Inference on Self‐Exciting Jumps in Prices and Volatility Using High‐Frequency Measures

Abstract

Dynamic jumps in the price and volatility of an asset are modelled using a joint Hawkes process in conjunction with a bivariate jump diffusion. A state space representation is used to link observed returns, plus nonparametric measures of integrated volatility and price jumps, to the specified model components; with Bayesian inference conducted using a Markov chain Monte Carlo algorithm. An evaluation of marginal likelihoods for the proposed model relative to a large number of alternative models, including some that have featured in the literature, is provided. An extensive empirical investigation is undertaken using data on the S&P500 market index over the 1996 to 2014 period, with substantial support for dynamic jump intensities -including in terms of predictive accuracy -documented.alternatives to the state space form.As in Bandi and Reno (2016) spot price data only is used to analyse all models, with the results unaffected as a consequence by the nature of -and potential dynamics in -volatility and jump risk premia (see Bollerslev, Gibson andManeesoonthorn, Martin, Forbes andGrose, 2012, for analyses in which such specifications do feature). However, and in contrast with Bandi and Reno, data measured at the daily frequency (including that which aggregates to the daily level over intraday observations) underpins the analysis. In common with the large part of the relevant literature (Bollerslev, Kretschmer, Pigorsch andTauchen, 2009, andLiu, Patton and Sheppard, 2015, amongst many others) we also choose to construct all measures using within-day observations only, thereby avoiding the need to model closeto-open movements in the index (as in, for example, Ahoniemi, Fuertes and Olmo, 2015, and Andersen, Bollerslev and Huang, 2011) and any specific dynamic movements therein. (See Hansen and Lunde, 2005, and Takahashi, Omori and Watanabe, 2009, for earlier discussions on the role played by non-trading periods in the construction of high frequency measures).The remainder of the paper is organized as follows. Section 2 describes our proposed asset price model and its main properties. The continuous time representation is presented first, followed by the discrete time state space structure adopted for inference. Details are given of the high frequency measures of volatility and price jumps that are used to supplement daily returns in defining the state space model. The Bayesian inferential approach is then outlined in Section 3, including the way in which the alternative specifications are to be assessed, relative to the most general model, both in terms of marginal likelihoods and cumulative log scores. Results from the extensive empirical analysis of the S&P500 index are presented and discussed in Section 4. The benefits of allowing for a very flexible dynamic specification for price and variance jumps are confirmed by both the within-sample and predictive assessments, with the bivariate Hawkes specification given strong support by the data, relative to other more restrictive models. The empirical results also indic...

Do Jumps Matter for Volatility Forecasting? Evidence from Energy Markets

“…, , , Tauchen and Zhou (2011), and Andersen et al (2012) propose a number of non-parametric tests to identify jumps. Aït-Sahalia et al (2014) and Maneesoonthorn et al (2014) model jumps as processes that are self-exciting and explore the implications of this modeling framework for derivatives prices. Aït-Sahalia et al (2014) and Maneesoonthorn et al (2014) model jumps as processes that are self-exciting and explore the implications of this modeling framework for derivatives prices.…”

“…Eraker et al (2003) and Eraker (2004) rely on tightly parameterized continuous-time models to estimate jumps. Aït-Sahalia et al (2014) and Maneesoonthorn et al (2014) model jumps as processes that are self-exciting and explore the implications of this modeling framework for derivatives prices. 2 We contribute to this literature by presenting a thorough and comprehensive model-free study on the dynamics of jumps in four leading energy markets.…”

Model Complexity and Out-of-Sample Performance: Evidence from S&P 500 Index Returns

“…Using high-frequency returns would also increase the computational burden which is already substantial given the large number of models we consider. 3 While our tests focus on daily observations, to integrate the benefits of high-frequency data we follow Maneesoonthorn et al (2017) and use intradaily realized volatility measures for model estimation. This approach reduces the computational burden compared to using intradaily returns directly and mitigates issues with comparing model forecasts at different observation frequencies.…”

Discussion of ‘Deep learning for finance: deep portfolios’

“…Individual time series of financial returns are well known to display distinctive features, including those characterized by strong positive autocorrelation in the second moment, known as volatility clustering, with occasional discontinuity caused by extreme events, or jumps. These long memory‐inducing features tend to occur either simultaneously, or with some small delay, in the returns of different assets, providing notions of systemic risk, volatility spillovers, and mutually exciting jumps (e.g., Brownlees and Engle , Diebold and Yilmaz and Maneesoonthorn, Forbes and Martin ). While modeling these features parametrically can be cumbersome, with inferential methods for the inevitable nonlinear models challenging, the resulting output is, at least, interpretable.…”