The DOI matches its Crossref record; 2 of the 2 references it cites were found in a registry or an index.
Hyperbolic Distributions in Finance
Abstract
Distributional assumptions for the returns on the underlying assets play a key role in valuation theories for derivative securities. Based on a data set consisting of daily prices of the 30 DAX shares over a three-year period, we investigate the distributional form of compound returns. After performing a number of statistical tests, it becomes clear that some of the standard assumptions cannot be justified. Instead, we introduce the class of hyperbolic distributions which can be fitted to the empirical returns with high accuracy. Two models based on hyperbolic L'evy motion are discussed. By studying the Esscher transform of the process with hyperbolic returns, we derive a valuation formula for derivative securities. The result suggests a correction of standard Black--Scholes pricing, especially for options close to expiration. Keywords Statistical analysis of stock price data, hyperbolic distributions, hyperbolic L'evy motion, Option pricing, absolute continuous change of measure. 1 ...
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Cites
Handbook of Mathematical Functions
McQuarrie, D. A. (1966) · American Journal of Physics · doi:10.1119/1.1972842 · Cited by 40,433
The pricing of options and corporate liabilities
Black, F., & Scholes, M. (1973) · Journal of Political Economy · doi:10.1086/260062 · Cited by 29,074
Cited by
Normal Inverse Gaussian Distributions and Stochastic Volatility Modelling
Barndorff‐Nielsen, O. E. (1997) · Scandinavian Journal of Statistics · doi:10.1111/1467-9469.00045 · Cited by 1,020
Metadata
- Authors
- Eberlein, E., & Keller, U.
- Venue
- Bernoulli
- Publisher
- JSTOR
- Published
- 1995-09
- Volume
- 1
- Issue
- 3
- Pages
- 281
- ISSN
- 1350-7265 (ISSN-L)
- OpenAlex
- W1994858552
- Cited by
- 958
- References
- 2
- FWCI
- 20.34
- Type
- journal article
- Language
- en
- Open access
- closed
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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