Hyperbolic Normal Stochastic Volatility Model
Journal of Futures Markets, 39(2):186-204, 2019
26 Pages Posted: 23 Jan 2018 Last revised: 11 Jan 2019
Date Written: September 7, 2018
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 SU distribution -- a popular heavy-tailed distribution originally proposed without stochastic process. It is argued that the SU distribution serves as an analytically superior alternative to the normal SABR model because the two distributions are empirically similar.
Keywords: Stochastic Volatility, SABR Model, Bougerol's Identity, Johnson's SU Distribution
JEL Classification: C15, C52, G13
Suggested Citation: Suggested Citation