Starting from a large tick asset, our approach enables us to reach the optimal tick size situation. Indeed, it is possible to obtain η = 1/2 and a spread close to one tick by changing the tick value only assuming that η increases continuously when the tick value decreases. Then, when modifying the tick value, the spread remains equal to one tick as long as α / 2-ηα ≥ 0. Indeed, if α * denotes the largest tick value such that η = 1/2 then for all α> α * market makers make positive profits with a spread of one tick and consequently maintain this spread Then, we obtain the following formula for the optimal tick value leading to η = 1/2:
α ≈ α0 (2η0) ^ (1 / (1-β / 2)).
Of course we do not pretend that in practice, applying such rule will exactly lead to an optimal tick value (in our sense). However, we do believe that this simple formula gives the right order of magnitude for the relevant tick value of a given asset.
Optimal tick value for small tick assets
A crucial point in our approach is that when changing the tick value of a large tick asset, the spread remains equal to one tick as long as market makers make profit with such a spread. So the spread (in tick unit) is invariant when the tick value is modified. For a small tick asset, when enlarging the tick value, both the spread and the number of trades adjust so that the spread and the volatility per trade have of the same order of magnitude. The way these two variables are jointly modified is intricate and this is why our method cannot, a priori, be used for small tick assets. However, let us stress the fact that it is still possible for the exchange to use a two steps procedure in the case of a small tick asset:
– Step 1: Enlarge sufficiently the tick value so that the asset becomes a large tick asset.
– Step 2: Use our methodology for large tick assets.
To contact the authors:
khalildayri@gmail.com
mathieu.rosenbaum@upmc.fr
Bibliography
- Dayri, K., and M. Rosenbaum, 2013, Large tick assets: implicit spread and optimal tick size, Preprint.
- Madhavan, A., Richardson, M., and M. Roomans, 1997, Why do security prices change? A transaction-level analysis of NYSE stocks, Review of Financial Studies 10, 1035-1064.
- Robert, CY, and M. Rosenbaum, 2011, A new approach for the dynamics of ultra-high-frequency data: The model with uncertainty zones, Journal of Financial Econometrics 9, 344-366.
- Wyart, M., Bouchaud, JP, Kockelkoren, J., Potters, M., and M. Vettorazzo, 2008, Relation between bid-ask spread, impact and volatility in double auction markets, Quantitative Finance 8, 41 – 57.
