Option Pricing Under a Double Exponential Jump Diffusion Model
Management Science
Option Pricing Under a Mixed-Exponential Jump Diffusion Model
Management Science
High-order approximation of Pearson diffusion processes
Journal of Computational and Applied Mathematics
Spectral Decomposition of Option Prices in Fast Mean-Reverting Stochastic Volatility Models
SIAM Journal on Financial Mathematics
Static Hedging under Time-Homogeneous Diffusions
SIAM Journal on Financial Mathematics
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This paper develops an eigenfunction expansion approach to pricing options on scalar diffusion processes. All contingent claims are unbundled into portfolios of primitive securities calledeigensecurities. 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.