Aït-Sahalia has made fundamental contributions to the estimation and testing of continuous-time models in financial economics. Quite often in empirical finance, the model that is estimated or tested is written in discrete-time and represents only an approximation to the theoretical continuous-time model which motivated the empirical investigation. Aït-Sahalia has developed methods to remove this approximation. His first contributions include the development of
nonparametric methods for estimating and testing these models, introducing the idea of comparing the densities predicted by the model to those estimated nonparametrically from the data at the same discrete frequency. These methods have been instrumental in uncovering nonlinearities in the dynamics of interest rates, volatility, and other variables. The fact that large samples of data are often available, combined with the fact that the precise specification of the model has a large influence on the end result, make nonparametric methods particularly appealing in empirical finance. Aït-Sahalia developed methods with
Andrew Lo to nonparametrically infer
Arrow-Debreu state prices, or risk-neutral densities, from observable market data and studied the representative agent preferences embedded in the joint collection of time-series data on the underlying asset dynamics and the cross-sectional option data. In many settings, economic theory only restricts the direction of the relationship between variables, not the particular functional form of their relationship. Motivated by the estimation of the risk-neutral density, which starts from a monotonic and convex option pricing function, nonparametric estimators were constructed to satisfy these shape restrictions, as a modification of nonparametric locally polynomial estimators. Aït-Sahalia developed series expansions based on Hermite polynomials to represent in closed-form the transition density of arbitrary continuous-time
diffusion models. His series expansion, which represents the transition density as a power series in the time interval starting from a base density, makes it possible to accurately implement
maximum-likelihood estimation of an arbitrary parametric continuous-time model using only discretely sampled data. This method has been shown to be the most accurate and fastest to represent the transition density of a diffusion model. He has made numerous advances in the estimation and testing of models using
high frequency data, with a particular focus on understanding the role and importance of
jumps in joint work with
Jean Jacod. His work has shown how distinguishing jumps from
volatility is possible, how to analyze the finer structure or spectrum of asset returns including testing whether jumps are present and estimating their degree of activity, and how to implement
principal component analysis in a high frequency setting. He also developed various methods to estimate volatility in situations where the high frequency data is noisy in joint work with Per Mykland and Lan Zhang. Aït-Sahalia proposed models with Julio Cacho-Diaz and Roger Laeven based on a
Hawkes process to represent asset returns and model contagion among them, along with estimation methods for these models based on discrete data. The optimization of portfolios when returns are subject to jumps, including possibly Hawkes jumps, was also studied in joint work with Tom Hurd. Some recent work with Chenxu Li and Chen Xu Li include the development of implied stochastic volatility models which are stochastic volatility models designed to fit the implied volatility surface of options. ==Awards==