Hyperbolic normal stochastic volatility model

Motivated for alternative option pricing models and heavy-tailed distributions, this study proposes and analyzes a continuous-time stochastic volatility (SV) model based on arithmetic Brownian motion. The normal... [ view full abstract ]

Motivated for alternative option pricing models and heavy-tailed distributions, this study proposes and analyzes a continuous-time stochastic volatility (SV) model based on arithmetic Brownian motion. The normal Stochastic-Alpha-Beta-Rho model is a special case of our model. Using the generalizations of Bougerol's identity from literature, we provide closed-form simulation scheme, efficient quadrature integration for vanilla option price, and fast moment-matching method. Furthermore, the transition probability of another special case is given by Johnson’s SU curve, a popular heavy-tailed distribution with superior analytical tractability. Therefore, our model serves as an analytically tractable SV model and heavy-tailed distribution backed by stochastic differential equation.