Estimating Stochastic Volatility and Jumps Using High-Frequency Data and Bayesian Methods

Abstract

We compare two approaches for estimation of stochastic volatility and jumps in the EUR/ /USD time series-the non-parametric power-variation approach using high-frequency returns and the parametric Bayesian approach (MCMC estimation of SVJD models) using daily returns. We have found that the estimated jump probabilities based on these two methods are surprisingly uncorrelated (using a rank correlation coefficient). This means that the two methods do not identify jumps on the same days. We further found that the non-parametrically identified jumps are in fact almost indistinguishable from the continuous price volatility at the daily frequency because they are too small. In most cases, the parametric approach using daily data does not in fact identify real jumps (i.e. discontinuous price changes) but rather only large returns caused by continuous price volatility. So if these unusually high daily returns are to be modelled, the parametric approach should be used, but if the goal is to identify the discontinuous price changes in the price evolution, the non-parametric high-frequency-based methods should be preferred. Among other results, we further found that the non-parametrically identified jumps exhibit only weak clustering (analyzed using the Hawkes process), but relatively strong size dependency. In the case of parametrically identified jumps, no clustering was present. We further found that after the beginning of 2012, the amount of jumps in the EUR/ /USD series greatly increased, but the results of our study still hold.

Residual Shape Risk on Natural Gas Market with Mixed Jump Diffusion

“…Gas prices commonly depart from normality by exhibiting heavy tails and a leptokurtic shape (Benth et al 2008). They also exhibit jumps (Cao et al 2018;Ficura & Witzany 2016;Mason & Wilmot 2014), a time-varying volatility (Baum et al 2018;Brix et al 2018), and a mean reversion (Brix et al 2018;Hsu et al 2017). Moreover, they are affected by many other factors like storage, weather, seasonality and political events and decisions (Gomez-Valle et al 2018).…”

Profitability of Trading in the Direction of Asset Price Jumps - Analysis of Multiple Assets and Frequencies

“…Advances in Bayesian estimation methods and stochastic-volatility jump-diffusion models, as well as in high-frequency data analysis and the asymptotic theory of power variations, have spurred a renewed interest among researchers in the area of jump modelling. Numerous studies analysing the jump dynamics emerged in the recent years, identifying effects such as jump self-exciting and clustering effects (Fulop et al, 2014;Fičura and Witzany, 2016), contagion effects between the jumps in different markets (Ait-Sahalia et al, 2015;Fičura, 2015), as well as positive impact of jumps on the future asset price volatility (Corsi et al, 2010;Bandi and Reno, 2016).…”

Identifying Price Jumps from Daily Data with Bayesian vs. Non-Parametric Methods

“…Jumps significantly increase the size of the tails of the short-horizon return distribution, playing an important role in short-horizon VaR calculation (Witzany, 2013or Janda, Kourilek, 2020) and short-maturity option pricing (Fulop, Li and Yu, 2014). In addition to that, jumps exhibit different kind of dynamics than the continuous price volatility, most notably self-excitation and size-dependency (Fičura and Witzany, 2016), playing an important role in volatility forecasting (Corsi, Pirino, Reno, 2010). Additionally, the jumps may have a negative impact on market making strategies, they violate the continuous semi-martingale condition, negatively influencing option delta-hedging strategies, they increase the option volatility risk premium (Todorov, 2010) and based on recent studies, they also seem to carry momentum-like trading signals that can be utilized in trading (Novotny et.…”

“…The MCMC based approach was used in Eraker, Johannes and Polson (2003), Eraker (2004) or Witzany (2013). While in earlier studies jump occurrences were usually assumed to be independent, following a Poisson process with constant intensity, in the recent years, models that extend the dynamics of the jump component have been proposed, by utilizing the self-exciting Hawkes process to model the jump clustering effects (Ait-Sahalia et al 2015, Fulop, Li and Yu 2014or Fičura and Witzany 2016.…”