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 t of stock return data. After a brief introduction into the theory supported by an appendix we use also secondary market data to compare the hyperbolic model to the classical Black-Scholes model. We study implicit volatilities, the smile e ect and the pricing performance. Exploiting the full power of the hyperbolic model, we construct an 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 valueat-risk calculations leading to new perspectives to cope with model risk.