This thesis documents the research and findings in the following three related areas of financial econometrics: The first essay examines whether volatility contains information to predict the likelihood of a price jump during the next trading day. It is motivated by the theoretical model of Bansal & Shaliastovich (2008) who develop a long-run learning model, arguing that market volatility should be able to predict the likelihood of jumps. I use S&P 500 futures prices and extensions of the GARCH jump model of Maheu & McCurdy (2004) to relate jump probabilities to conditional volatility. Since volatility is a latent variable, which can be measured using different variables, I consider predictions based upon squared daily return, at-the-money implied volatility, model-free im- plied volatility and high-frequency realized volatility. I find evidence that volatility can predict jump likelihood and the best predictive variable is the model-free implied volatility: which is constructed using cross-section of option prices. Therefore, this thesis contributes to the current literature by documenting the information efficiency of option prices when predicting the future likelihood of jumps. In addition. I also develop a new approach based on Poisson regression which compares the jump intensity obtained from the GARCH jump model with the intraday jump numbers counted using the method of Andersen et al. (2007b). I find the two measures of jumps match fairly well with each other in the period from 1990 to 1997. However, any such relationship seems to disappear in the later period from 1998 to 2004. The second essay is motivated by the affine jump-diffusion model of Duffie et al. (2000), which allows jump intensity to be an affine function of state variables. I examine whether volatility can predict the intensity of price jumps in stochastic volatility jump models, estimated using Markov Chain Monte Carlo simulation. Comparing implied volatility with high-frequency realized volatility, I find allowing the jump intensity to be an affine function of model-free implied volatility yields the best model, based on either the Deviance Information Criterion or on diagnostic tests. Further comparison are made for candidate AR(l) process which specify the stochastic volatility. I find a jump model with the log variance an AR( 1) process performs better than a jump model with Ornstein-Uhlenbeck stochastic volatility. In a Monte Carlo simulation, I find the Deviance Information Criterion is a reliable criterion to differentiate between competing equity price dynamics when there are price jumps and volatility is stochastic. In addition to examining univariate equity return models, in the third essay I also develop a bivariate equity return model which simultaneously captures time-varying correlation and volatility spillovers in the international equity markets. This model is calibrated using the weekly equity index returns from the US. UK, Germany, India and Brazil stock markets and it is compared with simplier model specifications. I find evidence that supports time varying correlation between equity markets in both developed and developing economics. How- ever, the volatility spillovers mainly exist from US equity returns to equity returns in other economies. This thesis concludes with a short discussion of its limitations and future research directions.
| Identifer | oai:union.ndltd.org:bl.uk/oai:ethos.bl.uk:556669 |
| Date | January 2010 |
| Creators | Xu, Gang |
| Publisher | Lancaster University |
| Source Sets | Ethos UK |
| Detected Language | English |
| Type | Electronic Thesis or Dissertation |
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