Measuring the resiliency of an electronic limit order book

An electronic limit order book is resilient when it reverts to its normal shape promptly after large trades. This paper suggests a continuous-time impulse response function based on intensities, which formalizes resiliency in terms of a time-frame and probability of order book replenishment. This is then estimated for trading on an LSE order book, using an appropriate parametric model which views orders and cancellations as a mutually-exciting ten-variate Hawkes point process. Consistent with findings in the related literature, in over 60 per cent of cases, the order book does not replenish reliably after a large trade. However, if it does replenish, it does so with a fairly fast half life of around 20 s. Various other dynamics are quantified.