Are financial markets becoming systemically more unstable?

Are financial markets becoming systemically more unstable? Lucio Maria Calcagnile joint work with Giacomo Bormetti, Michele Treccani, Stefano Marmi, Fabrizio Lillo www.list-group.com www.quantlab.it Parma, 29 th January 25 XVI Workshop on Quantitative Finance / 6

Systemic instabilities and high-frequency trading Financial markets are intrinsically unstable and display large price changes There is growing concern about the possible role of automated High Frequency Trading as responsible of large price jumps HFT as means of contagion? (Gerig 22) Debate partly driven by the Flash Crash of 6th May 2 Market interconnection and automated high frequency trading may trigger endogenous mechanisms leading to systemic events. Questions motivating our study: How frequent are systemic events? Has their frequency changed over time? 2 Have they an exogenous origin (reaction to a news) or an endogenous one? 3 How can we model their self-exciting dynamics? 2 / 6

Talk outline Data Instability definition and detection Historical evolution of systemic instabilities (years 2 23) Exogenous (news-related) vs endogenous Modelling the self-exciting character of instabilities 3 / 6

Data Financial data years 2 23 stocks from the Russell 3 Index (US equity markets, mostly NYSE and NASDAQ) 4 highly liquid stocks for each year -minute closing price data, regular trading session 9:3 a.m. 4: p.m. News data preannounced macroeconomic news (Existing/New Home Sales, monetary policy announcements by FOMC, Manifacturing Index, Consumer Confidence/Sentiment,... ) with announcement time within the US trading session 5 26 news per year 4 / 6

Defining and detecting instabilities Jump: r t σ t > θ r t = ln pt p t (logarithmic returns) σ 2 t = cα i ( α)i r t i r t i, α /3 (proxy of local volatility) θ = 4, 5, 6,... (jump threshold) We study the statistical properties of the cojump multiplicity time series: M t = {assets} { rt σt >θ} M t {,,..., N = 4} 5 / 6

Introduction and preliminaries Historical view Exogenous vs endogenous The model Conclusions Historical view 2 M 5 6 M M 2 2 M 4 4 M 8 8 M 4 4 PM 3 PM 2 PM PM 2 AM AM AM 9 AM Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec FOMC eight announcements per year recognisable around 2:5 p.m. in 2 (left) many low-multiplicity cojumps and few high-multiplicity cojumps; in 23 (right) it is quite the opposite from 2 to 23 synchronisation of instabilities increased significantly indication that modern financial markets have become more systemically unstable 6 / 6

Historical view log (Minutes with jump) Cojump frequency (%) 5 4 3 θ = 4 θ = 8 θ = 6 θ = 2 2 23 25 27 29 2 23 2 23 25 27 29 2 23 Year Cojump frequency log CCDF 5 M 2 M M 3 M 6 2 23 25 27 29 2 23 Year Year θ = 4 2 29 θ = 6 23 2 2 θ = 8 25 θ = -2 27 23 absolute frequency of all instabilities has decreased over the years (true for Left: number of minutes with M all values of θ) -4-2 M.5 2-4 22-6 7-6 Right (θ = 4): number of minutes with M 2,, 3, 6 divided by the number of minutes with M (normalised to the 2 value) relative frequency of systemic events has actually increased Multiplicity (M) the higher the cojump multiplicity, the more intense this effect 7 / 6

θ = 4 θ = 8 θ = 6 θ = log ( Historical 2 view Cojump frequency (%) 2 2 23 25 27 29 2 23 θ = 4 θ = 6 θ = 8 θ = Year 2 23 25 27 29 2 23 Year Co log CCDF 2 23 25 27 29 2 23-2 Year 2 23 25 27-4 -2 M.5 2-4 22-6 7-6 Multiplicity (M) 29 2 23 Left (M 3): sensitivity of the results to the jump threshold θ the increase of systemic events is robust with respect to θ Right: overall multiplicity distribution multiplicity seems to follow a power-law distribution and thus the probability of systemic cojumps is quite large multiplicity distributions become fatter-tailed over the years tail exponent is close to.5 (2, 22), similarly to what observed in Joulin et al. (28) 8 / 6

Exogenous vs endogenous instabilities Fractionb b 2 M 2 4 6 8 2 4 min min 5 min 5 min 2 M M 3 M 6 b bfraction 2 23 25 27 29 2 23 Top: for every multiplicity M (x-axis), fraction of systemic events of multiplicity M preceded by a macroeconomic news in the last (synchronous), 5,, 5 minutes. Year synchronous co-occurrences are quite rare letting some minutes ( 5) to pass after a news, we are able to attribute many systemic events to a news, but waiting more (, 5 minutes) does not provide a further significant gain We thus say that a systemic instability event has an exogenous origin if it happens within a 5-minute time window from a news release. 9 / 6

Exogenous vs endogenous instabilities Fractionb b 2 M 2 4 6 8 2 4 min min 5 min 5 min 2 M M 3 M 6 b bfraction 2 23 25 27 29 2 23 Year Bottom: fraction of systemic instabilities with exogenous origin less than 5% of systemic instability events is exogenous exogenous systemic instabilities are diminishing in recent years? endogenously generated systemic instabilities seem to be a worryingly large part of all instabilities / 6

Self-exciting cojumps Bormetti et al. (24) showed the strong self-exciting character of market price instabilities: the single-asset jump dynamics is well described by a -D Hawkes process an asset-based Hawkes factor model captures the self and cross-asset jump clustering features (factor: M 4 when N = 2, M 6 when N = 4) However, the factor model approach ignores the cojump multiplicity above the factor-defining threshold. Deeper investigation on the role of the multiplicity: (To what degree) does a higher multiplicity of a systemic instability anticipate more systemic instabilities? [ ] P t (t, t + τ] s.t. M t J M t M 2 (To what degree) does a higher multiplicity of a systemic instability precede systemic instabilities of higher multiplicity? [ ] E M t M t M, t (t, t + τ] s.t. M t > G. Bormetti, L. M. Calcagnile, M. Treccani, F. Corsi, S. Marmi, F. Lillo, Modelling systemic price cojumps with Hawkes factor models, Quantitative Finance 24 (to appear), DOI:.8/4697688.24.996586. / 6

Hawkes processes (Hawkes, 97) A Hawkes process is a self-exciting point process defined by the intensity λ(t) = µ + ν(t t i ) = µ + α e β(t t i ), t i <t t i <t where µ is a deterministic function called the base intensity and ν is a positive decreasing weight function. 2 / 6

Hawkes processes (Hawkes, 97) A Hawkes process is a self-exciting point process defined by the intensity λ(t) = µ + ν(t t i ) = µ + α e β(t t i ), t i <t t i <t where µ is a deterministic function called the base intensity and ν is a positive decreasing weight function. A multidimensional Hawkes process is defined by a vector of intensities N λ i (t) = µ i + α ij e β ij (t t i ), i =,..., N. j= t j <t Multidimensional Hawkes processes are able to describe self and cross excitation between signals, but are difficult to calibrate. 2 / 6

A multivariate Hawkes model for the cojump multiplicities We apply a multivariate Hawkes process to the vector of multiplicities,..., N ι(t) = (ι (t),..., ι N (t)), ι i (t) = {Mt =i} Intensity vector λ(t) = (λ (t),..., λ N (t)) λ i (t) = µ i + N j= t j <t α ij e β ij (t t i ), i =,..., N Γ ij = α ij β ij ; the process is stationary if ρ(γ) < E [λ(t)] = (I N Γ) µ 3 / 6

A multivariate Hawkes model for the cojump multiplicities We apply a multivariate Hawkes process to the vector of multiplicities,..., N ι(t) = (ι (t),..., ι N (t)), ι i (t) = {Mt =i} Intensity vector λ(t) = (λ (t),..., λ N (t)) λ i (t) = µ i + N j= t j <t α ij e β ij (t t i ), i =,..., N Γ ij = α ij β ij ; the process is stationary if ρ(γ) < E [λ(t)] = (I N Γ) µ Model specifications: β ij β > µ = η E [λ(t)], with < η < Γ ij = ( η) E[λ i (t)] Nk= E[λ k (t)] ( i k +) γ ( i j + ) γ β =.6 η =.5 γ = 2.65 3 / 6

i N-dimensional Hawkes model: results log Γij 4 Γii 2.75.5 5 4.25 5 4 j 6 5 4 i - log CCDF -2-3.85.5 Eigenvalues ρ (Γ) = η -4 Data Hawkes -5 Multiplicity 5 4 4 / 6

N-dimensional Hawkes model: results Higher multiplicity implies a higher probability of observing systemic events in the near future (τ = 5 min) Higher multiplicity anticipates systemic events of higher multiplicity P [Mt<t t+τ Mt M] P [Mt<t t+τ 6 Mt M].5 5.5 Data Poisson Data Poisson Hawkes Hawkes 5 Multiplicity (M) P [Mt<t t+τ 3 Mt M] E [Mt<t t+τ Mt M, Mt<t t+τ > ].5 5 75 5 25 Data Poisson Data Poisson Hawkes Hawkes 5 Multiplicity (M) 5 / 6

Conclusions In recent years (from 2 to 23) cross-asset synchronisation of price instabilities increased significantly While the number of single-asset instabilities has diminished, modern financial markets have become more systemically unstable Cojump multiplicity distributions are fatter-tailed in recent years, showing that systemic instabilities involving larger and larger parts of the markets are becoming more and more frequent Only a fraction of all systemic instabilities has a clear exogenous origin, while many others may be endogenously generated Higher cojump multiplicity implies both higher probability of new systemic events in the near future and systemic events with higher multiplicity An N-dimensional Hawkes process applied to the vector of multiplicities, 2,..., N = 4 effectively describes these two effects 6 / 6

Macroeconomic news dataset Table : Number of news announcements, divided by year and news category. 2 22 23 24 25 26 27 28 29 2 2 22 23 all years ADP Employment Report MEA 2 Beige Book MEA 8 8 8 7 8 8 8 8 8 8 8 8 8 3 Business Inventories MEA 3 6 5 2 2 2 2 2 2 2 2 Chairman Press Conference MMI 3 3 5 4 2 Chicago PMI MEA 2 2 2 2 2 2 2 2 2 2 2 2 55 Construction Spending MEA 2 2 2 2 2 2 2 2 2 2 2 2 2 56 Consumer Confidence MEA 2 2 2 2 2 2 2 2 2 3 2 2 56 Consumer Sentiment MEA 2 23 24 23 24 24 24 24 24 24 24 24 24 298 Dallas Fed Mfg Survey MEA 8 2 2 32 Durable Goods Orders MMI 2 EIA Petroleum Status Report MEA 4 5 52 52 53 52 52 52 52 52 482 Empire State Mfg Survey MEA Existing Home Sales MMI 2 2 2 2 2 2 2 2 2 2 2 2 2 56 Factory Orders MEA 2 2 2 2 2 2 2 2 2 2 2 2 2 56 FOMC Forecasts MMI 5 4 9 FOMC Meeting Announcement MMI 8 8 8 8 8 8 8 8 8 8 8 8 8 4 FOMC Minutes MMI 8 8 8 8 8 8 8 8 8 8 8 8 7 3 Housing Market Index MEA 2 2 2 2 2 2 2 2 96 ISM Mfg Index MMI 2 2 2 2 2 2 2 2 2 2 2 2 2 56 ISM Non-Manufacturing MEA 2 23 Employment Index Motor Vehicle Sales MEA 2 2 New Home Sales MMI 3 2 2 2 2 2 2 2 2 2 2 2 2 57 Pending Home Sales Index MEA 2 2 2 2 3 2 2 2 97 Personal Income and Outlays MMI Philadelphia Fed Survey MMI 2 2 2 2 2 2 2 2 2 2 2 2 2 56 Retail Sales MMI Treasury Budget MEA 2 2 2 2 2 2 2 2 2 2 2 53 all categories 47 69 59 74 22 245 244 256 256 246 255 266 259 2888 2 Merit Extra Attention (Econoday) 3 Market Moving Indicator (Econoday) 6 / 6

Model parameter estimation MLE of our model s parameters would require the development of an ad hoc code to make it computationally feasible. We follow instead a heuristic calibration procedure, exploring the parameter region on a.5-spaced mesh Weighted least squares approach to measure the discrepancy between results on real data and model data We consider χ 2 = M {5,,...65,7} (a d a m) 2 δ 2 d + δ2 m where a d (M), a m(m) are the average values of the indicator functions on real data and on model data (see figure at slide 5) and δ d (M), δ m(m) the standard errors We search parameter values that minimise χ 2,3 +.5 χ 2 2 For the 23 data we find: η =.5, β =.6, γ = 2.65, 6 / 6