Hyperbolic normal stochastic volatility model

Code

• github.com/PyFE/NSVh-R
  Officialnone★ 0

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.

Tasks

Reproductions