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An appropriate approach to pricing European-style options with the Adomian decomposition method. (English) Zbl 1387.35582

Summary: We study the numerical Adomian decomposition method for the pricing of European options under the well-known Black-Scholes model. However, because of the nondifferentiability of the pay-off function for such options, applying the Adomian decomposition method to the Black-Scholes model is not straightforward. Previous works on this assume that the pay-off function is differentiable or is approximated by a continuous estimation. Upon showing that these approximations lead to incorrect results, we provide a proper approach, in which the singular point is relocated to infinity through a coordinate transformation. Further, we show that our technique can be extended to pricing digital options and European options under the Vasicek interest rate model, in both of which the pay-off functions are singular. Numerical results show that our approach overcomes the difficulty of directly dealing with the singularity within the Adomian decomposition method and gives very accurate results.

MSC:

35Q91 PDEs in connection with game theory, economics, social and behavioral sciences
35E15 Initial value problems for PDEs and systems of PDEs with constant coefficients
91G60 Numerical methods (including Monte Carlo methods)
91G20 Derivative securities (option pricing, hedging, etc.)
91B24 Microeconomic theory (price theory and economic markets)
65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
65D20 Computation of special functions and constants, construction of tables

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References:

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