Hyperbolic normal stochastic volatility model

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.

arXiv comment26 pages, 4 figures, 5 tables

References in corpus (3)

• Exponential functionals of Brownian motion, I: Probability laws at fixed time
• Exponential functionals of Brownian motion, II: Some related diffusion processes
• Fine-tune your smile: Correction to Hagan et al

Cited by in corpus (6)

• A Black-Scholes user's guide to the Bachelier model
• Simulation schemes for the Heston model with Poisson conditioning
• A note on the option price and 'Mass at zero in the uncorrelated SABR model and implied volatility asymptotics'
• The equivalent constant-elasticity-of-variance (CEV) volatility of the stochastic-alpha-beta-rho (SABR) model
• Exact simulation scheme for the Ornstein-Uhlenbeck driven stochastic volatility model with the Karhunen-Loève expansions
• Efficient and accurate simulation of the stochastic-alpha-beta-rho model