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arXiv · 1809.04035

Hyperbolic normal stochastic volatility model

Jaehyuk Choi·Chenru Liu·Byoung Ki Seo
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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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Jaehyuk Choi, Chenru Liu, Byoung Ki Seo. 2018-09-11. Hyperbolic normal stochastic volatility model. https://doi.org/10.1002/fut.21967

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