Our derivation of the distribution function for future returns is based on the risk neutral approach which gives a functional dependence for the European call (put) option price, C(K), given the strike price, K, and the distribution function of the returns. We derive this distribution function...

In the Black-Scholes context we consider the probability distribution function (PDF) of financial returns implied by volatility smile and we study the relation between the decay of its tails and the fitting parameters of the smile. We show that, considering a scaling law derived from data, it is...

This work presents an asset pricing model that under rational expectation equilibrium perspective shows how, depending on risk aversion and noise volatility, a risky-asset has one equilibrium price that differs in term of efficiency: an informational efficient one (similar to Campbell and Kyle...

Estimating the Credit Valuation Adjustment (CVA) for unlisted companies is a challenging issue since the risk neutral default probability cannot be estimated either from CDS par spread or from equity stock. This work proposes a calibration method that easily estimates the market risk premium...