Barrier Option Pricing under the 2-Hypergeometric Stochastic Volatility Model

TL;DR

This paper develops an explicit approximation formula for barrier option pricing within the 2-hypergeometric stochastic volatility model, capturing market-observed volatility features and validated through numerical examples.

Contribution

It introduces a novel, analytically tractable model and a perturbation-based approximation method for barrier option pricing, with proven convergence and improved accuracy techniques.

Findings

The model reproduces volatility smile and skew effects.

The approximation formula is explicit and computationally efficient.

Numerical examples demonstrate the method's accuracy.

Abstract

We investigate the pricing of financial options under the 2-hypergeometric stochastic volatility model. This is an analytically tractable model that reproduces the volatility smile and skew effects observed in empirical market data. Using a regular perturbation method from asymptotic analysis of partial differential equations, we derive an explicit and easily computable approximate formula for the pricing of barrier options under the 2-hypergeometric stochastic volatility model. The asymptotic convergence of the method is proved under appropriate regularity conditions, and a multi-stage method for improving the quality of the approximation is discussed. Numerical examples are also provided.