Bayesian fill rate from a Beta prior

Question

A trading desk wants to estimate the chance $p$ that a resting limit order gets filled. Before seeing today's flow, your belief about $p$ is a $\text{Beta}(2, 2)$ distribution: centered at one-half and fairly wide, as if you had already watched 2 fills and 2 misses. Today you place 12 orders and 9 of them fill.

Using Bayesian updating, what is your new best estimate (the posterior mean) for the fill probability $p$ ?

Accepted Answer

Intuition first. A Beta prior is a convenient stand-in for "pretend I already saw some fills and some misses." 	ext{Beta}(2,2) behaves like 2 pretend fills and 2 pretend misses. Updating it with real yes/no data is then almost pure bookkeeping: add the real fills to the first number and the real misses to the second. The rule. Beta is the conjugate partner for fill/miss (Bernoulli) data, which just means the answer stays a Beta: 	ext{Beta}(a,b)\ +\ k 	ext{ successes and } (n-k) 	ext{ failures}\ ightarrow\ 	ext{Beta}(a+k,\ b+n-k). In plain words: new first number = old first number + fi…

Bayesian fill rate from a Beta prior

Your answer

Discussion

Learn the concepts

Related questions