Market option prices in last 20 years confirmed deviations from the Black and Scholes (BS) models assumptions, especially on the BS implied volatility. Implied binomialtrees (IBT) models capture the variations of the implied volatility known as \volatility smile". They provide a discrete...

State price densities (SPD) are an important element in applied quantitativefinance. In a Black-Scholes model they are lognormal distributions with constant volatility parameter. In practice volatility changes and the distribution deviates from log-normality. We estimate SPDs using EUREX option...

The Black-Scholes formula, one of the major breakthroughs of modern finance,allows for an easy and fast computation of option prices. But some of its assumptions, like constant volatility or log-normal distribution of asset prices,do not find justification in the markets. More complex models,...

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...

The analysis of volatility in financial markets has become a first rank issue in modern financial theory and practice: Whether in risk management, portfolio hedging, or option pricing, we need to have a precise notion of the market's expectation of volatility. Much research has been done on the...