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Barrier option pricing under the 2-hypergeometric stochastic volatility model. (English) Zbl 1405.91651

Summary: 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.

MSC:

91G20 Derivative securities (option pricing, hedging, etc.)
60H30 Applications of stochastic analysis (to PDEs, etc.)
35C20 Asymptotic expansions of solutions to PDEs
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