Partial Differential Equation Pricing of Contingent Claims under Stochastic Correlation
| Autor: | Nat Chun-Ho Leung, Christina C. Christara, Duy-Minh Dang |
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| Rok vydání: | 2018 |
| Předmět: |
FTCS scheme
Mathematical optimization Computation Monte Carlo method First-order partial differential equation 01 natural sciences Correlation 010104 statistics & probability Stochastic differential equation Convergence (routing) 0502 economics and business Applied mathematics Boundary value problem Finite difference methods for option pricing 0101 mathematics 050207 economics Mathematics 050208 finance Partial differential equation Applied Mathematics 05 social sciences Order of accuracy Quadrature (mathematics) Stochastic partial differential equation Computational Mathematics Valuation of options Hyperbolic partial differential equation |
| Zdroj: | SIAM Journal on Scientific Computing. 40:B1-B31 |
| ISSN: | 1095-7197 1064-8275 |
| Popis: | In this paper, we study a partial differential equation (PDE) framework for option pricing where the underlying factors exhibit stochastic correlation, with an emphasis on computation. We derive a multi-dimensional time-dependent PDE for the corresponding pricing problem, and present a numerical PDE solution. We prove a stability result, and study numerical issues regarding the boundary conditions used. Moreover, we develop and analyze an asymptotic analytical approximation to the solution, leading to a novel computational asymptotic approach based on quadrature with a perturbed transition density. Numerical results are presented to verify second order convergence of the numerical PDE solution and to demonstrate its agreement with the asymptotic approximation and Monte Carlo simulations. The effect of certain problem parameters to the PDE solution, as well as to the asymptotic approximation solution, is also studied. |
| Databáze: | OpenAIRE |
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