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Estimating Implied Volatility When Options Markets Are Illiquid

Article Quant Q&A · Author: CasusBelli
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Summary

The note discusses how to construct a provisional volatility surface when options on the target market trade rarely. It outlines three approaches: use implied volatilities from a related underlying as a proxy, estimate historical statistical volatility, or derive strike- and expiry-specific breakeven volatility by simulating the terminal profit and loss of delta-hedged options and finding the volatility that makes it zero.

Historical volatility does not vary by strike, while the breakeven approach can capture strike and expiry differences. When a proxy options market exists, its implied volatility can be supplemented with the target market’s statistical or breakeven volatility differences, including at-the-money and wing spreads. These estimates are synthetic guides rather than observations from a liquid target options market. The note offers no empirical validation, calibration procedure, or assessment of how well the proxy relationship holds, so the resulting surface depends on assumptions that require market-specific scrutiny.

Key ideas

  • Proxy implied volatility from a related underlying can provide a starting point.
  • Historical price data supports statistical volatility estimates, but these are not strike-specific.
  • Breakeven volatility can be estimated by simulating delta-hedged option outcomes across strikes and expiries.
  • Proxy volatility can be adjusted using estimated target-market spreads at the money and in the wings.
  • Synthetic estimates remain uncertain when target options trade infrequently.

Tags

VolatilityOptionsCommoditiesDerivatives pricing
Full text
# Implied volatility of hypothetical options market


# Implied volatility of hypothetical options market












I am attempting to create a volatility surface for a US electricity market that has a liquid futures market but nearly non-existent options market (<5 trades per month across all strikes and expiration dates). Options in the natural gas market for the region are not particularly liquid either -- and, even so, natural gas is used only a few months out of the year. Is this exercise feasible? Where would be a good place to start? Thank you for your time and assistance!

## Answer by ir7 (score 6, accepted)

https://quant.stackexchange.com/a/55335

The three ways to manufacture pseudo-implied vols I know of are:

- Find a related underlying and, even if only few options trade on it, 'borrow' its implied vols.

- Compute statistical vol from historical underlying prices (not strike dependent, still useful to know).

- Compute breakeven vol, still based on historical underlying prices, strike dependent, by simulating terminal PnL for delta-hedged options with various strikes and expiry times and finding the vol that makes it null. See this reference and references therein (in particular Bruno Dupire's ones which I can't findon the net).

The 'borrowing' can be refined: one can always have statistical and breakeven vols for any underlying, so we just want to get the 'spreads' (ATM and wings) against the implied vols for the proxy underlying (if available).

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.