Estimation and Inference Methods for Continuous-Time Models

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This research project involves developing new estimation and inference tools for continuous-time semimartingale models sampled at high frequency. The semimartingale model is the most general model for asset prices that precludes arbitrage opportunities and, as a result, has been the workhorse model in modern asset pricing.Semimartingales have different components: a stochastic drift capturing the smooth movement of the asset price, a continuous martingale part modeling diffusive volatility and a jump part capturing abrupt movements of the asset price. While each component plays a distinct role in applications, it is statistically nontrivial to disentangle one component from the others. The objective of this project is to develop a novel statistical estimation and inference procedure for the jump component of the semimartingale. Compared with the existing methods, the new procedure will be more robust, especially when price jumps are difficult to identify from the data.While the motivating examples in the proposed activity are those of financial models, the methods developed in this project are valid for generic semimartingales. Semimartingales play a central role in the general theory of stochastic processes and stochastic calculus. Besides economics and finance, semimartingales have also been used in biological, chemical, and electrical applications. The econometric and statistical methods developed here may find applications in these fields provided that observations are available at high frequencies.The project integrates research and education by working closely with graduate students in the form of research assistantships. The proposed methodologies involve new implementation procedures whose code will be made publicly available. The results will be disseminated broadly through publications and presentations at seminars, conferences and professional association meetings.