Solving a 37-Year-Old Structural Problem in Interest Rate Theory

At Shunya, we care deeply about the difference between using a model and understanding its structure.

A model may work well in practice, a pricing shortcut may be widely used, and a decomposition may become standard in the literature. But beneath all of that sits a harder question: when does the structure really hold, and when does it fail?

That question sits at the heart of a new research result developed as part of Shunya’s research efforts: a structural resolution of the exact obstruction to the Jamshidian decomposition in multifactor affine models.

This may sound specialized, but it touches something fundamental in mathematical finance. For nearly four decades, Jamshidian’s decomposition has remained one of the most elegant observations in interest-rate option pricing. In the one-factor setting, it turns a European option on a coupon bond into a finite portfolio of zero-coupon bond options with deterministic component strikes. That is not just computationally convenient. It reveals a deep monotonicity structure inside the model.

What was widely understood, but not fully characterized in exact structural terms, was why this logic breaks in genuine multifactor settings.

Our paper addresses that directly.

The classical insight, and the missing boundary

Jamshidian’s 1989 result is powerful because it reduces a more complicated coupon-bond option problem to a family of simpler zero-coupon bond option problems. In one-factor affine term-structure models, all bond prices at expiry are monotone functions of the same scalar state variable. That shared monotonicity makes the decomposition work pathwise.

The usual understanding in the literature has long been that this is “a one-factor trick” and that the decomposition fails in multifactor models. But that description leaves an important question open:

Exactly what structural condition makes deterministic-strike Jamshidian decomposition possible, and exactly what geometric obstruction destroys it?

That is the problem our research set out to solve.

What the paper proves

The core result is clean and exact.

Within the exponential-affine family of bond prices,

an exact deterministic-strike Jamshidian decomposition exists if and only if the loading vectors of the zero-coupon bonds are positively collinear.

In plain terms, the geometry of the factor loadings must collapse onto a single positive ray in factor space. If that positive collinearity fails, the deterministic-strike decomposition fails as well.

This is not just a sufficient condition. It is an if and only if characterization.

That matters because it turns a widely cited intuition into an exact structural theorem. Instead of saying vaguely that the trick is “one-factor in spirit,” we can now describe the precise boundary between exact reducibility and genuine multifactor obstruction.

Why this is interesting

There are at least three reasons this result matters.

1. It sharpens a classical idea into an exact theorem

A lot of mathematical finance rests on beautiful structural tricks that are known to work in special settings. But often the exact frontier of validity remains underdescribed. Here, the paper identifies that frontier precisely.

2. It shows that the obstruction is geometric, not merely computational

The decomposition does not fail in multifactor models simply because the algebra becomes messy. It fails because the exercise geometry itself changes. Once the factor loadings cease to align on a single positive ray, the common threshold structure breaks.

3. It opens a disciplined way to think about approximation

The paper does not stop at the exact theorem. It also develops a near-collinearity framework showing that when loadings are close to a common direction, a projected deterministic-strike approximation remains quantitatively controlled. The error is confined to a strip around a projected one-factor exercise hyperplane, and the projected strikes are shown to be minimax-optimal under the stated criterion.

That gives the theory both structural sharpness and practical relevance.

What makes the work distinctive

One thing we value at Shunya is not just answering whether something works, but understanding why it works and how it breaks.

That is what makes this result especially satisfying.

The work contributes at several levels:

• an exact characterization theorem for deterministic-strike decomposition,
• a simultaneous-threshold argument that isolates the sign-coherence requirement,
• a quantitative near-collinearity theory,
• and structural extensions showing why natural escape routes do not truly evade the obstruction.

Those extensions are particularly elegant. The paper shows that:

• unrestricted state-dependent strikes trivialize the decomposition problem,
• numéraire changes do not alter the relevant exercise geometry,
• and nonlinear scalar-factor reparameterizations do not escape the same positive-collinearity obstruction in exponential-affine families.

So the obstruction is not cosmetic. It is structural.

Why this belongs on Shunya

Shunya is not just a consulting identity for us. It is also a place for deep research, exact thinking, and structurally serious work.

This paper reflects that ethos well.

It is the kind of work we want associated with the Shunya name:

• mathematically rigorous,
• conceptually clean,
• and aimed at clarifying first-principles questions rather than merely producing surface-level commentary.

In a world where much of technical discourse is driven by incremental adjustment, there is real value in solving an old problem by identifying its exact structure.

A broader lesson

There is a broader lesson here beyond this particular result.

In quantitative finance, many important ideas survive for decades in a partly informal state. People know how to use them, know roughly when they work, and know where the approximations begin. But there is a difference between practical familiarity and exact structural understanding.

Closing that gap is not glamorous in the usual marketing sense. But it is often where the deepest intellectual value lies.

That is one reason we are proud to present this as part of Shunya’s research work.

The paper

Title: On the Exact Obstruction to the Jamshidian Decomposition in Multifactor Affine Models
Author: Aryan Ayyar
Date: April 4, 2026

The paper shows that, within the exponential-affine bond-pricing class, exact deterministic-strike Jamshidian decomposition is possible if and only if the relevant loading vectors are positively collinear. It then develops a near-collinearity approximation theory and several structural extensions that clarify the geometry of the problem.

Closing note

At Shunya, we want to do work that combines rigor with originality. Sometimes that means building tools. Sometimes it means framing problems better. And sometimes, as in this case, it means resolving a structural question that has remained quietly open for decades.

This result is part of that journey.

If you are interested in mathematical finance, term-structure theory, or research-led problem solving, we would be glad to share more of the thinking behind the work.