Quantifying risks with exact analytical solutions of derivative pricing distribution

Kun Zhang, Jing Liu, Erkang Wang and Jin Wang

Physica A: Statistical Mechanics and its Applications, 2017, vol. 471, issue C, 757-766

Abstract: Derivative (i.e. option) pricing is essential for modern financial instrumentations. Despite of the previous efforts, the exact analytical forms of the derivative pricing distributions are still challenging to obtain. In this study, we established a quantitative framework using path integrals to obtain the exact analytical solutions of the statistical distribution for bond and bond option pricing for the Vasicek model. We discuss the importance of statistical fluctuations away from the expected option pricing characterized by the distribution tail and their associations to value at risk (VaR). The framework established here is general and can be applied to other financial derivatives for quantifying the underlying statistical distributions.

Keywords: Option pricing; Distribution; Risk (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (4)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:471:y:2017:i:c:p:757-766

DOI: 10.1016/j.physa.2016.12.044

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