which makes options the raw material for hedging, leverage, and expressing views on volatility rather than direction. Exercise style matters mechanically: European options exercise only at expiry, American options anytime, and the early-exercise premium on American puts is a classic pricing puzzle. Listed and OTC options trade across equities, rates, FX, and commodities, and their quoted prices imply the volatility surface that the volatility track builds on.