Arrow–Debreu State Prices and Green’s Functions in Bond Models

Summary

The document asks how Arrow–Debreu prices relate intuitively to Green’s functions, especially in the Black–Derman–Toy interest-rate model. It notes that some model discussions use “Green’s function” or “pricing kernel” without explaining the connection to the differential-equation meaning, where a Green’s function describes a system’s response to a point input such as a Dirac delta.

The question seeks an explanation of how that mathematical concept translates into pricing practice. It provides context for the question but no answer, derivation, pricing example, or empirical evidence. Readers should therefore treat it as a prompt for clarifying terminology and interpretation, rather than as a worked method. The relationship between state-contingent prices and Green’s functions remains unresolved in the document.

Key ideas

• The document asks how Arrow–Debreu state prices relate to Green’s functions in interest-rate models.
• It highlights the use of Green’s function as another name for a pricing kernel in some discussions.
• It contrasts that usage with Green’s functions as responses to point inputs in differential equations.
• The document poses the question but does not provide a derivation or practical pricing example.

Tags

# Arrow Debreu Price vs Green's function


# Arrow Debreu Price vs Green's function












How is the Arrow Debreu Price related to Green's function at an intuitive level and how is this used in practice?

Note Added 2021/02/01

I came across this in the Black Derman Toy model paper by Boyle, Seng Tian (2000) and see Green's function used without explanation in other BDT articles. Green's function is also referred to as a pricing kernel. I struggle to see how this use is related to my understanding of Green's functions in context of ODE/PDE differential operators and Dirac Delta and hence my request for an intuitive explanation.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.