What Is Fair Value?
Fair value is your best estimate of what an instrument is worth at this instant. Everything else in market making hangs off it: quotes are centred on it, inventory decisions reference it, and P&L is measured against it.
It is also unobservable. You never learn the "true" price, only a stream of noisy evidence about it.
Why the mid is a weak default
The obvious starting point is the order book midpoint:
It is convenient and frequently wrong, because it ignores size. Consider:
| Bid size | Bid | Ask | Ask size |
|---|---|---|---|
| 5,000 | 99.98 | 100.02 | 200 |
The mid is 100.00, but the book is not balanced. There is 25 times more size bid than offered, which says buyers are far more eager. Fair value is probably above the mid.
The standard correction is the microprice, weighting each side by the size on the opposite side:
Here that gives
pulling the estimate toward the ask, where the scarce liquidity is. Quoting around 100.0185 rather than 100.00 is a materially different decision.
Move the two sizes and watch the mid refuse to react. It cannot: it is built from prices alone. Balance the sizes and the two estimates agree, which is the only case where the mid was ever the right answer.
The mid ignores size and is therefore biased whenever the book is imbalanced. The microprice is the cheapest available improvement and costs one line of arithmetic.
The other inputs
Last trade. Real information, since someone committed capital at that price. Note whether it was a buy or a sell aggressor: a trade at the ask is different evidence from a trade at the bid.
Correlated instruments. Often the strongest signal. If you make a market in a single stock, index futures move first and drag the stock with them. If you price an option, the underlying is most of your answer. Much of a market maker's fair value comes from instruments other than the one being quoted.
Theoretical models. For derivatives, fair value is largely computed rather than observed: Black-Scholes for options, cost-of-carry for futures, net asset value for an ETF. The model gives a value the market should converge to, and deviations are trading opportunities.
News and events. Discrete jumps in fair value that no order book statistic will anticipate.
It is a distribution, not a number
Treating fair value as a point estimate loses the most useful part. In reality you have an estimate and an uncertainty, and the uncertainty determines your spread. A confident estimate supports tight quotes; a shaky one demands width, which is the subject of volatility and confidence intervals.
Being wrong about fair value is far more expensive than quoting a slightly suboptimal spread. If you get the centre wrong by a tick, every fill on one side is a loss regardless of how well you sized the spread.
The feedback loop
Fair value estimation is continuous. You quote around your estimate, observe which side trades, and update. Repeated fills on one side are evidence your estimate is off, and treating that evidence properly is Bayesian updating in everything but name: prior estimate, evidence from flow, revised estimate.
How far to move on a single fill is the harder half, and it depends entirely on who you think traded with you. Reading your counterparty works through the two failure modes, moving too little and moving too far, and why the second is both more common and more exploitable.