## New Insights Into Smile, Mispricing and Value At Risk: The Hyperbolic Model (1998)

Venue: | Journal of Business |

Citations: | 79 - 7 self |

### BibTeX

@ARTICLE{Eberlein98newinsights,

author = {Ernst Eberlein and Ulrich Keller and Karsten Prause},

title = {New Insights Into Smile, Mispricing and Value At Risk: The Hyperbolic Model},

journal = {Journal of Business},

year = {1998},

volume = {71},

pages = {371--406}

}

### Years of Citing Articles

### OpenURL

### Abstract

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 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 effect 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. I Introduction There is little doubt that the Black-Scholes model has become the standard in the finance industry and is applied on a large scale in everyday trading operations. On the other side its deficiencies have become a standard topic in research. Given the vast literature where refinements a...