Pricing Options on Scalar Diffusions: An Eigenfunction Expansion Approach

Dmitry Davydov () and Vadim Linetsky ()
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Dmitry Davydov: Equities Quantitative Strategies, UBS Warburg, Stamford, Connecticut 06901
Vadim Linetsky: Department of Industrial Engineering and Management Sciences, McCormick School of Engineering and Applied Sciences, Northwestern University, Evanston, Illinios 60208

Operations Research, 2003, vol. 51, issue 2, 185-209

Abstract: 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.

Keywords: Finance; asset pricing: option pricing; CEV model; CIR model; Finance; securities: barrier options; Probability; diffusion: spectral theory; barrier crossing; generalized Bessel process (search for similar items in EconPapers)
Date: 2003
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Citations: View citations in EconPapers (54)

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