On Stablecoin Price Processes and Arbitrage

Abstract

This study applies the Caginalp and Balenovic (1999) model for asset flow dynamics to fully collateralized stablecoins. The analysis provides novel insights on how trend-reversion and reactions to peg deviations work together to keep stablecoin prices close to the price they are targeting. A fixed-effects panel regression indicates that the model’s abstraction of trading motivations indeed fits stablecoin price processes well. The results convey first indication that theoretic stablecoin models might benefit from modeling price dynamics to switch between two market regimes: one for day-to-day price formation and limited arbitrage activity; and one for extraordinary market situations.

I thank Gunduz Caginalp for his invaluable input and enlightening conversations. I also thank Martin Florian and Anna Almosova for their constructive feedback.

Appendices

A Robustness

The dataset applied in this study combines 11 timeseries of differing lengths and might thus be described as an unbalanced timeseries panel. While a large $T$ dimension is generally beneficial, simple panel data approaches might be misspecified. A first issue is serial correlation. In most financial time series prior realizations affect coming ones. Including lagged data might thus be useful to capture serial correlation in the data - this is usually referred to as dynamic panel modeling. Instead of including lagged data explicitly, in this study, the trend variable is carrying auto-regressive information.Using simple fixed-effects models jointly with lagged variables, however, induces the so-called Nickell bias as the lagged variable causes endogeneity in the regressors [42]. As argued by [21, p.163], including fixed-effects into dynamic specifications of panel data regressions, even for simple OLS estimates, can mitigate the issue to some degree. Their coefficients, however, are still seriously biased for small $T$. In our case, including coin-fixed-effects and considering that $T$ is very large, Nickell’s bias should be negligible.⁸ There are other issues known from time-series analysis, though. [46] warned about relying on the above for inference for non-stationary data (which might lead to spurious regression results) and suggested to check the error term for heteroskedasticity, serial correlation and nonnormality. To counter this problem, this study ensures stationarity using the Levin-Lin-Chu unit root test [37]. As the test does not reject the presence of a unit root for token supply and volatility, we take first differences of these variables.

As discussed earlier, we apply coin-FE panel regressions based on simple OLS-estimation. As a consequence, several assumptions are to be ensured. Residuals ought to display a mean of zero and be free of heteroscedasticity, cross-sectional, and serial correlation. Breusch-Pagan Lagrange Multiplier tests and Pesaran cross-sectional dependence tests are used to test for cross-sectional dependence in the residuals. Additionally, Student’s t-tests have been applied to check the residuals for a mean of zero. Breusch-Godfrey/Wooldridge tests have been applied to test for serial correlation. Breusch-Pagan tests are used for detecting heteroskedasticity. While a deviation from zero for the residuals is strongly rejected, unfortunately, the remaining tests reveal heteroscedasticity, serial, and also cross-sectional correlation. In other words, residuals are showing variance clusters and are depending on their own- and even lags across coins. As a consequence, the simple OLS estimator is biased. To still draw robust inferences from the estimated model, spacial correlation consistent (SCC) estimators introduced in [24] are used. The approach adapts Newey-West estimators to the panel setting and leads to robust standard errors even in the presence of heteroscedasticity and cross-sectional and serial correlation.

For tables and further details on the above robustness checks, please refer to the full paper.

B Tables

Table 1. Outliers.

Table 2. Coin-FE regression.