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This paper develops a rigorous asymptotic expansion method with its numerical scheme for the Cauchy-Dirichlet problem in second order parabolic partial differential equations (PDEs). As an application, we propose a new approximation formula for pricing barrier option in the log-normal SABR...
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This paper derives a new semi closed-form approximation formula for pricing an up-and-out barrier option under a certain type of stochastic volatility model including SABR model by applying a rigorous asymptotic expansion method developed by Kato, Takahashi and Yamada (2012). We also demonstrate...
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This paper proposes a new scheme for the static replication of European options and their portfolios. First, we derive a general approximation formula for efficient static replication as an extension of Carr and Chou (1997, 2002) and Carr and Wu (2002). Second, we present a concrete procedure...
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