An Asymptotic Expansion for Solutions of Cauchy-Dirichlet Problem for Second Order Parabolic PDEs and its Application to Pricing Barrier Options

Details An Asymptotic Expansion for Solutions of Cauchy-Dirichlet Problem for Second Order Parabolic PDEs and its Application to Pricing Barrier Options An Asymptotic Expansion for Solutions of Cauchy-Dirichlet Problem for Second Order Parabolic PDEs and its Application to Pricing Barrier Options

2012-02-14

arxiv.org/abs/1202.3002v3

Economy

Quantitative Finance

Computational Finance

28 pages

Scientific paper

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 a barrier option under a certain type of
stochastic volatility model including the log-normal SABR model.

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