## Abstract

We investigate the effects of a Financial Transaction Tax (FTT) in an order-driven artificial financial market. FTTs are meant to limit short-term speculative behavior by reducing the amount of excess liquidity in the system. To quantify these effects, adjustments in trading strategies and their effects on liquidity need to be taken into account. We model an agent-based continuous double-auction, allowing for a continuum of investment strategies within the chartist/fundamentalist framework. For certain parameter combinations, our model is able to reproduce certain stylized facts of financial time-series. We find largely positive effects of the FTT for small tax rates. Additionally, for large tax rates we find the effects not to be as negative as previously found.

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## Notes

These revenues are estimated to range between 1 and 3 % of national GDPs. See, e.g. Pollin et al. (2003).

We should note, however, that many economists actually favor HFT, arguing that more liquid markets should be much more resilient, cf. Brogaard (2010). This might be justified if HFT activities were largely equivalent to market making. However, insofar as many of these strategies might have a destabilizing tendency, their ‘net effect’ on market efficiency and volatility might be ambiguous.

Liquidity is the ability to trade large size quickly, at low costs, see Harris (2003).

Bordo et al. (2001) find that the frequency of crises since 1973 has been twice that of the Bretton Woods and classical gold standard periods. Two important explanatory factors are financial globalization and expectations of bail-outs encouraging financial institutions to take on higher risks.

The different activity patterns of financial markets and goods markets are also emphasized by Aoki and Yoshikawa (2007), chapter 10.

We are currently dealing with point (4) as well. The basic idea is to have two asset markets where only one of them is being taxed.

An early example is Beja and Goldman (1980). See also LeBaron et al. (1999), Challet and Zhang (1997), Chiarella and Iori (2002), Lux and Marchesi (1999, 2000), Lux and Schornstein (2005), Raberto et al. (2003) and Chiarella et al. (2009). Among others, Allen and Taylor (1990) and Menkhoff (1998) provide empirical evidence on the use of chartist and fundamentalist strategies.

For two ex-ante identical markets, with one country unilaterally introducing the tax, Westerhoff and Dieci (2006) finds that the taxed market is stabilized while volatility in the tax haven strongly increases. Using laboratory experiments with markets of different size, Hanke et al. (2010) find that volatility decreases (increases), when the tax is introduced in the large (small) market.

Below, we will impose symmetry between the trend horizons, i.e. set \(H^b=H^t\).

Note how time- and price-priority favor the buying agent, i.e. the trade initiator, in the Example: He submitted a limit price of \(100.50\) but only pays \(100.00\).

Dividend payments are negligible on a short-term basis, since they are only paid once a year and usually only have a small effect on wealth. Ignoring dividend payments simplifies the analysis, since (without the FTT and with cash earning zero interest) the total amount of stocks and cash is constant over time.

We model trading dynamics on very short time-scales where the fundamental value is unlikely to change significantly. Furthermore, this assumption makes it possible to ignore adverse selection problems due to news arrival. As long as the fundamental volatility is relatively small (compared to the volatility of noise traders expectations), this does not affect many of the qualitative results.

Of course, ‘true’ fundamentals are unobservable in reality. Another interesting feature would be to model costly acquisition of the fundamental value.

Liquidity providers would be another possible label for the group of noise traders. The term noise traders however, emphasizes the random nature of their random limit price determination.

For example, the noise traders in Raberto et al. (2003) are constructed exactly in such a way, i.e. in their model informed traders are not necessary to reproduce volatility clustering and excess kurtosis. However, this is a very ‘direct’ way to guarantee volatility clustering in a model. It is not clear why agents should behave like this and there is in fact some evidence that past price volatility tends to lead the arrival of limit orders, see Zovko and Farmer (2002).

Note that since the width of the distribution is fixed, noise traders are more likely to submit market orders when the spread is small, while they are more likely to submit limit orders when the spread is large. This is in line with empirical findings, e.g. Biais et al. (1995), Bae et al. (2003), and Foucault et al. (2005).

See Giardina and Bouchaud (2003) for a similar explanation.

See Franke and Asada (2008).

Note that rule-of-thumb behavior, although having the weakness of being ‘ad-hoc’, is more realistic in terms of how actual people make decisions, see Gigerenzer (2008).

As an alternative, we could make agents’ aggressiveness explicitly dependent on economic variables (such as volatility) or on the relative weight of chartism and fundamentalism. In such a setting, the aggressiveness of chartists would be higher, since chartists are usually found to be less risk-averse than fundamentalists, see e.g. Menkhoff and Schmidt (2005). In order to reduce the complexity of the current model, we leave that for future research.

This ensures that agents do not run out of assets/cash.

See Harris (2003), Ch. 15.

Farmer and Lillo (2004) have shown that roughly 87 % of the market orders creating an immediate price change have a volume equal to the volume at the opposite best, while 97 % of the market orders creating an immediate price change have a volume at most of the sum of volumes available at the two best opposite prices.

See e.g. Cao et al. (2008). Note that fundamental traders will post limit orders with prices far away from the best quotes. If the agent is not patient enough, he will cancel his order prematurely.

See also Challet and Stinchcombe (2001).

Thus the probability of a particular agent being chosen equals \( (H^{w,i})^{-1} \). Agents with relatively small investment horizons are thus acting more frequently than those with longer horizons.

Hence, we ignore strategic considerations on behalf of the agents on the exact (intraday) time of approaching the market.

Recall that we also replaced the backward trend horizon by the forward trend horizon.

We will see below that the variablitiy across simulations is typically quite small, so this small number of runs is indeed already sufficient.

In principle, we would be happy to use an approach similar to Franke and Westerhoff (2012), where the ‘optimal’ parameters (with respect to the stylized facts) are estimated via moment-matching criteria. However, given the complexity of our model, and the related high-number of degrees-of-freedom, parameter estimation would be prohibitive.

See e.g. Lux (2008).

See Bouchaud et al. (2008) for an extensive overview.

For the estimation of the tail parameter, we used the usual Hill (1975) estimator based on the top 15 % observations of the absolute returns, i.e. ignoring signs. The values are not affected by focusing on positive or negative returns only.

The simulated prices are qualitatively very similar to the results for the unstable case in Youssefmir et al. (1998). There, the analysis is based on a much simpler version of the model, solved based on a mean-field approximation.

In simple terms, the leverage effect corresponds to a negative correlation between past returns and future volatility, see e.g. Bouchad et al. (2001).

See e.g. Thurner et al. (2012).

We used the following tax rates (in percent): 0 (baseline scenario), \(0.01, 0.02, 0.03, \ldots , 0.18\) %. We use 0.18 % as the maximum value, since the LOB may be empty at times for larger tax rates and we require at least one order to be on each side of the book to be existent at any point in time.

Note the relatively large change for very small tax rates (also present in the transaction volumes and the distortion). This effect is mostly driven by liquidity reductions from very short-term oriented informed traders, whose trades become unprofitable even for these very small tax rates. For larger tax rates, also longer-term oriented strategies are affected and the distortion increases again.

For larger tax rates, the volatility increases substantially. We do not show the results, since the LOB might become very sparse, with only few or no orders present at certain points in time.

The maximum tax rate used here is only 0.0035 %.

We tested a variety of (social) learning algorithms, using genetic algorithms, where successful strategies tend to replicate and spread through the population.

See e.g. Zovko and Farmer (2002).

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## Additional information

Funding for an earlier version of this paper by the Paul Woolley Centre for the Study of Capital Market Dysfunctionality at the University of Technology Sydney is acknowledged. We are grateful for helpful comments by Karl Finger, Reiner Franke, Tony He, and Daniel Ladley.

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Fricke, D., Lux, T. The effects of a financial transaction tax in an artificial financial market.
*J Econ Interact Coord* **10**, 119–150 (2015). https://doi.org/10.1007/s11403-013-0116-y

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DOI: https://doi.org/10.1007/s11403-013-0116-y

### Keywords

- Transaction tax
- Tobin tax
- Market microstructure
- Agent-based models
- Speculative bubbles

### JEL Classification

- H20
- C63
- D44