Essays on stochastic volatility models with jump clustering

This thesis investigates models of stochastic volatility which are able to accommodate the clustering of jumps typical of many high-frequency financial time series, both in terms of describing significant features of the data, and forecasting. Chapter 1 gives an overview on the jump-diffusion stochastic volatility models, clustering behaviours of jumps and contributions of this thesis to current literature. Chapter 2 examines the clustering behaviour of price and variance jumps using high-frequency data, modelled as a marked Hawkes process embedded in a bivariate jump-diffusion model with intraday seasonal effects. We find that the jumps of both individual stocks and a broad index exhibit self-exciting behaviour. The three dimensions of the model, namely positive price jumps, negative price jumps and variance jumps, impact one another in an asymmetric manner, that is positively and significantly correlated with jump size. We estimate model parameters using Bayesian inference by Markov Chain Monte Carlo, and find that the inclusion of the jump parameters improves model fitness. We quantify the jump intensity and study characteristics of jump clusters, we find under high-frequency settings, jump clustering activities can last 2.5 to 6 hours in average, we also find that the model with marked Hawkes process models mostly outperform others in terms of reproducing two cluster-related characteristics. Chapter 3 uses a bivariate jump-diffusion model incorporating jump clustering features by embedding a multivariate marked Hawkes process for high-frequency forecasting. In the out-of-sample period, we use a particle filter to estimate variance at each state and forward simulating return and variance distributions. We apply i a Kalman filter to correct errors that arise with microstructure noises in the highfrequency data. The simulation studies show the effectiveness of the Kalman filter. We show that the inclusion of jump clustering significantly improves the performance of high-frequency volatility forecasting and daily realised volatility forecasting. In high-frequency volatility forecasting, we find that forecasting performance is especially better with forecasting horizons of less than two hours. We also show that expected losses of two risk measures, value-at-risk and expected shortfall, can be reduced by up to 15% using models with jump clustering features. Chapter 4 forecasts Bitcoin’s returns and return jumps using a self-exciting process embedded in a stochastic volatility model. We show the existence of the jump clustering feature, which varies depending on the frequency of the data. In an out-of-sample setting, we use a particle filter to sample latent states and conduct one-step-ahead probabilistic forecasting on future jumps (underlying intensities). We assess the forecasts by a continuous ranked probability score. We further develop a statistic that takes the discrepancies between the predicted probabilities of positive and negative jumps. We find that high and low values of the difference in predicted probabilities of positive and negative jumps is able to predict returns, and that a trading strategy based on this has a Sharpe ratio of 4.36. Lastly, Chapter 5 concludes the thesis and discusses future research.