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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.

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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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    $\begingroup$ These methods make a lot of sense, except when you say "straight forward Black-Scholes". How can I use BS to price when I don't have an IV? Are you saying to first get the IV using method 1 (GARCH + premium)? $\endgroup$
    – theorangehobo
    Apr 7, 2022 at 20:25
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    $\begingroup$ The robustness result for Black-Scholes is basically if realised vol is less than implied vol you make money selling options. So price your option book using some expert view of what the maximum reasonable realised vol over the future horizon would be. No skew, nothing fancy just old pre 1987 option pricing. $\endgroup$
    – river_rat
    Apr 8, 2022 at 21:14

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