S&P 500 Options Reveal Bond Yields That Match Treasury Curves Best at the Money

If bond and stock markets seem like separate worlds, this paper argues they can share the same pricing language. The authors treat a zero-coupon bond as a European option with a fixed payoff, so it can be priced under the same risk-neutral measure that governs equity derivatives. Using put-call parity, they extract option-implied zero-coupon yield curves from S&P 500 index options and compare them with U.S. daily Treasury par yield curves. Because the implied curves depend on both maturity time T and strike price K, they also test how the curve changes with strike. The headline result is clear: at-the-money option-implied yield curves come closest to the Treasury par yield curves. That suggests the equity options market carries information that is highly relevant for the term structure of interest rates, the curve that tracks how interest rates change across maturities. The paper’s bigger claim is not just about one dataset, but about a new organizing principle: bond valuation should use the same risk-neutral measure revealed by equity derivatives.

On one side sit S&P 500 options. On the other sit U.S. Treasury yield curves. They usually live in different rooms of finance. This study says they can share a pricing language. It treats a zero-coupon bond as a European option. That means a contract that pays only at the end. Put-call parity links the price of a call and a put with the same strike and date. That link lets stock options reveal bond yields. The sharpest signal comes from at-the-money contracts. Those are the contracts whose strike sits near the market level. If you care about borrowing costs, that twist matters. It shows rates and stocks are never far apart.

Why a bond can hide inside an option

The cleanest result comes from the strike price. The model builds zero-coupon yield curves from S&P 500 index options. It then compares them with U.S. daily Treasury par yield curves, a standard benchmark for government borrowing costs. A zero-coupon bond pays once, at maturity. Put-call parity, a pricing rule that links call and put options, makes the extraction possible. The implied yield curve depends on two knobs. One is maturity time, or T. The other is strike price, or K. The study checks how the curve shifts as K moves. The closest match appears at the money. That means the strike sits near the market level. Equity options carry rate clues. Those clues matter for the term structure of interest rates. That curve tracks borrowing costs across maturities.

How put-call parity pulls out the curve

Put-call parity is the bridge here. It says a call and a put with the same strike and date fit together. You can use a European option only at expiry. That makes its payoff simple. The zero-coupon bond has a simple payoff too. It pays one fixed amount at maturity. The framework treats that bond like an option with a known payout. Then one risk-neutral measure, a pricing rule that strips out risk taste, prices both sides. The curve comes from S&P 500 index option prices. The study also checks how the answer changes when K moves away from the money. That second step tests how much the strike matters.

Why the equity options market matters for rates

This result gives the equity options market a new job. It is not only a bet on share prices. It is also a place to look for rate information. That matters because one risk-neutral measure, the pricing rule that ignores risk taste, ties the two markets together. One measure instead of two gives the field a cleaner map. It also makes strike choice feel less like a footnote. At-the-money contracts gave the closest Treasury match. So any option-implied yield curve should watch where K sits. Bond and stock markets stay different. But they may share a deeper pricing skeleton.

What to test in S&P 500 options next

The next test is the strike gap in S&P 500 options. Does the at-the-money edge stay strong when K moves farther from the market level? That question matters because the whole bridge leans on strike choice. If the answer stays yes, stock options can give you a Treasury-like yield curve with one clear rule. If the answer fades, at-the-money becomes the guardrail. Either way, the surprise survives. A bond does not need a bond desk to speak. In this framework, an options chain can say something about rates.