New insights into smile, mispricing, and value at risk: The hyperbolic model

We investigate a new basic model for asset pricing, the hyperbolic model, which allows an almost perfect statistical fit of stock return data. After a detailed introduction into the theory we use secondary market data to compare the hyperbolic model to the classical Black-Scholes model. We study implicit volatilities, the smile effect: and pricing performance. Exploiting the full power of the hyperbolic model, we construct all option value process from a statistical point of view by estimating the implicit :risk-neutral density :Function from option data. Finally, we present some new value-at-risk calculations leading to;new perspectives to cope with model risk.