Testing for Jumps and Modeling Volatility in Asset Prices

Observers of financial markets have long noted that asset prices are very volatileand commonly exhibit jumps (price spikes). Thus, the assumption of a continuousprocess for asset price behavior is often violated in practice. Although empiricalstudies have found that the impact of such jumps is transitory, the shortterm effectin the volatility may nonetheless be considerable with important financial implicationsfor the valuation of derivatives, asset allocation and risk management.This dissertation contributes to the literature in two areas. First, I evaluate thesmall sample properties of a nonparametric method for identifying jumps. I focus onthe implication of adding noise to the prices and recent methods developed to contendwith such market frictions. Initially, I examine the properties and convergence resultsof the power variations that constitute the jump statistics. Then I document theasymptotic results of these jump statistics. Finally, I estimate their size and power. Iexamine these properties using a stochastic volatility model incorporating alternativenoise and jump processes. I find that the properties of the statistics remain close to theasymptotics when methods for managing the effects of noise are applied judiciously.Improper use leads to invalid tests or tests with low power. Empirical evidencedemonstrates that the nonparametric method performs well for alternative models,noise processes, and jump distributions.In the second essay, I present a study on market data from U.S. energy futuresmarkets. I apply a nonparametric method to identify jumps in futures prices ofcrude oil, heating oil and natural gas contracts traded on the New York MercantileExchange. The sample period of the intraday data covers January 1990 to January2008. Alternative methods such as staggered returns and optimal sampling frequencymethods are used to remove the effects of microstructure noise which biases the testsagainst detecting jumps.I obtain several important empirical results: (i) The realized volatility of naturalgas futures exceeds that of heating oil and crude oil. (ii) In these commodities,large volatility days are often associated with large jump components and large jumpcomponents are often associated with weekly announcements of inventory levels. (iii)The realized volatility and smooth volatility components in natural gas and heatingoil futures are higher in winter months than in summer months. Moreover, coldweather and inventory surprises cause the volatility in natural gas and heating oil toincrease during the winter season. (iv) The jump component produces a transitorysurge in total volatility, and there is a strong reversal in volatility on days followinga significant jump day. (v) I find that including jump and seasonal componentsas explanatory variables significantly improves the modeling and forecasting of therealized volatility.