Hyperbolic normal stochastic volatility model

Jaehyuk Choi, Chenru Liu, Byoung Ki Seo
9/11/2018
q-fin.MFstat.AP

Official code: quants-net/PyfengForPapers (47 stars, GPL-3.0, last commit 2026-06-23).

Abstract

For option pricing models and heavy-tailed distributions, this study proposes a continuous-time stochastic volatility model based on an arithmetic Brownian motion: a one-parameter extension of the normal stochastic alpha-beta-rho (SABR) model. Using two generalized Bougerol's identities in the literature, the study shows that our model has a closed-form Monte-Carlo simulation scheme and that the transition probability for one special case follows Johnson's $S_U$ distribution---a popular heavy-tailed distribution originally proposed without stochastic process. It is argued that the $S_U$ distribution serves as an analytically superior alternative to the normal SABR model because the two distributions are empirically similar.

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Cite this paper

@article{choi2018hyperbolic,
  title  = {Hyperbolic normal stochastic volatility model},
  author = {Jaehyuk Choi and Chenru Liu and Byoung Ki Seo},
  year   = {2018},
  eprint = {1809.04035},
  archivePrefix = {arXiv},
  url    = {https://arxiv.org/abs/1809.04035}
}

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