Fitting Implied Volatility Curves with Missing Strike Quotes
Summary
The document addresses updating a volatility curve for front-month vanilla commodity options when some strikes lose their two-way markets. With liquid quotes across strikes, a smoothing spline can provide a usable fit; when observations disappear, the challenge is to retain a plausible curve while incorporating fresh market data.
One answer recommends interpolating implied variance, defined as implied volatility squared times maturity, against log moneyness, the log of strike relative to forward. It cites asymptotic behavior that supports a curve becoming linear at extreme moneyness and aligns with natural spline boundary conditions. For missing observations, another answer suggests carrying forward the previous tick when available or trying cubic and other interpolation methods. The discussion offers no canonical solution for extrapolation across strikes and time, and gives no comparative tests; it favors keeping the model as simple as practical.
Key ideas
- Implied variance against log moneyness is suggested as a useful interpolation space.
- At extreme moneyness, asymptotic results support linear behavior in the chosen coordinates.
- A previous tick can fill a missing quote when recent data is available.
- Cubic or other interpolation methods can be explored for illiquid strikes.
- The document presents no definitive method for missing data across strikes and time.
Tags
Full text
# Constructing a minute-by-minute volatility curve # Constructing a minute-by-minute volatility curve For market making in front month vanilla commodity options we need a volatility curve that updates every second or so as the underlying and the options change prices. If all the strikes have a good two-way market then a simple smoothing spline produces a usable curve. But when the bids disappear in a few strikes, how should we preserve the shape of the curve and fit it to the new market data? Should we be working with strikes or in log(strike) space? ## Answer by q.t.f. (score 3) https://quant.stackexchange.com/a/24463 For simple interpolation, implied variance (i.e. implied vol squared times maturity) vs. log moneyness (i.e. log of strike over forward) is probably the best choice. In these coordinates, Roger Lee results on the asymptotics imply the curve flattens to linear in the high and low moneyness limits, which fits with natural spline boundary conditions. There is no canonical solution for the full problem you face of interpolating/extrapolating missing data across strikes and time. You can make modelling approaches as complicated as you want; it just is a hard problem. I would suggest to do the simplest thing you can tolerate. Complex solutions have a way of causing more problems than they solve. ## Answer by pyCthon (score 1) https://quant.stackexchange.com/a/22851 For the first question there are two approaches, the first is you can simply backfill and use the last minutes tick if it exists. If there is no liquidity, the second way is you can try cubic or other interpolations to see if it creates a better curve.
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