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Hyperbolic Normal Stochastic Volatility Model

For alternative options pricing models and heavy-tailed distributions, this study proposes and analyzes a continuous-time stochastic volatility (SV) model based on an arithmetic Brownian motion. The normal stochastic alpha-beta-rho model is a special case of our model. Using the generalizations from Bougerol's identity in the literature, we propose a closed-form simulation scheme, efficient quadrature integration for vanilla options pricing, 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 equations.