Weight Option Model Fits by Bid-Ask Spread
Summary
The document discusses fitting a Heston option pricing model when short-dated quotes have wide bid-ask spreads. It recommends using quote uncertainty in the calibration objective: take the midpoint as the observed price, then give tighter-spread quotes more influence and wider-spread quotes less. Suggested weighting schemes make weights decrease as the spread grows, including inverse and exponential relationships.
The rationale is that the fair option value is expected to lie between bid and ask, so a narrower market interval provides a more informative constraint on the model. A second response emphasizes screening or treating quotes before computing midpoints, since a poor quote can distort the implied volatility smile. The document does not prescribe a single weighting function or filtering threshold, and it offers no empirical comparison of alternatives. The appropriate approach may depend on whether calibration is performed in price or volatility space and on the quality of the available quotes.
Key ideas
- A quote’s bid-ask spread can serve as a measure of uncertainty in model calibration.
- Use mid-prices as observations while assigning less weight to wider-spread quotes.
- Inverse or exponentially declining weights are possible ways to encode spread uncertainty.
- Inspect and filter quote quality because a simple midpoint can be distorted by a bad quote.
- The discussion does not establish one universally best weighting or filtering rule.
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Full text
# Working with wide bid ask spreads in option pricing model
# Working with wide bid ask spreads in option pricing model
I'm trying to fit an Heston model to market data. But market is data has some terms (<3M) with quite wide bid-ask spreads (12%-25%). Should I just use mid volatility? Is there maybe a model to pre-process market data that helps to solve this kind of problem?
## Answer by Chris Taylor (score 1)
https://quant.stackexchange.com/a/82429
You can use the bid/offer spread to weight each quote in your model fit. The intuition is that the "fair" price of an option satisfies
$$ p_{\rm bid} \leq p_{\rm fair} \leq p_{\rm ask} $$
so a narrow bid/offer spread indicates greater certainty about the value of the fair price (or fair volatility, depending on whether you are fitting in price space or volatility space). Quotes with narrow spreads should get more weight, quotes with wide spreads should get less weight.
If you are fitting a model which depends on some parameters $\theta$, your loss function can be written
$$ L(\theta) = \sum_{i=1}^n w_i \left( p_i - f(\theta) \right)^2 $$
where the $w_i$ are the weights of each observation in the fit, and $p_i$ are the mid-prices (derived in the usual way, as the average of bid and offer prices). Common approaches include setting the weight to be inversely proportional to the bid-offer spread, or setting the weight to be exponentially decreasing in the bid-offer spread.
## Answer by KT8 (score 0)
https://quant.stackexchange.com/a/82159
I'd suggest doing some data treatment before-hand. Note that a spread of more than 5-10% basically means that any curve would work. Use the bid and ask quotes to decide how to filter the data and how to define a "meaningful mid". Computing a mid straight-forward from untreated bid-ask quotes mean that a bad price can disturb your smile quite substantially.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.