Constructing the Implied Volatility Surface: From Market Quotes to an Arbitrage-Free Fit
Why This Matters For vanilla options, the simple models are usually sufficient. A plain call or put can be priced off Black-Scholes directly; we often do not need to reach for local volatility or a stochastic volatility model. Those heavier models earn their place with exotics, where the payoff depends on how the smile behaves rather than just its level today. For a vanilla option, we take the market’s implied volatility at the relevant strike and maturity and feed it into Black-Scholes. That assumes a volatility surface already exists. Before Black-Scholes can price anything, the surface it reads from has to be built, and building it can be less straightforward than it appears. ...