The Journal of Finance

The Relationship between Arbitrage and First Order Stochastic Dominance

Published: 09/01/1986   |   DOI: 10.1111/j.1540-6261.1986.tb04556.x

ROBERT JARROW

This paper joins together two fields of research in financial economics. The first field studies stochastic dominance, while the second field studies arbitrage pricing. The two fields are linked together through the derivation and the proof of a characterization theorem. The characterization theorem gives necessary and sufficient conditions for the existence of arbitrage opportunities in terms of the existence of two assets, one of which first order stochastically dominates the other and the price of a particular contingent claim. Examples are provided to demonstrate the theorem's content.

Heterogeneous Expectations, Restrictions on Short Sales, and Equilibrium Asset Prices

Published: 12/01/1980   |   DOI: 10.1111/j.1540-6261.1980.tb02198.x

ROBERT JARROW

Under heterogeneous expectations, the mean–variance model of capital market equilibrium is employed to determine the effect restricting short sales has on equilibrium asset prices. Two equivalent markets differing only with respect to short sale restrictions are compared. It is shown that, in general, risky asset prices can either rise or fall due to short sale constraints. However, under a homogeneity of beliefs for the covariance matrix of future prices, short sale constraints will only increase risky asset prices.

Consensus Beliefs Equilibrium and Market Efficiency

Published: 06/01/1983   |   DOI: 10.1111/j.1540-6261.1983.tb02509.x

DAVID EASLEY, ROBERT A. JARROW

This paper presents an analysis of the concept of consensus beliefs and its relation to market efficiency. We show that unless traders have rational expectations, the two published interpretations of consensus beliefs are not useful for considerations of market efficiency. One interpretation (see Verrecchia [6]) has no implication for market efficiency. Under the second interpretation (see Verrecchia [7], [8]) consensus beliefs equilibria are efficient, but they typically do not exist unless traders have rational expectations.

THE RELATIONSHIP BETWEEN YIELD, RISK, AND RETURN OF CORPORATE BONDS

Published: 09/01/1978   |   DOI: 10.1111/j.1540-6261.1978.tb02061.x

Robert A. Jarrow

Primes and Scores: An Essay on Market Imperfections

Published: 12/01/1989   |   DOI: 10.1111/j.1540-6261.1989.tb02653.x

ROBERT A. JARROW, MAUREEN O'HARA

This paper investigates the reported relative mispricing of primes and scores to the underlying stock. Given transaction costs, we establish arbitrage‐based bounds on prime and score prices. We then develop a new nonparametric statistical technique to test whether prime and score prices violate these bounds. We find that prime and score prices do exceed stock prices, and often by a considerable amount. We demonstrate that this increased value is most likely due to the score's ability to save on the costs of dynamic hedging. We also show how short sale and trust size constraints impede the ability to arbitrage price disparities.

Pricing Derivatives on Financial Securities Subject to Credit Risk

Published: 03/01/1995   |   DOI: 10.1111/j.1540-6261.1995.tb05167.x

ROBERT A. JARROW, STUART M. TURNBULL

This article provides a new methodology for pricing and hedging derivative securities involving credit risk. Two types of credit risks are considered. The first is where the asset underlying the derivative security may default. The second is where the writer of the derivative security may default. We apply the foreign currency analogy of Jarrow and Turnbull (1991) to decompose the dollar payoff from a risky security into a certain payoff and a “spot exchange rate.” Arbitrage‐free valuation techniques are then employed. This methodology can be applied to corporate debt and over the counter derivatives, such as swaps and caps.

Counterparty Risk and the Pricing of Defaultable Securities

Published: 12/17/2002   |   DOI: 10.1111/0022-1082.00389

Robert A. Jarrow, Fan Yu

Motivated by recent financial crises in East Asia and the United States where the downfall of a small number of firms had an economy‐wide impact, this paper generalizes existing reduced‐form models to include default intensities dependent on the default of a counterparty. In this model, firms have correlated defaults due not only to an exposure to common risk factors, but also to firm‐specific risks that are termed “counterparty risks.” Numerical examples illustrate the effect of counterparty risk on the pricing of defaultable bonds and credit derivatives such as default swaps.

Arbitrage, Continuous Trading, and Margin Requirements

Published: 12/01/1987   |   DOI: 10.1111/j.1540-6261.1987.tb04357.x

DAVID C. HEATH, ROBERT A. JARROW

This paper studies the impact that margin requirements have on both the existence of arbitrage opportunities and the valuation of call options. In the context of the Black‐Scholes economy, margin restrictions are shown to exclude continuous‐trading arbitrage opportunities and, with two additional hypotheses, still to allow the Black‐Scholes call model to apply. The Black‐Scholes economy consists of a continuously traded stock with a price process that follows a geometric Brownian motion and a continuously traded bond with a price process that is deterministic.

Interest Rate Caps “Smile” Too! But Can the LIBOR Market Models Capture the Smile?

Published: 01/11/2007   |   DOI: 10.1111/j.1540-6261.2007.01209.x

ROBERT JARROW, HAITAO LI, FENG ZHAO

Using 3 years of interest rate caps price data, we provide a comprehensive documentation of volatility smiles in the caps market. To capture the volatility smiles, we develop a multifactor term structure model with stochastic volatility and jumps that yields a closed‐form formula for cap prices. We show that although a three‐factor stochastic volatility model can price at‐the‐money caps well, significant negative jumps in interest rates are needed to capture the smile. The volatility smile contains information that is not available using only at‐the‐money caps, and this information is important for understanding term structure models.