Fitting Option Volatility Surfaces Within Bid–Ask Bounds
Summary
The document discusses how to infer implied volatility from an option’s bid and ask prices. It compares averaging the prices before solving for implied volatility with solving for each quote’s implied volatility and averaging those values. Although the approaches can coincide in the example, bid-side inversion may converge to zero for deep in-the-money or out-of-the-money options, making the resulting average unstable.
The response recommends fitting a volatility model such as SVI against the bid–ask interval rather than treating a midpoint as a meaningful target. A fitted surface is considered adequate when its prices fall within the quoted spreads. Wide spreads in illiquid options make midpoint estimates especially unreliable. The document offers practical guidance rather than a formal fitting procedure or empirical comparison, and it does not specify an optimization objective or how to handle arbitrage constraints.
Key ideas
- Implied volatility at the midpoint price need not equal the average of bid and ask implied volatilities.
- Bid-side inversion can be unstable for deep in-the-money or out-of-the-money options.
- Fit a volatility model to the bid–ask bounds instead of relying on a midpoint target.
- Wide spreads in illiquid options make midpoint prices and volatilities less dependable.
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# Best approach to solving for an option’s mid price IV? # Best approach to solving for an option’s mid price IV? As the title implies, I’m having trouble figuring out which approach is best suited to solving for mid price IV, given only a bid price and ask price for an option (assume we also have all necessary parameters to solve for IV such as S, K, T, r, etc). Approach A - avg the bid price and ask price, the solve for iv on this mid price (Im using Barone-Adesi Whaley to solve for IV). Ex: Bid price = 1.80 Ask price = 1.90. Therefore Mid price = (1.80+1.90)/2 = 1.85. Then plug 1.85 into pricing model and solve for IV at the mid to get hypothetical Mid IV = .35 Approach B - solve for iv at the bid price and also solve for iv at the ask price, then avg those 2 results to get mid IV. Ex: Bid price = 1.80 Ask price = 1.90. Plug 1.80 into a pricing model to get hypothetical IV of .3 and then do the same for 1.90 to get hypothetical IV of .4. Therefore Mid IV = (.3+.4)/2 = .35 As you can see, both approaches reach the same solution of .35 IV at the mid, however my issue lies in deep otm / itm options, where solving for IV on the bid price can lead to a convergence at 0 for the bid IV. This can cause the mid IV to be wildly different between approaches A and B. My goal is to eventually take these mid IVs and interpolate them using something like SVI, but im stuck on which approach is better, and im struggling to find literature that speaks about this issue specifically. Any advice is appreciated, and if you have alternative approaches that you think are superior, id be interested to learn more. ## Answer by QuantCalc.net (score 1) https://quant.stackexchange.com/a/85280 Don’t worry about the mid vol or mid price. It doesn’t mean anything. You can just fit your vol model like SVI with bid-ask spread. As long as your vol model is inside the bid-ask spread for all strikes, it is a good fit. When it lacks liquidity, the bid-ask spread could be very wide and the mid vol or mid price could oscillate in this case. You definitely would not want to fit against the mid in this case.
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