A Semigroup Expansion for Pricing Barrier Options
Copyright policy )A Semigroup Expansion for Pricing Barrier Options
This paper presents a new asymptotic expansion method for pricing continuously monitoring barrier options. In particular, we develop a semigroup expansion scheme for the Cauchy-Dirichlet problem in the second-order parabolic partial differential equations (PDEs) arising in barrier option pricing. As an application, we propose a concrete approximation formula under a stochastic volatility model and demonstrate its validity by some numerical experiments.
- Osaka University Japan
- University of Tokyo Japan
- Mitsubishi Japan
Probability (math.PR), Computational Finance (q-fin.CP), Asymptotic expansions of solutions to PDEs, 91G20 (Primary), 35C20 (Secondary), 35B20, FOS: Economics and business, Quantitative Finance - Computational Finance, Mathematics - Analysis of PDEs, Derivative securities (option pricing, hedging, etc.), PDEs in connection with game theory, economics, social and behavioral sciences, FOS: Mathematics, Initial value problems for second-order parabolic equations, Financial applications of other theories, Mathematics - Probability, Analysis of PDEs (math.AP)
Probability (math.PR), Computational Finance (q-fin.CP), Asymptotic expansions of solutions to PDEs, 91G20 (Primary), 35C20 (Secondary), 35B20, FOS: Economics and business, Quantitative Finance - Computational Finance, Mathematics - Analysis of PDEs, Derivative securities (option pricing, hedging, etc.), PDEs in connection with game theory, economics, social and behavioral sciences, FOS: Mathematics, Initial value problems for second-order parabolic equations, Financial applications of other theories, Mathematics - Probability, Analysis of PDEs (math.AP)
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