Market making with inventory control and order book information

Abstract

We introduce a new market making algorithm, the Signal-adaptive (SA) strategy, that takes into account the empirical recurrences of the historical intra-day price series of IPOs and the current risk properties addressed by the market maker. Empirical analysis on IPO high-frequency data allows to compare the performance of the SA strategy with two state-of-art competing strategies, suggesting that the SA strategy could be suitable for the price support activity of the IPO in the first days of its issuance.

Keywords:

• Algorithmic trading
• High-frequency trading
• Initial public offerings
• Underwriter
• Fintech

JEL classifications:

• G14
• G18

Acknowledgments

The authors would like to thank the referees and Paolo Pagnottoni for helpful comments and suggestions.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 In terms of information efficiency (Zhang 2010), volatility (Hagströmer and Nordén 2013, Brogaard et al. 2014, Caivano 2015) and liquidity (Menkveld 2013, Kirilenko et al. 2017)

2 For completeness, robustness test for values of $\alpha =[0.4;0.6]$ and $\text{β}=[0.6;0.4]$ result in qualitatively similar results and are available in Appendix 4. Research is high on the agenda for the development of data-driven methods to select the optimal values of α and β.

3 We use AMF Euronext Paris data obtained via BEDOFIH. This database includes trades and orders with the highest frequency contained in the most important European Stock Markets such as London Stock Exchange, BATS, CHI-X, Deutsche Boerse Xetra, AMF Euronext Paris and Eurex (Derivatives Markets).

4 We assume that the sequence of orders in the provided database follows the temporary arrival of the orders in the market.

5 I.e. CurrentOB input parameter of Algorithm 2.

6 In the Signal-Adaptive case, the input parameters are inventory and total queue sizes.

7 The assumption of constant order size is in line with previous research works such as Law and Viens (2020), Huang et al. (2015), Lu and Abergel (2018), and Baldacci et al. (2020).

8 The backtesting state in which the market makers start with an inventory containing zero stocks is in line with previous research work such as Guéant et al. (2013).

9 The transaction costs were not considered during the backtesting in previous research such as Lu and Abergel (2018).

10 The assumption of zero latency in the positioning of market maker's orders in the market is in line qith previous research work such as Fushimi and Rojas (2018).

11 Notice that (5(5) $\begin{array}{rl}{\mathrm{W}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{t}\mathrm{h}\mathrm{M}\mathrm{M}}_t& ={\mathrm{Q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}\mathrm{o}\mathrm{f}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{c}\mathrm{k}\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{n}\mathrm{v}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{o}\mathrm{r}\mathrm{y}}_t\times {\mathrm{B}\mathrm{e}\mathrm{s}\mathrm{t}\mathrm{B}\mathrm{I}\mathrm{D}}_t\\ & +{\mathrm{C}\mathrm{a}\mathrm{s}\mathrm{h}}_t\end{array}$(5) ) and (6(6) $\begin{array}{rl}{\mathrm{W}\mathrm{e}\mathrm{a}\mathrm{l}\mathrm{t}\mathrm{h}\mathrm{M}\mathrm{M}}_t& ={\mathrm{Q}\mathrm{u}\mathrm{a}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{t}\mathrm{y}\mathrm{o}\mathrm{f}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{c}\mathrm{k}\mathrm{s}\mathrm{i}\mathrm{n}\mathrm{i}\mathrm{n}\mathrm{v}\mathrm{e}\mathrm{n}\mathrm{t}\mathrm{o}\mathrm{r}\mathrm{y}}_t\\ & \times {\mathrm{B}\mathrm{e}\mathrm{s}\mathrm{t}\mathrm{A}\mathrm{S}\mathrm{K}}_t+{\mathrm{C}\mathrm{a}\mathrm{s}\mathrm{h}}_t\end{array}$(6) ) assume unlimited liquidity on both ASK and BID (as the quantity at time t can be infinite, as per the unlimited cash availability, which is an assumption we rely on.