Characterizing financial crises using high-frequency data

Abstract

Recent advances in high-frequency financial econometrics enable us to characterize which components of the data generating processes change in crisis, and which do not. This paper introduces a new statistic which captures large discontinuities in the composition of a given price series. Monte Carlo simulations suggest that this statistic is useful in characterizing the tail behavior across different sample periods. An application to US Treasury market provides evidence consistent with identifying periods of stress via flight-to-cash behavior which results in increased abrupt price falls at the short end of the term structure and decreased negative price jumps at the long end.

Keywords:

• High-frequency data
• Tail behavior
• Financial crisis
• US Treasury markets

JEL Classifications:

• C58
• G01
• G12

Acknowledgments

Mardi Dungey passed away in January 2019, shortly after this paper was completed. We are grateful for discussions with Yacine Ait-Sahalia, Michael Fleming, Neil Shephard and comments from Jan Jacobs, Denise Osborn, Andrew Patton and participants at SoFiE, the Cambridge-Princeton Exchange, the Marie-Curie Training Workshop on High Frequency. We also thank Shabir AA Saleem for able research assistance. We are grateful to Ross Adams for managing the database.

Disclosure statement

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

Notes

1 For example almost all existing models of the transmission of crises through contagion can be characterized in this way. See the overview of modeling frameworks in Dungey et al. (2005).

2 Although Pukthuanthong and Roll (2015) use the jumps technology developed for high-frequency data, they apply it to daily data.

3 A closely related statistic is the activity signature function proposed by Todorov and Tauchen (2010).

4 The activity signature function of Todorov and Tauchen (2010) examines the same decomposition.

5 Aït-Sahalia and Jacod (2009a) also include tests for infinite activity and no Brownian motion, but as they are not germane to the application here and thus omitted from our discussion.

6 In practice, the degree of jump activity, β, needs to be estimated from the data. See Aït-Sahalia and Jacod (2009a), Aït-Sahalia and Jacod (2012b) for estimators of β which are based on the same series of truncated statistics. We use the estimator proposed in Aït-Sahalia and Jacod (2009a) to estimate β in the empirical application in Section 4.

7 A continuous random variable Z with probability density function $f\left(z\right)=2\varphi \left(z\right)\mathrm{\Phi }\left(\alpha z\right)$, where $\varphi \left(z\right)=\exp \left(\frac{-z^2}{2}\right)/\sqrt{2\pi }$ is a normal density, $\mathrm{\Phi }\left(\alpha z\right)={\int }_{-\mathrm{\infty }}^{\alpha z}\varphi \left(t\right)$ is a normal distribution function, α is the shape parameter that affects the skewness of the random variable. In the simulation the shape parameter is set to be $\alpha =4$, implying a skewness of 0.78, which is consistent with the skewness observed in financial returns data (see for example Fry et al. 2010).

8 In order to produce the main features of stochastic volatility model, we generate instantaneous log-returns by the continuous-time martingale: $\mathrm{d}p\left(t\right)=\sigma \left(t\right)\mathrm{d}{W}_p\left(t\right)$, where $W_p\left(t\right)$ denotes a standard Wiener process, and $\sigma \left(t\right)$ is given by a separate continuous time diffusion process. For, a diffusion limit of the GARCH(1,1) process is specified for $\sigma \left(t\right)$: $\mathrm{d}{\sigma }^2\left(t\right)=\theta (\omega -{\sigma }^2(t\left)\right)\mathrm{d}t+\left(2\lambda \theta {)}^{1/2}{\sigma }^2\right(t\left)\mathrm{d}{W}_{\sigma }\right(t),$ where $\omega >0$, $\theta >0$, $0<\lambda <1$, and the Wiener processes, $W_p\left(t\right)$ and $W_{\sigma }\left(t\right)$, are independent. The parameters values $\omega =0.636$, $\theta =0.035$, and $\lambda =0.296$ are chosen according to Andersen and Bollerslev (1998).

9 This is motivated by the literature which proposes a regime switching framework during crises, such as Akay et al. (2013).

10 Trading for the secondary US Treasury bond market is open for 9.5 hours per day from 8:00 am to 5:30 pm, which amounts to 114 observations with 5-minute intervals.

11 There are many chronologies of the crisis events of 2007–2008, including Rose and Spiegel (2012) and Bordo (2008).

12 Aït-Sahalia and Jacod (2012a) emphasize that unequally spaced data would potentially be more informative but the theory is not yet available to fully account for the endogeneity issue (see Aït-Sahalia and Jacod 2012a, page 1013). Thus the models used in this paper only use regular sampling.

13 The theoretical limit of $S_J$ is 1/k when additive noise dominates, is $1/\sqrt{k}$ when rounding error dominates. See Aït-Sahalia and Jacod (2012a) for details.

Additional information

Funding

Dungey and Yao acknowledge support from Australian Research Council [grant number DP130100168]. Yalaman acknowledges support from an Eskisehir Osmangazi University Research [grant number 201717A234].