Pricing Options on Scalar Diffusions: An Eigenfunction Expansion Approach
This paper develops an eigenfunction expansion approach to pricing options on scalar diffusion processes. All contingent claims are unbundled into portfolios of primitive securities called eigensecurities . Eigensecurities are eigenvectors (eigenfunctions) of the pricing operator (present value oper...
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| Veröffentlicht in: | Operations research 2003-03, Vol.51 (2), p.185-209 |
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| creator | Davydov, Dmitry Linetsky, Vadim |
| description | This paper develops an eigenfunction expansion approach to pricing options on scalar diffusion processes. All contingent claims are unbundled into portfolios of primitive securities called eigensecurities . Eigensecurities are eigenvectors (eigenfunctions) of the pricing operator (present value operator). All computational work is at the stage of finding eigenvalues and eigenfunctions of the pricing operator. The pricing is then immediate by the linearity of the pricing operator and the eigenvector property of eigensecurities. To illustrate the computational power of the method, we develop two applications:pricing vanilla, single- and double-barrier options under the constant elasticity of variance (CEV) process and interest rate knock-out options in the Cox-Ingersoll-Ross (CIR) term-structure model. |
| doi_str_mv | 10.1287/opre.51.2.185.12782 |
| format | Article |
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All contingent claims are unbundled into portfolios of primitive securities called eigensecurities . Eigensecurities are eigenvectors (eigenfunctions) of the pricing operator (present value operator). All computational work is at the stage of finding eigenvalues and eigenfunctions of the pricing operator. The pricing is then immediate by the linearity of the pricing operator and the eigenvector property of eigensecurities. 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All contingent claims are unbundled into portfolios of primitive securities called eigensecurities . Eigensecurities are eigenvectors (eigenfunctions) of the pricing operator (present value operator). All computational work is at the stage of finding eigenvalues and eigenfunctions of the pricing operator. The pricing is then immediate by the linearity of the pricing operator and the eigenvector property of eigensecurities. 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| subjects | Assets Boundary conditions Coefficients Diffusion Eigenfunctions Eigenvalues Eigenvectors Equation roots Finance, asset pricing: option pricing, CEV model, CIR model Finance, securities: barrier options Financial services Greens function Handbooks Hedging Interest rates Laplace transformation Markov analysis Mathematical functions Mathematical models Operations research Ordinary differential equations Partial differential equations Portfolio management Present value Pricing policies Probability, diffusion: spectral theory, barrier crossing, generalized Bessel process Put & call options Scalars Securities Securities prices Stochastic models Studies Valuation |
| title | Pricing Options on Scalar Diffusions: An Eigenfunction Expansion Approach |
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