Thread by @rebootdude

In the modeling world we use a term marking a model to market.

If you have a pricing model and use that to estimate price of a security, how far off are your estimates compared to the market?

The mismatch between the model price and the market price is your model error.

With some models we let the error ride. With others we need to calibrate it down to zero.

A family of models where the pricing model is calibrated to match current market prices is called an arbitrage free model.

Remember the BTC model we built a few days ago. Not arb-free.

You can see the fit is not strong. There is a significant mismatch between actual market prices and model prices.

Here are two variations of the same model with market price calibration related adjustments. Still not arbitrage free, but much better fit.

How did we get here?

We changed the criteria for regression fit. Rather than using absolute prices for fit we used relative change. The same dataset, same technique much better fit.

But you can see it is not arbitrage free.

Same concept, different market. Bond prices.

We model the underlying rate curve, fit prices of bond on the curve and then match the same prices to market prices by tweaking the model till we get perfect fit.

This is what the end result looks like. Arbitrage free.

Now option markets.

With calls and puts we get a range of instruments across maturity horizon and strike prices.

Think yield curves in bond markets. Think a curve of volatility in option markets. Except not a curve but a surface.

Each point on the surface maps to an option

Your model uses a volatility estimate to price an option.

The price from your model may not match the market price. You change the volatility to get to a point where prices match.

Implied volatility is the volatility estimate where market and model prices match.