Impact of Electronic Liquidity Providers Within a High-Frequency Agent-Based Modeling Framework

Abstract

The current contribution addresses the impact of high-frequency electronic liquidity provision strategies on the intraday dynamics of financial markets, by means of an artificial stock market. As novel design feature, an event-based intraday time implementation is proposed, allowing for the generation of time-stamped intraday events, which make possible both the aggregation of time series at various time frequencies, as well as the correct simulation of trading strategies that follow different temporal frequencies, e.g., low- and high-frequency. We provide new insights with respect to the determinants of extreme events, such as flash crashes. Finally, we compare the causal chains and the effectiveness of two potential regulatory policies under the same market circumstances, i.e., minimum resting time and financial-transaction taxes, not only with respect to their flash crash prevention power, but also regarding their impact on market participants and market quality, shedding new light on the policy trade-offs.

Appendices

A The Order Placement Model

As in Mandes (2015), the objective function $f(\mathbb {1}_{\mathtt {M}},\Delta )$ to be minimized captures the trade-off between execution cost and non-execution risk, balanced by agent’s sense of urgency $\lambda _u$:

$$\begin{aligned} f(\mathbb {1}_{\mathtt {M}},\Delta ) = \mathtt {cost}(\mathbb {1}_{\mathtt {M}},\Delta ) + \underbrace{ \lambda _u\,(1-\mathbb {1}_{\mathtt {M}})\,\mathtt {risk}(\Delta ) }_{\text {adjusted risk for limit orders}}, \end{aligned}$$

(7)

where $\mathbb {1}_{\mathtt {M}}$ is the binary decision variable discriminating between a market and a limit order, $\Delta$ is the relative limit distance for the limit order case, i.e., when $\mathbb {1}_{\mathtt {M}} = 0$.

The cost component $\mathtt {cost}(\mathbb {1}_{\mathtt {M}},\Delta )$ captures what is known as the implementation shortfall, i.e., the difference between a given benchmark, such as the current mid-price, and the effective order execution price. In order to discourage execution prices that are too far away beyond a certain short-term volatility threshold $\sigma _{is}$—and which are corresponding to highly unfavorable executions—the cost function penalizes executions outside the volatility-range, as follows:

$$\begin{aligned} \mathtt {cost}(\mathbb {1}_{\mathtt {M}},\Delta ) = {\left\{ \begin{array}{ll} \mathtt {imp.sh}(\mathbb {1}_{\mathtt {M}},\Delta ) &{} \mathtt {imp.sh}(\cdot ) \le \sigma _{is}\\ \beta \,\sigma _{is}\,\left( \mathtt {imp.sh}(\mathbb {1}_{\mathtt {M}},\Delta )/\sigma _{is}\right) ^{2} &{} \mathtt {imp.sh}(\cdot ) > \sigma _{is} \end{array}\right. }, \end{aligned}$$

(8)

where $\beta > 1$ is the penalty parameter.

The execution probability of a limit order expressed by $\mathtt {risk}(\Delta )$ depends on: order flow proxied by the order book imbalance $\mathtt {flow}(OBI)$, short-term market volatility $\mathtt {dyn}(\Delta )$ and order queue in front of the limit order $\mathtt {queue}(\Delta )$. Also included is an opportunity cost, which is a penalty function of order size $\mathtt {size}(V)$. The aggregate non-execution risk function is given by:

$$\begin{aligned} \mathtt {risk}(\Delta ) = \mathtt {flow}(OBI)\,\mathtt {size}(V)\,(\alpha _0 + \alpha _1\,\mathtt {dyn}(\Delta ) + \alpha _2\,\mathtt {queue}(\Delta )), \end{aligned}$$

(9)

where parameters $\alpha _0$, $\alpha _1$, $\alpha _2$ tune the general preference for market and limit orders, as well as the distribution of relative limit distances.

The functional forms of the four non-execution risk components are:

$$\begin{aligned} \mathtt {flow}(OBI) = \mu ^{OBI}, \end{aligned}$$

(10)

where $\mu$ is a parameter and OBI is the Order Book Imbalance indicator, which quantifies the difference between the cumulated volumes up to a certain depth level N on each side of the order book.

$$\begin{aligned} \mathtt {dyn}(\Delta ) = \sigma _{dyn}\,\left( \frac{\Delta -BM_{dyn}}{\sigma _{dyn}}\right) ^2, \end{aligned}$$

(11)

where the range $\sigma _{dyn}$ and the central benchmark $BM_{dyn}$ define the bands inside which the non-execution risk for limit orders increases sub-linearly.

$$\begin{aligned} \mathtt {size}(V) = \exp (V^{\eta }), \end{aligned}$$

(12)

where $\eta$ is a model parameter and the exponential assures that the values are always bigger than one.

Finally, the effective order queue effect $\mathtt {queue}(\Delta )$ reflects the cumulative size of the book queue situated in front of the client limit order, without assuming any functional form.

B Model Parameters

See Table 8.

Table 8 Model parameters