Essays in financial econometrics.
详细信息
文摘
The huge amount of tick-by-tick data provides rich and timely information regarding fluctuations of traded assets and their co-movements. Nevertheless, the existence of market microstructure noise interferes with estimation, especially when the sampling frequency increases to beyond every five minutes. The first chapter introduces the Quasi-Maximum Likelihood Estimator of volatility as a solution to this problem. In theory, the proposed approach is consistent, rate-efficient, and shares the model-free feature with non-parametric alternatives. In practice, it is also convenient and has better small sample performance without any tuning parameters. When measuring covariance and correlation, the fact that the two assets may not trade or otherwise be observed at exactly the same time, known as observation asynchronycity, is another issue that may distort the estimates. The second chapter, jointly written with Yacine Ait-Sahalia and Jianqing Fan, extends the Quasi-Maximum Likelihood Estimator to explore asynchronous and noisy data, with the help of generalized synchronization scheme. A fundamental problem in option pricing is to find explicit pricing formulae or efficient pricing algorithms. However, closed-form pricing formulae are very sparse, whereas numerical or simulation-based methods are computationally expensive and deliver no insight into the structure of the option price. The third chapter fills in the gap between closed-form solutions and numerical methods through expansions of option prices. This approach works with general dynamics without any requirement on affine dynamics or explicit characteristic functions, and quantitatively characterizes the relative importance of model parameters as the option approaches expiration. With closed-form expansions, we translate model features into option prices, such as stochastic interest rate, mean-reverting drift, and self-exciting or skewed jumps. Numerical examples illustrate the accuracy of this approach.