TL;DR
This paper introduces a non-parametric, closed-form method for estimating smooth discount curves from market data using Moore-Penrose pseudoinverse, ensuring perfect fit and maximal smoothness.
Contribution
It provides a novel, easy-to-implement linear algebra-based approach for exact, smooth discount curve estimation with a comprehensive theoretical foundation.
Findings
The method reproduces market quotes exactly.
It produces the smoothest possible discount curve.
The approach is computationally simple and practically applicable.
Abstract
We present a non-parametric method to estimate the discount curve from market quotes based on the Moore-Penrose pseudoinverse. The discount curve reproduces the market quotes perfectly, has maximal smoothness, and is given in closed-form. The method is easy to implement and requires only basic linear algebra operations. We provide a full theoretical framework as well as several practical applications.
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