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 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 value-at-risk calculations leading to new perspectives to cope with model risk