This paper models the spread of a pair (or any mean reverting synthetic asset) as a discrete Ornstein-Uhlenbeck (O-U) process. It then uses the Kalman filter to estimated the “true” (or hidden) price for the spread. When the observed price is bigger than the estimated true price by a threshold, we sell; otherwise we buy. The threshold and average holding time of a trade can be computed from the properties of the O-U process.
The paper describes two ways to estimate the parameters in the state process (for the spread):
- Shumway and Stoﬀer (1982) smoother approach (offline)
- Elliott and Krishnamurthy (1999) ﬁlter approach (online)
There seems to be some typos in the equations in the 2nd approach (the online algorithm) in the original publication.