SIEVE ESTIMATION OF THE MINIMAL ENTROPY MARTINGALE MARGINAL DENSITY WITH APPLICATION TO PRICING KERNEL ESTIMATION

We study the problem of nonparametric estimation of the risk-neutral densities from options data. The underlying statistical problem is known to be ill-posed and needs to be regularized. We propose a novel regularized empirical sieve approach for the estimation of the risk-neutral densities which relies on the notion of the minimal martingale entropy measure. The proposed approach can be used to estimate the so-called pricing kernels which play an important role in assessing the risk aversion over equity returns. The asymptotic properties of the resulting estimate are analyzed and its empirical performance is illustrated.

Sieve estimation in a Markov illness-death process under dual censoring

Semiparametric methods are well established for the analysis of a progressive Markov illness-death process observed up to a noninformative right censoring time. However, often the intermediate and terminal events are censored in different ways, leading to a dual censoring scheme. In such settings, unbiased estimation of the cumulative transition intensity functions cannot be achieved without some degree of smoothing. To overcome this problem, we develop a sieve maximum likelihood approach for inference on the hazard ratio. A simulation study shows that the sieve estimator offers improved finite-sample performance over common imputation-based alternatives and is robust to some forms of dependent censoring. The proposed method is illustrated using data from cancer trials.