Measuring Bubbles via Put-Call Disparity: A Model-Free Approach
Robert A. Jarrow (Cornell U.) and Simon Kwok (U. of Sydney)
May 2026
This paper introduces simple, model-free lower and upper bounds for measuring the size of asset price bubbles. Assuming only that the market satisfies no-free-lunch-with-vanishing-risk and that all trading strategies are admissible, our framework avoids restrictive parametric models and the no-dominance assumption. We demonstrate that put-call disparity provides an observable lower bound, and is economically justified by short-sale constraints. Additionally, the lowest price of an out-of-the-money (OTM) call option determines the upper bound. To ensure empirical reliability, we modify these bounds using data-driven regularization and bootstrap methods to disentangle genuine bubble signals from market microstructure noise and to reduce reliance on thinly traded deep OTM options. Using S&P 500 index option prices from 1996 to 2025, we document a sustained bubble during the COVID-19 era and capture market exuberance preceding the 2000 dot-com and 2008 financial crashes. In addition, the empirical study suggests that the market violates no-dominance and is incomplete.
Trailing Yields: Major Asset Classes | 4 June 2026
US junk bonds continue to post the highest trailing one‑year yields for the major asset classes, based on a set of ETFs through June 3. Roughly half of the funds are reporting payout rates above the current pace of annual consumer inflation.
Energy Shock Looms, but Q2 GDP Still Looks Surprisingly Strong
The US economy isn’t immune to the energy shock continuing to reverberate from the Middle East, but the fallout may be hard to spot in the upcoming second‑quarter GDP report. That, at least, is the message in current nowcasts.
Continue readingTotal Return Forecasts: Major Asset Classes | 2 June 2026
The expected long-term total return for the Global Market Index (GMI) continued to tick higher in May, rising to the highest level in recent history. Although the annualized performance outlook has edged up to a mid-7% forecast, the current outlook remains well below GMI’s realized return over the trailing ten-year window.
Major Asset Classes | May 2026 | Performance Review
Most markets continued to rise in May, extending April’s bounce-back after March’s broad and deep selloff, based on a set of ETFs. The main exception among the major asset classes: commodities, which fell sharply, posting the first monthly decline this year.
Off the Grid, Italy Edition…
The Capital Spectator is taking an extended Memorial Day holiday and trading NJ for Italy for the week ahead. Postings will be light to (probably) non-existent during the interim. The US-based routine resumes again on June 2. Ciao!
Book Bits: 23 May 2026
● Yuppies: The Bankers, Lawyers, Joggers, and Gourmands Who Conquered New York
Dylan Gottlieb
Review via The Wall Street Journal
“Violent gentrification” is an eye-catching phrase akin to “Canadian depravity” or “Luxembourgish aggression.” If it exists, it isn’t obvious. In “Yuppies: The Bankers, Lawyers, Joggers, and Gourmands Who Conquered New York,” Dylan Gottlieb does his best to alarm readers about his subject and their nefarious doings, such as moving into dicey neighborhoods and turning them into havens for fragrant bakeries and adorable cafes.
The term “yuppie” is as closely tied to the 1980s as “hippie” is to the ’60s. Young urban professionals have usually been discussed in comic terms, by such writers as Tom Wolfe and P.J. O’Rourke, with gentle mockery or even wry affection. Mr. Gottlieb, a professor of history at Bentley University, produces nearly 300 pages on the topic without a trace of humor, except in quotation.
Headline Inflation Surges, but Core Measures Keep the Fed on Hold
Inflation has climbed in the wake of the energy shock stemming from the Middle East, and economists expect the upward pressure to persist in the months ahead. The Federal Reserve is monitoring the data closely, but it left interest rates unchanged at its most recent policy meeting late last month. The Fed funds futures market is still assigning high odds to the Fed holding steady at the next several meetings. The question now is how high inflation will rise before the central bank feels compelled to resume rate hikes.
US Growth Nowcast for Q2 Holds Firm as Inflation Risks Mount
US economic growth remains on track to post a modestly stronger increase in the second quarter compared with Q1, according to the median nowcast from a set of estimates compiled by CapitalSpectator.com. Despite heightened inflation risks stemming from the Middle East energy shock, output appears relatively resilient so far for GDP in the current quarter.
Real Yields Near 20-Year Highs As Energy Shock Continues
The 10‑year real US Treasury yield is hovering near a 20‑year high, with the 5‑year not far behind. Whether this is a good moment to lock in inflation‑indexed yields may hinge on how the Gulf crisis evolves in the months ahead.