22 Dec

Schneider, M. and Lillo, F. (2016) Cross-Impact and No-Dynamic-Arbitrage


We extend the “No-dynamic-arbitrage and market impact”-framework of Jim Gatheral [Quantitative Finance, 10(7): 749-759 (2010)] to the multidimensional case where trading in one asset has a cross-impact on the price of other assets. From the condition of absence of dynamical arbitrage we derive theoretical limits for the size and form of cross-impact that can be directly verified on data. For bounded decay kernels we find that cross-impact must be an odd and linear function of trading intensity and cross-impact from asset i to asset j must be equal to the one from j to i. To test these constraints we estimate cross-impact among sovereign bonds traded on the electronic platform MOT. While we find significant violations of the above symmetry condition of cross-impact, we show that these are not arbitrageable with simple strategies because of the presence of the bid-ask spread.



28 Sep

Schneider, M., Lillo, F., and Pelizzon, L. (2016) How Has Sovereign Bond Market Liquidity Changed? – An Illiquidity Spillover Analysis. SAFE Working Paper No. 151


Amid increasing regulation, structural changes of the market and Quantitative Easing as well as extremely low yields, concerns about the market liquidity of the Eurozone sovereign debt markets have been raised. We aim to quantify illiquidity risks, especially such related to liquidity dry-ups, and illiquidity spillover across maturities by examining the reaction to illiquidity shocks at high frequencies in two ways:
a) the regular response to shocks using a variance decomposition and,
b) the response to shocks in the extremes by detecting illiquidity shocks and modeling those as ultivariate Hawkes processes.
We find that:
a) market liquidity is more fragile and less predictable when an asset is very illiquid and,
b) the response to shocks in the extremes is structurally different from the regular response.
In 2015 long-term bonds are less liquid and the medium-term bonds are liquid, although we observe that in the extremes the medium-term bonds are increasingly driven by illiquidity spillover from the long-term titles.


27 Apr

Taranto, D. E., Bormetti, G., Bouchaud, J.-P., Toth, B., and Lillo, F. (2016). Linear models for the impact of order flow on prices II. The Mixture Transition Distribution model


Modeling the impact of the order flow on asset prices is of primary importance to understand the behavior of financial markets. Part I of this paper reported the remarkable improvements in the description of the price dynamics which can be obtained when one incorporates the impact of past returns on the future order flow. However, impact models presented in Part I consider the order flow as an exogenous process, only characterized by its two-point correlations. This assumption seriously limits the forecasting ability of the model. Here we attempt to model directly the stream of discrete events with a so-called Mixture Transition Distribution (MTD) framework, introduced originally by Raftery (1985). We distinguish between price-changing and non price-changing events and combine them with the order sign in order to reduce the order flow dynamics to the dynamics of a four-state discrete random variable. The MTD represents a parsimonious approximation of a full high-order Markov chain. The new approach captures with adequate realism the conditional correlation functions between signed events for both small and large tick stocks and signature plots. From a methodological viewpoint, we discuss a novel and flexible way to calibrate a large class of MTD models with a very large number of parameters. In spite of this large number of parameters, an out-of-sample analysis confirms that the model does not overfit the data.


12 Feb

Taranto, D. E., Bormetti, G., Bouchaud, J.-P., Toth, B., and Lillo, F. (2016). Linear models for the impact of order flow on prices I. Propagators: Transient vs. History Dependent Impact


Market impact is a key concept in the study of financial markets and several models have been proposed in the literature so far. The Transient Impact Model (TIM) posits that the price at high frequency time scales is a linear combination of the signs of the past executed market orders, weighted by a so-called propagator function. An alternative description — the History Dependent Impact Model (HDIM) — assumes that the deviation between the realised order sign and its expected level impacts the price linearly and permanently. The two models, however, should be extended since prices are a priori influenced not only by the past order flow, but also by the past realisation of returns themselves. In this paper, we propose a two-event framework, where price-changing and non price-changing events are considered separately. Two-event propagator models provide a remarkable improvement of the description of the market impact, especially for large tick stocks, where the events of price changes are very rare and very informative. Specifically the extended approach captures the excess anti-correlation between past returns and subsequent order flow which is missing in one-event models. Our results document the superior performances of the HDIMs even though only in minor relative terms compared to TIMs. This is somewhat surprising, because HDIMs are well grounded theoretically, while TIMs are, strictly speaking, inconsistent.


22 May

Corsi, F., Lillo, F. and Pirino, D. (2015). Measuring Flight-to-Quality with Granger-Causality Tail Risk Networks.

We introduce an econometric method to detect and analyze events of flight-to-quality by financial institutions. Specifically, using the recently proposed test for the detection of Granger causality in risk (Hong et al. 2009), we construct a bipartite network of systemically important banks and sovereign bonds, where the presence of a link between two nodes indicates the existence of a tail causal relation. This means that tail events in the equity variation of a bank helps in forecasting a tail event in the price variation of a bond. Inspired by a simple theoretical model of flight-to-quality, we interpret links of the bipartite networks as distressed trading of banks directed toward the sovereign debt market and we use them for defining indicators of flight-to-quality episodes. Based on the quality of the involved bonds, we distinguish different patterns of flight-to-quality in the 2006-2014 period. In particular, we document that, during the recent Eurozone crisis, banks with a considerable systemic importance have significantly impacted the sovereign debt market chasing the top-quality government bonds. Finally, an out of sample analysis shows that connectedness and centrality network metrics have a significant cross-sectional forecasting power of bond quality measures.

14 Nov

Sabelli, C., Pioppi, M., Sitzia, L. and Bormetti, G. (2014). Multi-curve HJM modelling for risk management.

We present a HJM approach to the projection of multiple yield curves developed to capture the volatility content of historical term structures for risk management purposes. Since we observe the empirical data at daily frequency and only for a finite number of time to maturity buckets, we propose a modelling framework which is inherently discrete. In particular, we show how to approximate the HJM continuous time description of the multi-curve dynamics by a Vector Autoregressive process of order one. The resulting dynamics lends itself to a feasible estimation of the model volatility-correlation structure. Then, resorting to the Principal Component Analysis we further simplify the dynamics reducing the number of covariance components. Applying the constant volatility version of our model on a sample of curves from the Euro area, we demonstrate its forecasting ability through an out-of-sample test.

Available at: http://arxiv.org/abs/1411.3977

20 Oct

Marmi, S., Nassigh, A. and Regoli, D. (2014). Sovereign Ratings Implied by Coupled CDS-Bond Market Data

We propose an approach to sovereign market implied ratings based on information coming both from Credit Default Swap spreads and bond spreads in a unified way. Operationally speaking, we implement a Support Vector Machine type of selection in the plane CDS-bond. Our numerical results seem to confirm that introducing the bond dimension accounts for implied ratings more accurate and with greater predictive power with respect to the 1-dimensional CDS implied ratings.

Available at http://ssrn.com/abstract=2512238

22 Jul

Bandi, F., Pirino, D. and Renò, R. (2013). EXcess Idle Time.

We introduce a novel stochastic quantity, named excess idle time (EXIT), measuring the extent of sluggishness in observed high-frequency financial prices. Using a limit theory robust to market microstructure noise, we provide econometric support for the fact that high-frequency transaction prices are, coherently with liquidity and asymmetric information theories of price determination, generally stickier than implied by the ubiquitous semimartingale assumptions (and its microstructure noise-contaminated counterpart). EXIT provides, for every asset and each trading day, a proxy for the extent of frictions (liquidity and asymmetric information) which is conceptually different from traditional price-impact measures. We relate it to existing measures and show its favorable performance under realistic data generating processes. We conclude by showing that EXIT uncovers an economically-meaningful short-term and long-term liquidity premium in market returns.

22 Jul

Bottazzi G. and Pirino D. (2010). Measuring Industry Relatedness and Corporate Coherence.

Since the seminal contribution of Teece et al. (1994), the strength, scope and quality of corporate diversification is often detected comparing the observed value of some statistics derived from the diversification patterns of a sample of firms, with its expected value. The latter is obtained under a null hypothesis which assumes some random assignment procedure of sectors to firms. The approaches generally adopted in the literature present two problems. First, being based on the observed value of a statistic, these methods could lead, depending on the nature of the sample, to noisy and non-homogeneous estimates. Second, the benchmark value used to identify the presence and strength of deterministic patterns are obtained under specific and privileged null hypothesis. Both effects could lead to the erroneous classification of spurious random effects as deterministic. This paper shows that the adoption of p-scores as measure of relatedness strongly alleviate the first problem, leading to cleaner and more homogeneous estimates. We design and implement a null hypothesis which rules out random artifacts and effectively identify new features in firm diversification pattern. Using the NBER database on patents, we apply our results to the study of the relationship between the coherence and the scope of corporate patent portfolios.