Many economists believe that asset price bubbles do not exist or that, due to a joint hypothesis, they are difficult if not impossible to empirically validate. This paper dispels this belief by providing definitive proof that bubbles exist for a set of digital assets that have no cashflows and a zero liquidation value, but trade with positive market prices.

ABSTRACT This paper uses violations of put‐call parity to provide simple lower and upper bounds for measuring the size of asset price bubbles. Assuming only no‐arbitrage, this bubble detection approach avoids restrictive parametric model assumptions. We show that put‐call disparity provides a bubble's lower bound, and the lowest price of an out‐of‐the‐money call option determines the bubble's upper bound. To enhance precision in the presence of market frictions, we implement data‐driven regularization and bootstrap. 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. The evidence also supports the assertion that stock markets are incomplete and often violates no‐dominance.

SOFR swap rates have remained below US Treasury rates since October 2018, posing a puzzling arbitrage opportunity because swaps are replicable in repo and bond markets. Traditional explanations for London Interbank Offered Rate (LIBOR)-swap spreads, such as credit risk, no longer apply since Secured Overnight Financing Rate (SOFR) is a nearly riskless rate. This paper builds on existing explanations for swap spreads - such as market frictions, regulations, and collateral effects - using a novel arbitrage-free replication framework in the SOFR setting. We show that observed spreads arise from three factors: bond market price quotes, repo transaction costs, and Basel III regulations.

Digital assets such as Bitcoin, Ethereum, and meme tokens generate no cash flows and have no underlying collateral pool, meaning their market prices are bubble driven under standard asset-pricing theory. Yet investors may still wish to trade these assets for speculative opportunities or potential diversification benefits. This article examines how to engage in these markets while maintaining normal, risk-adjusted expected returns despite the eventual collapse of such bubbles. Traditional strategies such as buy-and-hold or outright shorting are shown to be suboptimal. Instead, the author proposes a disciplined market-timing strategy in which the investor holds the asset during its rise and exits at a predetermined price barrier to lock in gains. This framework provides a practical method for incorporating nonfundamental digital assets into modern portfolio management.

Shopping centers represent a rare example wherein prices reflect the internalization of externalities. The relatively lower rent anchors pay which other tenants subsidize proxies for positive externalities anchors create. A related proxy we theoretically model and empirically analyze are co-tenancy lease provisions which capture the cost of negative externalities triggered when an anchor leaves. This real option provides temporary rent relief and early lease termination. We show this option price increases (decreases) with base rent (rent abatement, lease term, bond price, and default time). We also show this option enhances property value if favorable market conditions prevail.

In this paper we study an incomplete Brownian motion market and use filtration reduction to obtain a complete market, and hence a unique pricing measure. We then uplift the obtained measure to the original market and study valuation and hedging via the uplifted measure. We show how a general market can be decomposed into a market corresponding to reduced information and a noise component. This allows us to give a precise meaning to the notion of irrelevant information in the context of filtration reduction.

This article proposes and estimates a tractable, arbitrage-free valuation model for corporate coupon bonds that includes a more realistic recovery rate process. Most existing studies use a recovery rate process that is misspecified because it includes recovery for coupons due after default. Misspecification errors from assuming recovery on all coupons can be substantial; they increase with recovery rates, coupons, maturity, and default probabilities. For a large sample of market transactions, i) our model has lower pricing errors than one assuming recovery on all coupons and ii) the magnitude of our model’s outperformance is linked to misspecification errors from assuming recovery on coupons.

The empirical evidence showing that a corporate bond's expected loss is only a small portion of a bond's credit spread is called the credit spread puzzle. This paper, using a reduced-form credit risk model, characterizes a risky bond's credit spread. This characterization provides a more general measure of a risky bond's credit risk and it shows that, in an arbitrage-free market, a bond's credit risk is only a fraction of the credit spread and not linearly related to the one-year, risk-neutral expected loss, resolving the credit spread puzzle.

In a standard no-arbitrage continuous-time model, this paper characterizes a digital asset’s price process as being decomposed into four components: its fundamental value and three different types of bubbles, labeled type 1, 2 and 3. Type 1 bubbles are permanent, type 2 are long-horizon, and type 3 are short-horizon. Only type 3 (short-horizon) bubbles are not martingales under an equivalent local martingale measure. This decomposition implies the standard derivative pricing methodology does not apply to digital assets whose market prices reflect type 3 (short-horizon) bubbles. Modifications to the existing derivative pricing theory needed for digital assets with price bubbles are explored herein.

We present a new approach to identifying asset price bubbles based on options data. Given their forward-looking nature, options are ideal instruments with which to investigate market expectations about the future evolution of asset prices, which are key to understanding price bubbles. By exploiting the differential pricing between put and call options, we can detect and quantify bubbles in the prices of underlying asset. We apply our methodology to two stock market indexes, the S&P 500 and the Nasdaq-100, and two technology stocks, Amazon and Facebook, over the 2014-2018 sample period. We find that, while indexes exhibit rare and modest bubbles, Amazon and Facebook show more frequent and much larger bubbles. Since our approach can be implemented in real time, it is useful to both policy-makers and investors. As an illustration, our methodology applied to GameStop identifies a significant bubble between December 2020 and January 2021.

We develop a unified modeling framework that connects two distinct types of bubbles defined in the literature: the rational bubbles (aka P-bubbles), and the local martingale bubbles (aka Q-bubbles). We show that the local martingale bubble model includes the classical rational bubble as a special case. We relate both types of bubbles to an equity's risk premium via a novel decomposition.

This paper provides a set of sufficient conditions for special classes of filtration expansions, such that the expanded information introduces no new arbitrage opportunities into a market. The information expansion corresponds to knowledge of the "true" price process. The theorem is based on comparing two distinct markets - the original and a fictitious - each associated with a different filtration, and employs the first fundamental theorem of asset pricing in both of these two markets.

This paper introduces a new methodology for estimating dynamically consistent forward rate curves, which are essential for obtaining arbitrage-free valuation and risk management models. Using U.S. Treasury data from January 2013 to June 2023, we fit dynamically consistent forward rates curves and test the goodness of fit between theoretical and observed prices. We compare the traditional static forward rate curve parameterizations (including Nelson-Siegel, Svensson, and cubic splines) with our new dynamically consistent methodology. The dynamically consistent forward rate curve estimates generally outperform the traditional static methods in reproducing market prices.

This paper posits that when an asset exhibits a bubble, its price process can be unbounded from above in finite time with positive probability if a quadratic variation (QV) risk premium is large enough. Based on the local martingale theory of bubbles, we provide sufficient conditions under which price explosion occurs via the QV channel provided that bubbles are present. This QV channel of price explosions is new to the literature and distinct from the explosive autoregressive (AR) dynamics, which is often identified with the presence of bubbles as defined in the time series literature. Using the S&P 500 index and a sample of individual stocks over 1996-2021, we document the existence of price explosions during periods when bubbles occur. Almost all price explosion episodes discovered are associated with the QV and not AR drift channel.

The purpose of this paper is to illustrate the pricing of options in an incomplete market using the new consistent uplifted martingale measure methodology introduced by Grigorian and Jarrow [2024, Filtration Reduction and Incomplete Markets, Frontiers of Mathematical Finance, 3(1), 78–105; 2023, Filtration Reduction and Completeness in Brownian Motion Models. Working Paper, Cornell University; 2024, Filtration Reduction and Completeness in Jump-Diffusion Models. Working Paper, Cornell University]. We apply it to an incomplete market where a stock has stochastic volatility. Two valuation formulas are generated, depending upon whether the trader is more concerned about volatility or price risk in the construction of a partial replicating portfolio for the option’s payoff.

Evidence of excess volatilities at high asset prices is associated with bubbles. We propose a new asset price bubble testing methodology based on volatility estimates. Examining the current U.S. equity bull market, we find that the S&P 500, Dow Jones, and Nasdaq do not exhibit bubbles. We investigate Lyft’s earnings error news and estimate that the bubble’s lifetime is approximately 3 months. Our methodology and results are robust to various adjustments for outliers.