Latency and liquidity provision in a limit order book Julius Bonart and Martin D. Gould

Transcription

1 Latency and liquidity provision in a limit order book Julius Bonart and Martin D. Gould Lorenzo Dall Amico Lorenzo Dall Amico Latency and liquidity provision in a limit order book Julius Bonart and Martin D. Gould 1 / 16

2 Problem under analysis Limit orders provide liquidity Market orders consume liquidity This mechanism is a self organized process in a LOB. Market order volume Liquidity well studied problem Liquidity Market order arrivals is the problem addressed in this paper Lorenzo Dall Amico Latency and liquidity provision in a limit order book Julius Bonart and Martin D. Gould 2 / 16

3 Rules and notation order x is placed at price p x with volume ω x and positive sign on the ask and negative on the bid (the opposite of what we did) π is the tick size V A/B (t) is the volume at the best ask/bid Consider a buy order (similarly for a sell) if p x b t active limit order if b t < p x < a t active limit order that changes the spread if p x a t market order This dynamic is finely tuned and one must keep into account some strategic considerations left behind in a zero intelligence model. Lorenzo Dall Amico Latency and liquidity provision in a limit order book Julius Bonart and Martin D. Gould 3 / 16

4 Dataset LOBSTER database : many positive aspects but information is provided only on NASDAQ attention to stock for which it is the primary venue. 5 highly liquid stocks from 01/03/15 to 01/09/15 (Nasdaq) π = 0.01 $ but focus on large ticks : s t π and it is unlikely to put a new order inside the spread Lorenzo Dall Amico Latency and liquidity provision in a limit order book Julius Bonart and Martin D. Gould 4 / 16

5 Methodology We here consider a t, b t constant Let {t i } be the set of arrival time of the orders. An order is T-separated if t i+1 t i T and is price maintaining if it doesn t change the spread, else it is called price changing. M(T ) is the set of T separated price maintaining orders. For a given market order we define the buy/sell cumulative net order flow as W A/B (t i, τ) = V A/B (t i + τ) V A/B (t i ), τ R + Lorenzo Dall Amico Latency and liquidity provision in a limit order book Julius Bonart and Martin D. Gould 5 / 16

6 Results : inter arrival times ECDF = empirical cumulative density functions Figure Empirical cumulative density functions (ECDFs) of inter-arrival times t i = t i+1 t i for (solid red) MSFT, (dashed blue) INTC, (dash-dotted green) CSCO, (dotted violet) YHOO, and (thin solid orange) MU market order arrivals. The left panel shows the ECDF for the t i directly ; the right panel shows the same plots after subtracting the minimum inter-arrival time for each stock (which is about 0.7 µs in each case). Lorenzo Dall Amico Latency and liquidity provision in a limit order book Julius Bonart and Martin D. Gould 6 / 16

7 Figure Upper tails of the ECDFs of inter-arrival times for (solid red) MSFT,(dashed blue) INTC, (dash-dotted green) CSCO, (dotted violet) YHOO, and (thin solid orange) MU market order arrivals. Each plot shows 1 minus the ECDF in doubly logarithmic coordinates. Lorenzo Dall Amico Latency and liquidity provision in a limit order book Julius Bonart and Martin D. Gould 7 / 16

8 Results : net order flow trajectories The net order flow trajectories are quite noisy and an average must be performed. Figure A selection of individual cumulative net order-flow trajectories at the same-side best quote for MSFT, after the arrival of a price-maintaining market order with a separation time of at least T = 1 second. The left plot shows 3 trajectories that we chose uniformly at random ; the right plot shows all the trajectories on 31 March 2015 Lorenzo Dall Amico Latency and liquidity provision in a limit order book Julius Bonart and Martin D. Gould 8 / 16

9 Same side cumulative net order flow V S (τ) := 1 M(τ) k M(τ) Opposite side cumulative net order flow V O (τ) := 1 M(τ) k M(τ) [ Θ(ωk )W B (t k, τ) + Θ( ω k )W A (t k, τ) ] [ Θ( ωk )W B (t k, τ) + Θ(ω k )W A (t k, τ) ] To keep into account the diversities of the various markets, V S/O (τ) is renormalized by the average number of shares at the best quote. Lorenzo Dall Amico Latency and liquidity provision in a limit order book Julius Bonart and Martin D. Gould 9 / 16

10 Results : V S right after the arrival of a market order Figure Mean cumulative net order flow for the same-side best queue V S for (solid red) MSFT, (dashed blue) INTC, (dash-dotted green) CSCO, (dotted violet) YHOO, and (thin solid orange) MU, during the given times immediately after the arrival of a price-maintaining market order Four regimes : Platform latency Response - latency phase High speed reaction phase Lower speed reaction phase Lorenzo Dall Amico Latency and liquidity provision in a limit order book Julius Bonart and Martin D. Gould 10 / 16

11 Results : V O right after the arrival of a market order Figure Mean cumulative net order flow for the same-side best queue V O for (solid red) MSFT, (dashed blue) INTC, (dash-dotted green) CSCO, (dotted violet) YHOO, and (thin solid orange) MU, during the given times immediately after the arrival of a price-maintaining market order Four regimes : Platform latency Response - latency phase High speed reaction phase Lower speed reaction phase Lorenzo Dall Amico Latency and liquidity provision in a limit order book Julius Bonart and Martin D. Gould 11 / 16

12 Results : V S right before the arrival of a market order Figure Mean cumulative net order flow for the same-side best queue V S for (solid red) MSFT, (dashed blue) INTC, (dash-dotted green) CSCO, (dotted violet) YHOO, and (thin solid orange) MU, during the given times immediately before the arrival of a price-maintaining market order Lorenzo Dall Amico Latency and liquidity provision in a limit order book Julius Bonart and Martin D. Gould 12 / 16

13 Results : V O right before the arrival of a market order Figure Mean cumulative net order flow for the same-side best queue V O for (solid red) MSFT, (dashed blue) INTC, (dash-dotted green) CSCO, (dotted violet) YHOO, and (thin solid orange) MU, during the given times immediately before the arrival of a price-maintaining market order Lorenzo Dall Amico Latency and liquidity provision in a limit order book Julius Bonart and Martin D. Gould 13 / 16

14 Note The analysis was performed also in the case of large cancellations giving different results : the empirical study is specific to market orders arrivals. Lorenzo Dall Amico Latency and liquidity provision in a limit order book Julius Bonart and Martin D. Gould 14 / 16

15 THANK YOU! :-) Lorenzo Dall Amico Latency and liquidity provision in a limit order book Julius Bonart and Martin D. Gould 15 / 16

16 Bibliography J Bonart, M.D. Gould Latency and liquidity provision in a limit order book, Quantitative Finance, 2017 Lorenzo Dall Amico Latency and liquidity provision in a limit order book Julius Bonart and Martin D. Gould 16 / 16