Mark Rubinstein
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The Recovery Theorem
The Recovery Theorem The MIT Faculty has made this article openly available. Please share how this access benefits you. Your story matters. Citation Ross, Steve. “The Recovery Theorem.” The Journal of Finance 70, no. 2 (April 2015): 615–48. As Published http://dx.doi.org/10.1111/jofi.12092 Publisher American Finance Association/Wiley Version Original manuscript Citable link http://hdl.handle.net/1721.1/99126 Terms of Use Creative Commons Attribution-Noncommercial-Share Alike Detailed Terms http://creativecommons.org/licenses/by-nc-sa/4.0/ The Recovery Theorem Journal of Finance forthcoming Steve Ross Franco Modigliani Professor of Financial Economics Sloan School, MIT Abstract We can only estimate the distribution of stock returns but from option prices we observe the distribution of state prices. State prices are the product of risk aversion – the pricing kernel – and the natural probability distribution. The Recovery Theorem enables us to separate these so as to determine the market’s forecast of returns and the market’s risk aversion from state prices alone. Among other things, this allows us to recover the pricing kernel, the market risk premium, the probability of a catastrophe, and to construct model free tests of the efficient market hypothesis. I want to thank the participants in the UCLA Finance workshop for their insightful comments as well as Richard Roll, Hanno Lustig, Rick Antle, Andrew Jeffrey, Peter Carr, Kevin Atteson, Jessica Wachter, Ian Martin, Leonid Kogan, Torben Andersen, John Cochrane, Dimitris Papanikolaou, William Mullins, Jon Ingersoll, Jerry Hausman, Andy Lo, Steve Leroy, George Skiadopoulos, Xavier Gabaix, Patrick Dennis, Phil Dybvig, Will Mullins, Nicolas Caramp, Rodrigo Adao, the referee and the associate editor and editor. -
A Discrete-Time Approach to Evaluate Path-Dependent Derivatives in a Regime-Switching Risk Model
risks Article A Discrete-Time Approach to Evaluate Path-Dependent Derivatives in a Regime-Switching Risk Model Emilio Russo Department of Economics, Statistics and Finance, University of Calabria, Ponte Bucci cubo 1C, 87036 Rende (CS), Italy; [email protected] Received: 29 November 2019; Accepted: 25 January 2020 ; Published: 29 January 2020 Abstract: This paper provides a discrete-time approach for evaluating financial and actuarial products characterized by path-dependent features in a regime-switching risk model. In each regime, a binomial discretization of the asset value is obtained by modifying the parameters used to generate the lattice in the highest-volatility regime, thus allowing a simultaneous asset description in all the regimes. The path-dependent feature is treated by computing representative values of the path-dependent function on a fixed number of effective trajectories reaching each lattice node. The prices of the analyzed products are calculated as the expected values of their payoffs registered over the lattice branches, invoking a quadratic interpolation technique if the regime changes, and capturing the switches among regimes by using a transition probability matrix. Some numerical applications are provided to support the model, which is also useful to accurately capture the market risk concerning path-dependent financial and actuarial instruments. Keywords: regime-switching risk; market risk; path-dependent derivatives; insurance policies; binomial lattices; discrete-time models 1. Introduction With the aim of providing an accurate evaluation of the risks affecting financial markets, a wide range of empirical research evidences that asset returns show stochastic volatility patterns and fatter tails with respect to the standard normal model. -
Module Outline
KEELE UNIVERSITY DEPARTMENT OF ECONOMICS ECO-30004 Options and Futures Contents: 1 Module 2 Aims and 3 Syllabus 4 Organisation 5 Reading and 6 Guidance Details Objectives and Assessment Resources and Feedback 1 Module Details: Module type: Principal Finance, Principal Management Science, Business Economics Session: 2007/08 Semester: Second Level: III CATS Credits: 15 Compulsory for: Principal Finance Pre-requisites: Asset Pricing Co-requisites: None Available to Socrates/Erasmus, exchange and visiting students: Yes Teaching and learning methods: Lectures/Classes (2 hours lectures and per week and one hour class per fortnight) Assessment method: Mixed (exam 80% and mid-term 20%) Hand-in Date: N/A Study time: 150 hours (of which approximately 20 hours lectures, 5 hours tutorials, 25 hours class preparation, 100 hours independent study) Module times: Tuesday 10.00-12.00 in CBA 0.060 Tutorial times: Tuesday 15.00-16.00, HORN-119; Tues 16.00-17.00, HORN-119; Thursday 10.00-11.00, CBA.0.005 and Friday 9.00-10.00 CBA.0.007. Weeks: 3, 4, 6, 8. Module coordinator: Prof. Tim Worrall Teaching staff: Karin Jõeveer and Tim Worrall Contact details: Karin Jõeveer: Room CBA.2.007, E-Mail [email protected]; Tim Worrall: Room CBA 2.021, E-Mail: [email protected]. Consultation times: KJ: Monday 2.30-4.30. TW: Thursday 11.30-12.30 and Friday 10.30-11.30. 2 Aims and Objectives: Aim of Module: The aim of the module is to introduce students to the market in derivative securities and to develop an understanding of the valuation of derivative securities Objectives of Module: This course deals with the valuation and hedging of options, forward contracts, swaps and other derivatives. -
(Very) Sophisticated Heuristics, Never the Black– Scholes–Merton Formula1
Option traders use (very) sophisticated heuristics, never the Black– Scholes–Merton formula1 Espen Gaarder Haug & Nassim Nicholas Taleb Version November 2010 Abstract: Option traders use a heuristically derived pricing formula which they adapt by fudging and changing the tails and skewness by varying one parameter, the standard deviation of a Gaussian. Such formula is popularly called “Black– Scholes–Merton” owing to an attributed eponymous discovery (though changing the standard deviation parameter is in contra- diction with it). However, we have historical evidence that: (1) the said Black, Scholes and Merton did not invent any formula, just found an argument to make a well known (and used) formula compatible with the economics establishment, by removing the “risk” parameter through “dynamic hedging”, (2) option traders use (and evidently have used since 1902) sophisticated heuristics and tricks more compatible with the previous versions of the formula of Louis Bachelier and Edward O. Thorp (that allow a broad choice of probability distributions) and removed the risk parameter using put-call parity, (3) option traders did not use the Black–Scholes–Merton formula or similar formulas after 1973 but continued their bottom-up heuristics more robust to the high impact rare event. The paper draws on historical trading methods and 19th and early 20th century references ignored by the finance literature. It is time to stop using the wrong designation for option pricing. 1 Thanks to Russ Arbuthnot for useful comments. Electronic copy available at: http://ssrn.com/abstract=1012075 THE BLACK-SCHOLES-MERTON “FORMULA” WAS AN BREAKING THE CHAIN OF TRANSMISSION ARGUMENT For us, practitioners, theories should arise from Option traders call the formula they use the “Black- practice2. -
Mark Rubinstein
Rational Markets: Yes or No? The Affirmative Case† Mark Rubinstein Paul Stephens Professor of Applied Investment Analysis University of California, Berkeley June 3, 2000 Abstract This paper presents the logic behind the increasingly neglected proposition that prices set in developed financial markets are determined as if all investors are rational. It contends that realistically, market rationality needs to be defined so as to allow investors to be uncertain about the characteristics of other investors in the market. It also argues that investor irrationality, to the extent it affects prices, is particularly likely to be manifest through overconfidence, which in turn is likely to make the market in an important sense too efficient, rather than less efficient, in reflecting information. To illustrate, the paper ends by re-examining some of the most serious evidence against market rationality: excess volatility, the risk premium puzzle, the size anomaly, calendar effects and the 1987 stock market crash. †I would like to thank the UC Berkeley Finance Group, who prepped me at several “research lunches” prior to the debate described in this paper, in particular, Jonathan Berk and Greg Duffee who commented as well on the written version. Rational Markets: Yes or No? The Affirmative Case In November, 1999, at the program put on by the Berkeley Program in Finance at the Silvarado Country Club in California’s Napa Valley, I was charged with debating Richard Thaler, one of the founders of behavioral finance. The issue was: “Rational Markets: Yes or No?” It struck me then, as I tried to marshal the arguments in the affirmative, how far modern financial economics has come unstuck from its roots. -
Managerial Responses to Incentives: Control of Firm Risk, Derivative Pricing Implications, and Outside Wealth Management
Munich Personal RePEc Archive Managerial Responses to Incentives: Control of Firm Risk, Derivative Pricing Implications, and Outside Wealth Management Jackwerth, Jens Carsten and Hodder, James E. Universität Konstanz, University of Wisconsin-Madison 25 February 2008 Online at https://mpra.ub.uni-muenchen.de/11643/ MPRA Paper No. 11643, posted 19 Nov 2008 06:48 UTC Managerial Responses to Incentives: Control of Firm Risk, Derivative Pricing Implications, and Outside Wealth Management by James E. Hodder and Jens Carsten Jackwerth February 25, 2008 James Hodder is from the University of Wisconsin-Madison, Finance Department, School of Business, 975 University Avenue, Madison, WI 53706, Tel: 608-262-8774, Fax: 608-265-4195, [email protected]. Jens Jackwerth is from the University of Konstanz, Department of Economics, PO Box D-134, 78457 Konstanz, Germany, Tel.: +49-(0)7531-88-2196, Fax: +49-(0)7531-88-3120, [email protected]. We would like to thank David Brown, George Constantinides, Sanjiv Das, Jin-Chuan Duan, Günter Franke, Ken Kavajecz, Bob Jarrow, Mark Ready, and Mark Rubinstein for helpful comments on earlier versions of the paper. We also thank seminar participants at the 15th Annual Derivative Securities and Risk Management Conference, Arlington,VA; the 2006 Frontiers of Finance Conference, Bonaire; ISCTE, Lisbon; Hebrew University; Manchester University; Tel Aviv University; University of Wisconsin-Madison; and Warwick University. Managerial Responses to Incentives: Control of Firm Risk, Derivative Pricing Implications, and Outside Wealth Management Abstract We model a firm’s value process controlled by a manager maximizing expected utility from restricted shares and employee stock options. The manager also dynamically controls allocation of his outside wealth. -
Curriculum Vitae Stephen A. Ross
Curriculum Vitae Stephen A. Ross Stephen A. Ross is the Franco Modigliani Professor of Financial Economics at the MIT (Massachusetts Institute of Technology) Sloan School of Management. Previously, he was the Sterling Professor of Economics and Finance at Yale University for 13 years and a Professor for Economics and Finance at the Wharton School of the University of Pennsylvania from 1975 to 1977. Ross is a fellow of the Econometric Society and a member of the American Academy of Arts and Sciences, serving as an associate editor of several economics and finance journals. In 1988, he was president of the American Finance Association. Stephen A. Ross is the author of more than 100 peer-reviewed articles in economics and finance and co-author of the best-selling textbook Corporate Finance. Furthermore, he has further acted as advisor to the financial sector, major corporations, and government departments such as the U.S. Treasury, the Commerce Department, the Internal Revenue Service, and the Export-Import Bank of the United States. He holds a PhD in Economics from Harvard University. Stephen A. Ross’ wide range of research interests include the economics of uncertainty, corporate finance, decision theory, and financial econometrics. He is known for his fundamental contribution to modern financial economics. His models have changed and advanced practice profoundly. They are widely applied and standard in academia and the financial industry. Most notably, Stephen A. Ross is the inventor of the Arbitrage Pricing Theory, a cornerstone of modern asset pricing theory and the Theory of Agency, which is omnipresent not just in corporate finance but also in many other spheres of economics. -
Fernando V. Ferreira
FERNANDO V. FERREIRA The Wharton School, University of Pennsylvania Phone: (215) 898-7181 430 Vance Hall Email: [email protected] 3733 Spruce Street http://real-faculty.wharton.upenn.edu/fferreir/ Philadelphia, PA 19104-6301 Updated: February 2021 EMPLOYMENT C. F. Koo Professor, The Wharton School, University of Pennsylvania Departments of Real Estate, and Business Economics and Public Policy, 2019-present C. F. Koo Associate Professor, The Wharton School, University of Pennsylvania Departments of Real Estate, and Business Economics and Public Policy, 2018-2019 Associate Professor, The Wharton School, University of Pennsylvania Departments of Real Estate, and Business Economics and Public Policy, 2011-2017 Assistant Professor, The Wharton School, Real Estate Department, 2004-2011 EDUCATION Ph.D. in Economics, University of California, Berkeley, 1999-2004 M.A. in Economics, Federal University of Rio Grande do Sul, Brazil, 1997-1999 B.A. in Economics, State University of Maringa, Brazil, 1992-1996 UNIVERSITY SERVICE Ph.D. Coordinator, Wharton Applied Economics Program, 2012-2014, 2016-2019 Ph.D. Co-Coordinator, Wharton Applied Economics Program, 2006-2011 Recruiting Committee Chair, 2012-2014, 2016, 2019 Graduate Council of the Faculties, 2012-2014 Wharton Dean’s Advisory Council, 2012-2013 PROFESSIONAL RESPONSIBILITIES AND OTHER POSITIONS Co-Organizer, NBER Summer Institute Real Estate Meeting, 2014-present Co-Editor, Journal of Public Economics, 2013-2018 Research Associate, National Bureau of Economic Research (NBER), 2008-present Faculty Fellow, Penn Institute for Urban Research, 2009-present Visiting Scholar, Federal Reserve Bank of Philadelphia, 2006-present Visiting Scholar, Federal Reserve Bank of New York, 2010, 2016, and 2017 Visiting Scholar, Nova School of Business and Economics, 2014-2015 RECENT CONSULTING ACTIVITIES Google X RESEARCH AND PUBLICATIONS Published and Forthcoming Articles “The Role of Price Spillovers in the American Housing Boom”, with Anthony DeFusco, Wenjie Ding, and Joseph Gyourko. -
Looking Out, Locking In: Financial Models and the Social Dynamics of Arbitrage Disasters
Looking Out, Locking In: Financial Models and the Social Dynamics of Arbitrage Disasters Daniel Beunza Department of Management London School of Economics [email protected] and David Stark Department of Sociology Columbia University [email protected] We are thankful to Michael Jensen, Katherine Kellogg, Jerry Kim, Bruce Kogut, Ko Kuwabara, David Ross, Susan Scott, Tano Santos, Stoyan Sgourev, Josh Whitford, Joanne Yates, Francesco Zirpoli and Ezra Zuckerman for comments on previous versions of the paper. Looking Out, Locking In: Financial Models and the Social Dynamics of Arbitrage Disasters Abstract This study analyzes the opportunities and dangers created by financial models. Through ethnographic observations in the derivatives trading room of a major investment bank, we found that traders use models in reverse to look out for possible errors in their financial estimates. We refer to this practice as reflexive modeling. The strength of reflexive modeling resides in leveraging the cognitive independence among dispersed, anonymous actors. But as our analysis demonstrates, it can also give rise to cognitive interdependence. When enough traders overlook a key issue, their positions send the wrong message to the rest of the market. The resulting lock-in leads to arbitrage disasters. Our analysis challenges behavioral finance by locating the root of systemic risk in the calculative tools used by the actors, rather than in their individual biases and limitations. 1 Looking out, locking in: Financial Models and the Social Dynamics of Arbitrage Disasters On June 12th, 2001 the European Commission stated its firm opposition to the planned merger between two Fortune 500 companies. The Commission’s ruling put an end to the proposed combination between General Electric and Honeywell International, initially announced in October 2000. -
On the Accounting Valuation of Employee Stock Options
On the Accounting Valuation of Employee Stock Options Mark Rubinstein† November 30, 1994 (published under the same title in Journal of Derivatives (Fall 1995)) Abstract In its Exposure Draft, "Accounting for Stock-based Compensation," FASB proposes that either the Black-Scholes or binomial option pricing model be used to expense employee stock options, and that the value of these options be measured on their grant date with typically modest ex-post adjustment. This brings the accounting profession squarely up against the Scylla of imposing too narrow a set rules that will force many firms to misstate considerably the value of their stock options and the Charybdis of granting considerable latitude which will increase non-comparability across financial statements of otherwise similar firms. This, of course, is a common tradeoff afflicting many rules for external financial accounting. It is not my intention to take a position on this issue, but merely to point out the inherent dangers in navigating between these twin perils. To examine this question, this paper develops a binomial valuation model which simultaneously takes into consideration the most significant differences between standard call options and employee stock options: longer maturity, delayed vesting, forfeiture, non-transferability, dilution, and taxes. The final model requires 16 input variables: stock price on grant date, stock volatility, stock payout rate, stock expected return, interest rate, option strike price, option years-to-expiration, option years-to-vesting, expected employee forfeiture rate, minimum and maximum forfeiture rate multipliers, employee's non-option wealth per owned option, employee's risk aversion, employee's tax rate, percentage dilution, and number of steps in the binomial tree. -
Registration Requirements for Foreign Securities
Financial Economists Roundtable Statement on Registration Requirements for Foreign Securities July 28, 1993 We the undersigned members of the Financial Economists Roundtable (FER) propose that American investors be allowed to trade the shares of major foreign companies as easily as they now trade the shares of U.S. companies. Our proposal should be viewed as a first step towards eliminating the regulatory impediments that now preclude the securities of most foreign firms from being traded on the principal U.S. equity markets. The Securities and Exchange Commission now requires foreign firms that wish to have their securities traded in these markets to register under the Securities Exchange Act of 1934, and, among other things, reconcile quantitatively their financial statements to U.S. generally accepted accounting principles (U.S. GAAP). This registration requirement hinders U.S. investors and exchanges in trading foreign shares. Eliminating impediments to the trading of foreign shares will enhance the competitive position of the United States in world equity markets and reduce the cost to U.S. investors, who trade these shares. Our proposal to facilitate the trading of foreign shares in U.S. markets is consistent with the principal elements of a recent suggestion made by the New York Stock Exchange. We propose that the equities of very large foreign companies be made eligible to be traded and/or listed in the United States on registered exchanges and on NASDAQ without conforming to all current SEC registration requirements. To be traded on U.S. equity markets, foreign companies would need to have available only their customary financial statements, independently audited, and have revenues of at least 3 billion dollars and a market capitalization of at least 1 billion dollars. -
Neoclassical Finance
PRINCETON LECTURES IN FINANCE Yacine Ait-Sahalia, Series Editor The Princeton Lectures in Finance, published by arrangement with the Bendheim Center for Finance of Princeton University, are based on annual lectures offered at Princeton University. Each year, the Bendheim Center invites a leading figure in the field of finance to deliver a set of lectures on a topic of major significance to researchers and professionals around the world. Stephen A. Ross, Neoclassical Finance Copyright © 2005 by Princeton University Press Published by Princeton University Press, 41 William Street, Princeton, New Jersey 08540 In the United Kingdom: Princeton University Press, 3 Market Place, Woodstock, Oxfordshire OX20 1SY All Rights Reserved Library of Congress Cataloging-in-Publication Data Ross, Stephen A. Neoclassical finance / Stephen A. Ross. p. cm. — (Princeton lectures in finance) Includes bibliographical references and index. ISBN 0-691-12138-9 (cloth : alk. paper) 1. Finance. 2. Efficient market theory. I. Title. II. Series. HG173.R675 2004 332.01—dc22 2004048901 British Library Cataloging-in-Publication Data is available Printed on acid-free paoer. ∞ pup.princeton.edu Printed in the United States of America 13579108642 To Carol, Kate, Jon, Doug, Lucy and my parents CONTENTS PREFACE ix ONE No Arbitrage: The Fundamental Theorem of Finance 1 TWO Bounding the Pricing Kernel, Asset Pricing, and Complete Markets 22 THREE Efficient Markets 42 FOUR A Neoclassical Look at Behavioral Finance: The Closed-End Fund Puzzle 66 BIBLIOGRAPHY 95 INDEX 101 PREFACE HIS MONOGRAPH IS based on the Princeton University Lectures in Finance that I gave in the spring of 2001. The Princeton lectures Tgave me a wonderful opportunity both to refine and expound on my views of modern finance.