The wide availability of high-frequency data for many financial instruments stimulates a upsurge interest in statistical research on the estimation of volatility. Jump-diffusion processes observed with market microstructure noise are frequently used to model high-frequency financial data. Yet,...

An aggregated method of nonparametric estimators based on time-domain and state-domain estimators is proposed and studied. To attenuate the curse of dimensionality, we propose a factor modeling strategy. We first investigate the asymptotic behavior of nonparametric estimators of the volatility...

We propose a new nonparametric test for detecting the presence of jumps in asset prices using discretely observed data. Compared with the test statistic in A\quot;{i}t-Sahalia and Jacod (2007), our new test statistic enjoys the same asymptotic properties but has smaller variance. These results...

Parametric option pricing models are largely used in Finance. These models capture several features of asset price dynamics. However, their pricing performance can be significantly enhanced when they are combined with nonparametric learning approaches that learn and correct empirically the...

We develop a specification test for discretely-sampled jump-diffusions, based on a comparison of a nonparametric estimate of the transition density or distribution function to their corresponding parametric counterparts. As a special case, our method applies to pure diffusions. We propose three...