Dimensionality Reduction
Why does fitting and pricing even matter for options, why can’t we just use the midprice of the market bid/ask for each option?
This is not as simple to answer as it seems. Without a vol fit model all we have is market prices, in price space, not even vol. To convert a price to a vol we need the correct borrow, dividends, rate, spot and settlement, and an American or European pricer, otherwise the vols implied from the options won't line up.
Blue calls · red puts · grey the picture with every input right, and its fit
A good volatility curve or surface fit is like a high quality mathematical model that can describe a high dimensional space with a small number of parameters. Once we have this “model” we can use it to describe how things evolve in that high dimensional space. In our case, we have thousands of options listed on an underlying stock/index, hundreds of strikes, call/put, and tens of expirations. A high quality vol fit reduces the dimensionality of this space by ~30x. Instead of needing thousands of individual variables to describe this vol surface we only need a handful.
Now, why is that helpful you may ask. Good question. Like any good model, when we reduce the dimensionality of a complex space we extract its meaning, its essence, with a handful of parameters. Then use this essence to predict, extrapolate, and identify issues.
Predict
Hide half the strikes and the fit still knows where they are.
Extrapolate
Quotes run out at the edges. The fit carries on.
Identify issues
One person putting a quote in the middle of the spread shouldn't make your fair values or greeks jump. A good model is robust.
With a vol fit we harmonize the pricing information embedded across all options. Stable vol fits also yield stable fitted prices that tell us a fair value for each option given the market prices for all options, and greeks that we can use to hedge, normalize and predict market movements.
See how much the details matter →