Anything that deviates from the normal is termed as risk. This definition looks simple but in real sense breaking it down into components is the most difficult thing. Analysis of what is “normal” and what is “abnormal” and also the measure for deviation is what researchers are exploring...

We introduce a data driven and model free approach for computing conditional expectations. The new method is based on classical techniques combined with machine learning methods. In particular, we consider kernel density estimation based on simulated risk factors combined with a control variate....

We propose a new method to estimate the empirical pricing kernel based on option data. We estimate the pricing kernel nonparametrically by using the ratio of the risk-neutral density estimator and the subjective density estimator. The risk-neutral density is approximated by a weighted kernel...