AppliedNumeric answer

A spread follows an Ornstein–Uhlenbeck process $dX = \theta(\mu - X)\,dt + \sigma\,dW$ with $\theta = 5$ per year. What is the half-life of a deviation, in trading days (252 a year), to one decimal?

Answer with a number. Fractions, powers and expressions like 23/6 or C(52,5) are read correctly in practice.

The worked solution is in Premium

The answer, the full working and the one idea to take away – for this and all 1,322 questions in the bank. Answer it in practice and your working is marked, with a known mistake named when you make one.

Start the 7-day free trial Practise it with Premium

Learn the method

Unit roots, spurious regression and the basis of pairs trading

Reported in interviews at

Jane Street, Citadel, Two Sigma

A spread follows an Ornstein–Uhlenbeck process dX=θ(μ−X) dt+σ dWdX = \theta(\mu - X)\,dt + \sigma\,dWdX=θ(μ−X)dt+σdW with θ=5\theta = 5θ=5 per year. What is the half-life of a deviation, in trading days (252 a year), to one decimal?

More time series questions

A spread follows an Ornstein–Uhlenbeck process $dX = \theta(\mu - X)\,dt + \sigma\,dW$ with $\theta = 5$ per year. What is the half-life of a deviation, in trading days (252 a year), to one decimal?