The Journal of Finance

Recovering Probability Distributions from Option Prices

Published: 12/1996,  Volume: 51,  Issue: 5  |  DOI: 10.1111/j.1540-6261.1996.tb05219.x  |  Cited by: 811

JENS CARSTEN JACKWERTH, MARK RUBINSTEIN

This article derives underlying asset risk‐neutral probability distributions of European options on the S&P 500 index. Nonparametric methods are used to choose probabilities that minimize an objective function subject to requiring that the probabilities are consistent with observed option and underlying asset prices. Alternative optimization specifications produce approximately the same implied distributions. A new and fast optimization technique for estimating probability distributions based on maximizing the smoothness of the resulting distribution is proposed. Since the crash, the risk‐neutral probability of a three (four) standard deviation decline in the index (about −36 percent (−46 percent) over a year) is about 10 (100) times more likely than under the assumption of lognormality.

Are Options on Index Futures Profitable for Risk‐Averse Investors? Empirical Evidence

Published: 7/19/2011,  Volume: 66,  Issue: 4  |  DOI: 10.1111/j.1540-6261.2011.01665.x  |  Cited by: 71

GEORGE M. CONSTANTINIDES, MICHAL CZERWONKO, JENS CARSTEN JACKWERTH, STYLIANOS PERRAKIS

American options on the S&P 500 index futures that violate the stochastic dominance bounds of Constantinides and Perrakis (2009) from 1983 to 2006 are identified as potentially profitable trades. Call bid prices more frequently violate their upper bound than put bid prices do, while violations of the lower bounds by ask prices are infrequent. In out‐of‐sample tests of stochastic dominance, the writing of options that violate the upper bound increases the expected utility of any risk‐averse investor holding the market and cash, net of transaction costs and bid‐ask spreads. The results are economically significant and robust.

Do Equity and Options Markets Agree about Volatility?

Published: 7/23/2026,  Volume: ,  Issue:   |  DOI: 10.1111/jofi.70070  |  Cited by: 0

CARSTEN H. CHONG, VIKTOR TODOROV

We derive tight pricing kernel restrictions from options with same‐day expiration (“0DTEs”). These restrictions concern the volatility of small and frequent asset price moves that the equity and options markets must agree on in a frictionless economy. Their violation leads to pseudo‐arbitrage opportunities, characterized by nontrivial reward‐to‐risk ratios over arbitrarily short horizons and achieved by a combined position in 0DTEs and the underlying asset. Empirically, we find no evidence of feasible pseudo‐arbitrage opportunities, as transaction costs, estimation risk, and short‐term volatility risk prevent investors from taking advantage of small and infrequent disagreements about volatility between equity and options markets.

Intraday Price Change and Trading Volume Relations in the Stock and Stock Option Markets

Published: 3/1990,  Volume: 45,  Issue: 1  |  DOI: 10.1111/j.1540-6261.1990.tb05087.x  |  Cited by: 357

JENS A. STEPHAN, ROBERT E. WHALEY

This study investigates intraday relations between price changes and trading volume of options and stocks for a sample of firms whose options traded on the CBOE during the first quarter of 1986. After purging the price change series of the effects of bid/ask spreads, multivariate time‐series analysis is used to estimate the lead/lag relation between the price changes in the option and stock markets. The results indicate that price changes in the stock market lead the option market by as much as fifteen minutes. The analysis of trading volume indicates that the stock market lead may be even longer.

In Search of Distress Risk

Published: 11/11/2008,  Volume: 63,  Issue: 6  |  DOI: 10.1111/j.1540-6261.2008.01416.x  |  Cited by: 1905

JOHN Y. CAMPBELL, JENS HILSCHER, JAN SZILAGYI

This paper explores the determinants of corporate failure and the pricing of financially distressed stocks whose failure probability, estimated from a dynamic logit model using accounting and market variables, is high. Since 1981, financially distressed stocks have delivered anomalously low returns. They have lower returns but much higher standard deviations, market betas, and loadings on value and small‐cap risk factors than stocks with low failure risk. These patterns are more pronounced for stocks with possible informational or arbitrage‐related frictions. They are inconsistent with the conjecture that the value and size effects are compensation for the risk of financial distress.

The Cost of Capital for Banks: Evidence from Analyst Earnings Forecasts

Published: 7/14/2022,  Volume: 77,  Issue: 5  |  DOI: 10.1111/jofi.13168  |  Cited by: 32

JENS DICK‐NIELSEN, JACOB GYNTELBERG, CHRISTOFFER THIMSEN

We extract cost of capital measures for banks using analyst earnings forecasts, which we show are unbiased. We find that the cost of equity and the cost of debt decrease in the Tier 1 ratio, whereas total cost of capital is uncorrelated with the Tier 1 ratio. These findings suggest that investors adjust their return expectations for banks in accordance with the Modigliani–Miller conservation‐of‐risk principle. Hence, increased capital requirements arenotmade socially costly based on a notion that market pricing violates risk conservation. Equity can nevertheless still be privately costly for banks because of reduced subsidies.

Investor Factors

Published: 8/7/2025,  Volume: 80,  Issue: 5  |  DOI: 10.1111/jofi.13474  |  Cited by: 4

SEBASTIEN BETERMIER, LAURENT E. CALVET, SAMULI KNÜPFER, JENS SOERLIE KVAERNER

This paper develops an empirical methodology for extracting pricing factors from investor portfolio data. We apply this approach to the stockholdings of Norwegian individual investors from 1997 to 2017. A two‐factor model, featuring the market portfolio and a long‐short portfolio constructed from the holdings of investors sorted by age or wealth, explains both the common variation in portfolio holdings and the cross section of stock returns. Portfolio tilts toward the long‐short investor factor correlate with indebtedness, macroeconomic exposure, gender, and investment experience. Our paper illustrates the benefits of using holdings data for explaining the risk premia of financial assets.

Nonstandard Errors

Published: 4/17/2024,  Volume: 79,  Issue: 3  |  DOI: 10.1111/jofi.13337  |  Cited by: 112

ALBERT J. MENKVELD, ANNA DREBER, FELIX HOLZMEISTER, JUERGEN HUBER, MAGNUS JOHANNESSON, MICHAEL KIRCHLER, SEBASTIAN NEUSÜß, MICHAEL RAZEN, UTZ WEITZEL, DAVID ABAD‐DÍAZ, MENACHEM (MENI) ABUDY, TOBIAS ADRIAN, YACINE AIT‐SAHALIA, OLIVIER AKMANSOY, JAMIE T. ALCOCK, VITALI ALEXEEV, ARASH ALOOSH, LIVIA AMATO, DIEGO AMAYA, JAMES J. ANGEL, ALEJANDRO T. AVETIKIAN, AMADEUS BACH, EDWIN BAIDOO, GAETAN BAKALLI, LI BAO, ANDREA BARBON, OKSANA BASHCHENKO, PARAMPREET C. BINDRA, GEIR H. BJØNNES, JEFFREY R. BLACK, BERNARD S. BLACK, DIMITAR BOGOEV, SANTIAGO BOHORQUEZ CORREA, OLEG BONDARENKO, CHARLES S. BOS, CIRIL BOSCH‐ROSA, ELIE BOURI, CHRISTIAN BROWNLEES, ANNA CALAMIA, VIET NGA CAO, GUNTHER CAPELLE‐BLANCARD, LAURA M. CAPERA ROMERO, MASSIMILIANO CAPORIN, ALLEN CARRION, TOLGA CASKURLU, BIDISHA CHAKRABARTY, JIAN CHEN, MIKHAIL CHERNOV, WILLIAM CHEUNG, LUDWIG B. CHINCARINI, TARUN CHORDIA, SHEUNG‐CHI CHOW, BENJAMIN CLAPHAM, JEAN‐EDOUARD COLLIARD, CAROLE COMERTON‐FORDE, EDWARD CURRAN, THONG DAO, WALE DARE, RYAN J. DAVIES, RICCARDO DE BLASIS, GIANLUCA F. DE NARD, FANY DECLERCK, OLEG DEEV, HANS DEGRYSE, SOLOMON Y. DEKU, CHRISTOPHE DESAGRE, MATHIJS A. VAN DIJK, CHUKWUMA DIM, THOMAS DIMPFL, YUN JIANG DONG, PHILIP A. DRUMMOND, TOM DUDDA, TEODOR DUEVSKI, ARIADNA DUMITRESCU, TEODOR DYAKOV, ANNE HAUBO DYHRBERG, MICHAŁ DZIELIŃSKI, ASLI EKSI, IZIDIN EL KALAK, SASKIA TER ELLEN, NICOLAS EUGSTER, MARTIN D. D. EVANS, MICHAEL FARRELL, ESTER FELEZ‐VINAS, GERARDO FERRARA, EL MEHDI FERROUHI, ANDREA FLORI, JONATHAN T. FLUHARTY‐JAIDEE, SEAN D. V. FOLEY, KINGSLEY Y. L. FONG, THIERRY FOUCAULT, TATIANA FRANUS, FRANCESCO FRANZONI, BART FRIJNS, MICHAEL FRÖMMEL, SERVANNA M. FU, SASCHA C. FÜLLBRUNN, BAOQING GAN, GE GAO, THOMAS P. GEHRIG, ROLAND GEMAYEL, DIRK GERRITSEN, JAVIER GIL‐BAZO, DUDLEY GILDER, LAWRENCE R. GLOSTEN, THOMAS GOMEZ, ARSENY GORBENKO, JOACHIM GRAMMIG, VINCENT GRÉGOIRE, UFUK GÜÇBILMEZ, BJÖRN HAGSTRÖMER, JULIEN HAMBUCKERS, ERIK HAPNES, JEFFREY H. HARRIS, LAWRENCE HARRIS, SIMON HARTMANN, JEAN‐BAPTISTE HASSE, NIKOLAUS HAUTSCH, XUE‐ZHONG (TONY) HE, DAVIDSON HEATH, SIMON HEDIGER, TERRENCE HENDERSHOTT, ANN MARIE HIBBERT, ERIK HJALMARSSON, SETH A. HOELSCHER, PETER HOFFMANN, CRAIG W. HOLDEN, ALEX R. HORENSTEIN, WENQIAN HUANG, DA HUANG, CHRISTOPHE HURLIN, KONRAD ILCZUK, ALEXEY IVASHCHENKO, SUBRAMANIAN R. IYER, HOSSEIN JAHANSHAHLOO, NAJI JALKH, CHARLES M. JONES, SIMON JURKATIS, PETRI JYLHÄ, ANDREAS T. KAECK, GABRIEL KAISER, ARZÉ KARAM, EGLE KARMAZIENE, BERNHARD KASSNER, MARKKU KAUSTIA, EKATERINA KAZAK, FEARGHAL KEARNEY, VINCENT VAN KERVEL, SAAD A. KHAN, MARTA K. KHOMYN, TONY KLEIN, OLGA KLEIN, ALEXANDER KLOS, MICHAEL KOETTER, ALEKSEY KOLOKOLOV, ROBERT A. KORAJCZYK, ROMAN KOZHAN, JAN P. KRAHNEN, PAUL KUHLE, AMY KWAN, QUENTIN LAJAUNIE, F. Y. ERIC C. LAM, MARIE LAMBERT, HUGUES LANGLOIS, JENS LAUSEN, TOBIAS LAUTER, MARKUS LEIPPOLD, VLADIMIR LEVIN, YIJIE LI, HUI LI, CHEE YOONG LIEW, THOMAS LINDNER, OLIVER LINTON, JIACHENG LIU, ANQI LIU, GUILLERMO LLORENTE, MATTHIJS LOF, ARIEL LOHR, FRANCIS LONGSTAFF, ALEJANDRO LOPEZ‐LIRA, SHAWN MANKAD, NICOLA MANO, ALEXIS MARCHAL, CHARLES MARTINEAU, FRANCESCO MAZZOLA, DEBRAH MELOSO, MICHAEL G. MI, ROXANA MIHET, VIJAY MOHAN, SOPHIE MOINAS, DAVID MOORE, LIANGYI MU, DMITRIY MURAVYEV, DERMOT MURPHY, GABOR NESZVEDA, CHRISTIAN NEUMEIER, ULF NIELSSON, MAHENDRARAJAH NIMALENDRAN, SVEN NOLTE, LARS L. NORDEN, PETER O'NEILL, KHALED OBAID, BERNT A. ØDEGAARD, PER ÖSTBERG, EMILIANO PAGNOTTA, MARCUS PAINTER, STEFAN PALAN, IMON J. PALIT, ANDREAS PARK, ROBERTO PASCUAL, PAOLO PASQUARIELLO, LUBOS PASTOR, VINAY PATEL, ANDREW J. PATTON, NEIL D. PEARSON, LORIANA PELIZZON, MICHELE PELLI, MATTHIAS PELSTER, CHRISTOPHE PÉRIGNON, CAMERON PFIFFER, RICHARD PHILIP, TOMÁŠ PLÍHAL, PUNEET PRAKASH, OLIVER‐ALEXANDER PRESS, TINA PRODROMOU, MARCEL PROKOPCZUK, TALIS PUTNINS, YA QIAN, GAURAV RAIZADA, DAVID RAKOWSKI, ANGELO RANALDO, LUCA REGIS, STEFAN REITZ, THOMAS RENAULT, REX W. RENJIE, ROBERTO RENO, STEVEN J. RIDDIOUGH, KALLE RINNE, PAUL RINTAMÄKI, RYAN RIORDAN, THOMAS RITTMANNSBERGER, IÑAKI RODRÍGUEZ LONGARELA, DOMINIK ROESCH, LAVINIA ROGNONE, BRIAN ROSEMAN, IOANID ROŞU, SAURABH ROY, NICOLAS RUDOLF, STEPHEN R. RUSH, KHALADDIN RZAYEV, ALEKSANDRA A. RZEŹNIK, ANTHONY SANFORD, HARIKUMAR SANKARAN, ASANI SARKAR, LUCIO SARNO, OLIVIER SCAILLET, STEFAN SCHARNOWSKI, KLAUS R. SCHENK‐HOPPÉ, ANDREA SCHERTLER, MICHAEL SCHNEIDER, FLORIAN SCHROEDER, NORMAN SCHÜRHOFF, PHILIPP SCHUSTER, MARCO A. SCHWARZ, MARK S. SEASHOLES, NORMAN J. SEEGER, OR SHACHAR, ANDRIY SHKILKO, JESSICA SHUI, MARIO SIKIC, GIORGIA SIMION, LEE A. SMALES, PAUL SÖDERLIND, ELVIRA SOJLI, KONSTANTIN SOKOLOV, JANTJE SÖNKSEN, LAIMA SPOKEVICIUTE, DENITSA STEFANOVA, MARTI G. SUBRAHMANYAM, BARNABAS SZASZI, OLEKSANDR TALAVERA, YUEHUA TANG, NICK TAYLOR, WING WAH THAM, ERIK THEISSEN, JULIAN THIMME, IAN TONKS, HAI TRAN, LUCA TRAPIN, ANDERS B. TROLLE, M. ANDREEA VADUVA, GIORGIO VALENTE, ROBERT A. VAN NESS, AURELIO VASQUEZ, THANOS VEROUSIS, PATRICK VERWIJMEREN, ANDERS VILHELMSSON, GRIGORY VILKOV, VLADIMIR VLADIMIROV, SEBASTIAN VOGEL, STEFAN VOIGT, WOLF WAGNER, THOMAS WALTHER, PATRICK WEISS, MICHEL VAN DER WEL, INGRID M. WERNER, P. JOAKIM WESTERHOLM, CHRISTIAN WESTHEIDE, HANS C. WIKA, EVERT WIPPLINGER, MICHAEL WOLF, CHRISTIAN C. P. WOLFF, LEONARD WOLK, WING‐KEUNG WONG, JAN WRAMPELMEYER, ZHEN‐XING WU, SHUO XIA, DACHENG XIU, KE XU, CAIHONG XU, PRADEEP K. YADAV, JOSÉ YAGÜE, CHENG YAN, ANTTI YANG, WOONGSUN YOO, WENJIA YU, YIHE YU, SHIHAO YU, BART Z. YUESHEN, DARYA YUFEROVA, MARCIN ZAMOJSKI, ABALFAZL ZAREEI, STEFAN M. ZEISBERGER, LU ZHANG, S. SARAH ZHANG, XIAOYU ZHANG, LU ZHAO, ZHUO ZHONG, Z. IVY ZHOU, CHEN ZHOU, XINGYU S. ZHU, MARIUS ZOICAN, REMCO ZWINKELS

In statistics, samples are drawn from a population in a data‐generating process (DGP). Standard errors measure the uncertainty in estimates of population parameters. In science, evidence is generated to test hypotheses in an evidence‐generating process (EGP). We claim that EGP variation across researchers adds uncertainty—nonstandard errors (NSEs). We study NSEs by letting 164 teams test the same hypotheses on the same data. NSEs turn out to be sizable, but smaller for more reproducible or higher rated research. Adding peer‐review stages reduces NSEs. We further find that this type of uncertainty is underestimated by participants.