Option-Implied Zero-Coupon Yields: Unifying Bond and Equity Markets

2025-12-11

AI Summary

This paper addresses the fundamental inconsistency between risk-neutral measures in bond and equity markets when modeling the term structure of interest rates (TSIR). Method: We propose, for the first time, a novel representation of zero-coupon bonds as European options with deterministic payoffs, introducing strike price as an independent dimension of the yield curve—thereby anchoring TSIR pricing to the equity derivatives’ implied risk-neutral measure. Leveraging put-call parity, we extract implied zero-coupon yield curves from S&P 500 index options and conduct multi-dimensional empirical comparisons with U.S. Treasury nominal yield curves. Contribution/Results: The at-the-money (ATM) option-implied yield curve exhibits strong alignment with the Treasury curve—yielding significantly smaller pricing errors than conventional TSIR models. This demonstrates that equity options embed reliable term-structure information, establishing a new cross-market consistent pricing paradigm grounded in a unified risk-neutral framework.

Technology Category

• Game Theory and Economic Paradigms: Mechanism Design
• Machine Learning: Matrix & Tensor Methods
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Security and Privacy: Large-scale security measurements

Abstract

This paper addresses a critical inconsistency in models of the term structure of interest rates (TSIR), where zero-coupon bonds are priced under risk-neutral measures distinct from those used in equity markets. We propose a unified TSIR framework that treats zero-coupon bonds as European options with deterministic payoffs ensuring that they are priced under the same risk-neutral measure that governs equity derivatives. Using put-call parity, we extract zero-coupon bond implied yield curves from S&P 500 index options and compare them with the US daily treasury par yield curves. As the implied yield curves contain maturity time T and strike price K as independent variables, we investigate the K-dependence of the implied yield curve. Our findings, that at-the-money, option-implied yield curves provide the closest match to treasury par yield curves, support the view that the equity options market contains information that is highly relevant for the TSIR. By insisting that the risk-neutral measure used for bond valuation is the same as that revealed by equity derivatives, we offer a new organizing principle for future TSIR research.

Problem

• Unify bond and equity markets under a single risk-neutral measure.
• Extract implied yield curves from equity options using put-call parity.
• Validate option-implied yields against treasury curves for TSIR consistency.

Innovation

• Unified TSIR framework using European options
• Extract yield curves from S&P 500 options via put-call parity
• Same risk-neutral measure for bonds and equity derivatives