Building an Equity Option Volatility Surface from Market Quotes
Summary
The document considers a prototype method for constructing an equity volatility surface to price European calls. The proposed workflow backs out Black–Scholes implied volatilities from option prices, fits a polynomial relationship involving local volatility model outputs, and uses cubic splines to interpolate across strikes and maturities. The response recommends interpolating after forming the surface and questions whether a separate spline step is needed if the fitting already provides interpolation.
The exchange also notes that a surface reflects changing market inputs and should be refreshed as conditions change. Sticky strike and sticky delta are mentioned as approximations for using a prior day's surface when current data is unavailable. The discussion does not assess the proposed fit in detail, demonstrate a specific construction method, or explain how to impose no-arbitrage constraints. It is an introductory pointer rather than a complete implementation guide; readers would need additional material to evaluate model choice, quote cleaning, interpolation behavior, and arbitrage controls.
Key ideas
- Implied volatility can be obtained by solving the Black–Scholes pricing formula against quoted option prices.
- A fitted volatility surface can support interpolation across strikes and expiries where quotes are missing.
- The response suggests interpolating after constructing the surface and questions whether an additional spline stage is necessary.
- Volatility surfaces change with market inputs, so a prior day's surface is only an approximation.
- Sticky strike and sticky delta are named as possible ways to adapt an older surface, but no arbitrage-control method is supplied.
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# Newbie question on volatility surface building # Newbie question on volatility surface building I am trying to build a prototype equity volatility surface for pricing european call options, as a way of learning a new programming language that I am looking at. Is there anything wrong with the following method which I have put together from research: - back out Black Scholes vols from quoted options prices (solve BS formula for volatility) - fit = do a polynomial regression between BS vols versus vols from a local volatility model - apply cubic splines (in two directions) to fitted vols to allow for interpolation where we don't have a vol point Questions: - Does my approach sound reasonable or is it completely stupid? - Should i interpolate missing market data before doing this procedure, for missing options quotes? Or should i interpolate the surface vols instead, once I have fitted the IVs? This I see as building the surface. I anticipate further interpolation will be needed for the days between contract expiries, on an adhoc basis if a user requests an IV for a date we don't have on the built surface. - Is this volatility surface only good for one day? Tomorrow, do i need to create a new surface to account for the changed inputs (eg. spot)? Or can i somehow roll forward todays surface tomorrow? Or can i simply use todays surface tomorrow? - How and when do you apply the no-arbitrage constraints that i have read about. Is it done during the fitting, somehow the fitting must consider the constraints? Thanks in advance for all pointers. I have not built a volatility surface from scratch before and would appreciate any useful tips. ## Answer by william smith (score 2) https://quant.stackexchange.com/a/59272 - Interpolate after building the surface. Won't your step #2 do this for you, do you really need step #3? - Definitely it changes every day. Look up "sticky strike" and "sticky delta" if you want to see how you can use a vol surface on a previous day as an approximation, if you don't have a fresher one.
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