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

TL;DR

This paper introduces a unified term structure of interest rates framework that aligns bond and equity market models by using equity options to infer zero-coupon yields, revealing that at-the-money options best match treasury yield curves.

Contribution

It proposes a novel unified TSIR model that treats bonds as European options, ensuring consistent risk-neutral measures across markets, and demonstrates the relevance of equity options for bond yield inference.

Findings

At-the-money implied yield curves closely match treasury yield curves.

Implied yield curves depend on strike price K, showing K-dependence.

Equity options market contains valuable information for TSIR modeling.

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.