The Exact Obstruction to Jamshidian’s Decomposition in Multifactor Affine Models

Abstract

The Jamshidian decomposition reduces a European coupon-bond option to a portfolio of zero-coupon bond options through a single deterministic set of component strikes. We study when such a decomposition can hold exactly in a general exponential-affine setting. Our main result shows that within the class P i (x) = A i eB ⊤ ix , an exact deterministic-strike Jamshidian decomposition exists if and only if all loading vectors {B i } are positively collinear, ie lie on a single ray in R d. We then develop a quantitative near-collinearity framework. For a fixed reference direction u, we define the associated transverse dispersion D u and show that the projected deterministic-strike approximation is a pathwise upper bound whose error is confined to a strip around the projected one-factor exercise hyperplane. We also show that the corresponding projected strikes are minimax-optimal for worst-case strip width under the stated criterion. Finally, we discuss several structural extensions. Unrestricted state-dependent strikes trivialize the decomposition problem; numeraire changes leave the exercise geometry unchanged; and a scalar-factor rigidity result shows that, for exponential-affine families, nonlinear scalar reparameterizations do not evade the positive-collinearity obstruction.

Keywords: Jamshidian decomposition, affine term structure models, coupon bond options, positive collinearity, scalar-factor rigidity, transverse dispersion, pathwise comonotonicity MSC 2020: 91G30

JEL Classification: G12, E43