Pricing Options on Scalar Diffusions: An Eigenfunction Expansion Approach

This paper develops an eigenfunction expansion approach to pricing options on scalar diffusion processes. All derivative securities are unbundled into portfolios of primitive securities termed eigensecurities. Eigensecurities are eigenvectors of the pricing operator (present value operator). Pricing is then immediate by the linearity property of the pricing operator and the eigenvector property of eigensecurities. To illustrate the computational power of the method, we develop two applications: pricing vanilla, singleand double-barrier options under the constant elasticity of variance (CEV) process and interest rate knock-out options in the Cox-IngersollRoss (CIR) term-structure model.