There is considerable evidence that asset prices are subject to occasional extreme movements. For example, surprise macroeconomic announcements trigger a discontinuous (jump) process in interest rates. Similarly, electricity spot prices display extreme price movements of magnitudes rarely seen in the financial markets. Prom a statistical perspective, this suggests that standard pure-diffusion (non-jump) models are inappropriate for modelling these price series. By construction, the process induced by the Wiener pure-diffusion framework is continuous, yet observed jumps clearly arrive at discrete intervals.
The presence of jumps has the potential to adversely impact on model estimation in a number of ways, and this in turn affects the pricing of securities and financial derivatives. Further, the pervasiveness of jumps presents serious challenges to practitioners attempting to measure and manage financial risks. Therefore, a thorough understanding of the prevailing impact of jumps on attempts to model asset prices is crucial. These issues motivate this thesis, which is divided into four separate but related essays.
Essay One studies the modelling of short-term interest rates in the presence of jumps. The typical linear mean-reverting drift model is augmented with both time-varying conditional heteroscedasticity (via the LEVELS and GARCH effects) and a Poisson jump factor. Empirical results show that non-jump pure-diffusion models are mis-specified in modelling the short-rate because they imply a spuriously high speed of mean-reversion and high degree of persistence in volatility. However, the model misspecification problems are mitigated via the combined GARCH and jump factors in the proposed jump-diffusion model.
While the existence of jumps in interest rates is well documented, their impact on key parameter estimates remains unexplored. In particular, there has been much debate over the 'evidence' of nonlinearity in short-rate drift. This motivates Essay Two to study the impact of jumps on estimates of drift nonlinearity. A very general specification for nonlinear drift is augmented with a jump factor to model various US short-rates. Simulation exercises and empirical findings document that the pervasiveness of jumps induces spurious nonlinearity in the drift estimates of the pure-diffusion models. This apparent nonlinearity diminishes once the jump factor is explicitly introduced via the jump-diffusion model.
Essay Three considers modelling electricity spot prices. Energy markets are subject to unique factors that result in price dynamics quite dissimilar to traditional financial assets. This presents a number of challenges when attempting to model electricity spot prices. The extant literature typically adopts jump-diffusion models developed in interest-rate contexts, yet there are strong reasons to believe that these models are inappropriate for electricity price modelling. Essay Three proposes a variation to the existing jump-diffusion framework to model electricity spot prices. It implements a simple pre-estimation filtering procedure to partition the returns into normal and jump regimes. Simulation experiments and empirical results suggest that, compared to the existing jump-diffusion framework, the proposed model is more likely to produce economically plausible parameter estimates, especially for the mean jump size and speed of mean-reversion.
Essay Four considers the choice of different models for use in electricity risk management. The unusual nature of electricity markets makes risk management extremely challenging. In particular, the presence of extreme price movements affects the tail of the distribution of electricity price changes. Essay Four develops a semi-parametric model based on Extreme Value Theory (which explicitly models the extreme tails of the return distribution) to forecast Value-at-Risk (VaR) for electricity spot prices. Further, the proposed model accommodates both autoregression in the conditional mean and seasonality and asymmetric effects in the conditional volatility of price changes. Empirical analysis shows that, compared to a number of parametric and nonparametric methods, the proposed semi-parametric model is superior in providing appropriate unconditional and conditional interval coverage in forecasting out-of-sample VaR.
Overall, this thesis contributes to the literature by emphasizing the importance of accounting for the presence of jumps in modelling the short-rate and electricity spot prices.