Building a Volatility Surface Without Options Quotes
Summary
The document considers how to estimate an implied volatility surface for an asset that has spot data but no options market. It outlines several practical approaches: estimate realized volatility with a model such as GARCH and add a chosen risk premium; scale a related, liquid instrument’s volatility surface as a proxy; use Black–Scholes; or fit a selected set of basis functions across strikes and maturities.
These are presented as practitioner suggestions rather than a validated recipe. The note gives no calibration procedure, empirical comparison, or evidence that one method works best. A proxy depends on how well the reference instrument represents the asset, and adding a premium or selecting a parameterization requires judgment. Without option prices, the surface is not directly identified by the market, so estimates should be treated as assumptions for pricing and risk management, with care around concentrated strike or tenor exposure.
Key ideas
- Spot returns can inform an estimate of realized volatility, which can then be adjusted by an assumed risk premium.
- A liquid related instrument can provide a proxy surface, possibly scaled to reflect differences in the underlying.
- Black–Scholes or a chosen basis-function parameterization can be used to construct a surface when market quotes are unavailable.
- Each approach relies on modeling choices because spot prices alone do not determine implied volatility skew and term structure.
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Full text
# How would one construct a volatility surface given only the spot price? # How would one construct a volatility surface given only the spot price? The traditional way to build a volatility surface is to pull options data and then do some form of interpolation. What happens if there is no existing options market and only a spot market for asset X? You could compute realized volatilities from the spot price, add a premium and then get your IV that way. As for the skew and smile, I guess you could assume it follows a similar shape to correlated assets that do have options markets? Curious if there is any literature on this. ## Answer by river_rat (score 3, accepted) https://quant.stackexchange.com/a/70434 This is the illiquid option problem, which hasn't and I doubt can be solved in a nice mathematical way. I have seen a few methods used in this space - GARCH + some fanciness to get a feel for the underlying's volatility. You then determine your own risk premium and add that to the volatility. - Proxy surface creation, using some sort of representative instrument. For example if you have a relatively well traded set of index options and need to generate a surface for a constituent of that index you could use some multiplier of the surface to build up your illiquid one. - Straight forward Black-Scholes. Black-Scholes is surprising robust, and provided you have a book without strike and tenor concentration risk works much better than the academic literature would have you believe - Mix-and-Match parameterization - choose your favourite set of basis functions and use that to map out the strike/vol/tenor space. Remember in some sense all volatility surfaces, in fact the prices of all instruments, have to be made up by someone as the market opens.
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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.