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Contingent-Claim-Based Expected Stock Returns∗
Contingent-Claim-Based Expected Stock Returns∗ Zhiyao Chen Ilya A. Strebulaev ICMA Centre Graduate School of Business University of Reading Stanford University and NBER ∗We thank Harjoat Bhamra, Chris Brooks, Wayne Ferson, Vito Gala, Andrea Gamba, Jo˜ao Gomes, Patrick Gagliardini, Chris Hennessy, Chris Juilliard, Nan Li, Rajnish Mehra, Stefan Nagel, Stavros Panageas, Marcel Prokopczuk, Michael Roberts, Ravindra Sastry, Stephan Siegel, Neal Stoughton, Yuri Tserlukevich, Kathy Yuan, Jeffrey Zwiebel and participants at the ASU Sonoran 2013 Winter Finance Conference, the European Financial Associations 2013 annual meetings and the American Financial Associations 2014 annual meetings for their helpful comments. Zhiyao Chen: ICMA Centre, University of Reading, UK, email: [email protected]; Ilya A. Strebulaev: Graduate School of Business, Stanford University, and NBER, email: [email protected]. Contingent-Claim-Based Expected Stock Returns Abstract We develop and test a parsimonious contingent claims model for cross-sectional returns of stock portfolios formed on market leverage, book-to-market equity, asset growth rate, and equity size. Since stocks are residual claims on firms’ assets that generate operating cash flows, stock returns are cash flow rates scaled by the sen- sitivities of stocks to cash flows. Our model performs well because the stock-cash flow sensitivities contain economic information. Value stocks, high-leverage stocks and low-asset-growth stocks are more sensitive to cash flows than growth stocks, low- leverage stocks and high-asset-growth stocks, particularly in recessions when default probabilities are high. Keywords: Stock-cash flow sensitivity, structural estimation, implied-state GMM, financial leverage, default probability, asset pricing anomalies JEL Classification: G12, G13, G33 2 1 Introduction Equity is a residual claim contingent on a firm’s assets that generate operating cash flows. -
Estimation of Employee Stock Option Exercise Rates and Firm Cost⇤
Estimation of Employee Stock Option Exercise Rates and Firm Cost⇤ Jennifer N. Carpenter Richard Stanton Nancy Wallace New York University U.C. Berkeley U.C. Berkeley December 1, 2017 Abstract We develop the first empirical model of employee-stock-option exercise that is suitable for valu- ation and allows for behavioral channels in the determination of employee option cost. We estimate exercise rates as functions of option, stock and employee characteristics in a sample of all employee exercises at 89 firms. Increasing vesting date frequency from annual to monthly reduces option value by 10-16%. Men exercise faster than women, reducing option value by 2-4%. Top employees exercise more slowly than lower-ranked, increasing value by 2-10%. Finally, we develop an analytic valuation approximation that is much more accurate than methods used in practice. ⇤Financial support from the Fisher Center for Real Estate and Urban Economics and the Society of Actuaries is gratefully acknowledged. For helpful comments and suggestions, we thank Daniel Abrams, Terry Adamson, Xavier Gabaix, Wenxuan Hou, James Lecher, Kai Li, Ulrike Malmendier, Kevin Mur- phy, Terry Odean, Nicholas Reitter, Jun Yang, David Yermack, and seminar participants at Cheung Kong Graduate School of Business, Erasmus University, Federal Reserve Bank of New York, Fudan University, Lancaster University, McGill University, New York University, The Ohio State University, Oxford Univer- sity, Peking University, Rice University, Securities and Exchange Commission, Shanghai Advanced Institute of Finance, Temple University, Tilburg University, Tsinghua University, and the 2017 Western Finance As- sociation meetings. We thank Terry Adamson at AON Consulting for providing some of the data used in this study. -
Valuation of Stock Options
VALUATION OF STOCK OPTIONS The right to buy or sell a given security at a specified time in the future is an option. Options are “derivatives’, i.e. they derive their value from the security that is to be traded in accordance with the option. Determining the value of publicly traded stock options is not a problem as the market sets the price. The value of a non-publicly traded option, however, depends on a number of factors: the price of the underlying security at the time of valuation, the time to exercise the option, the volatility of the underlying security, the risk free interest rate, the dividend rate, and the strike price. In addition to these financial variables, subjective variables also play a role. For example, in the case of employee stock options, the employee and the employer have different reasons for valuation, and, therefore, differing needs result in a different valuation for each party. This appendix discusses the reasons for the valuation of non-publicly traded options, explores and compares the two predominant valuation models, and attempts to identify the appropriate valuation methods for a variety of situations. We do not attempt to explain option-pricing theory in depth nor do we attempt mathematical proofs of the models. We focus on the practical aspects of option valuation, directing the reader to the location of computer calculators and sources of the data needed to enter into those calculators. Why Value? The need for valuation arises in a variety of circumstances. In the valuation of a business, for example, options owned by that business must be valued like any other investment asset. -
Contingent Claims Valuation When the Security Price Is a Combination of an 11"O Process and a Random Point Process
Stochastic Processes and their Applications 28 (1988) 185-220 185 North-Holland CONTINGENT CLAIMS VALUATION WHEN THE SECURITY PRICE IS A COMBINATION OF AN 11"O PROCESS AND A RANDOM POINT PROCESS Knut K. AASE Norwegian School of Economics and Business Administration, Institute of Insurance, Helleveien 30, N-5035 Bergen.Sandviken, Norway Received 18 September 1986 Revised 30 November 1987 This paper develops several results in the modern theory of contingent claims valuation in a frictionless security m~rket with continuous trading. The price model is a semi-martingale with a certain structure, making the return of the security a sum of an Ito-process and a random, marked point process. Dynamic equilibrium prices are known to be of this form in an Arrow- Debreu economy, so there is no real limitation in our approach. This class of models is also advantageous from an applied point of view. Within this framework we investigate how the model behaves under the equivalent martingale measure in the P*-equilibrium economy, where discounted security prices are marginales. Here we present some new results showing how the marked point process affects prices of contingent claims in equilibrium. We derive a new class of option pricing formulas when the Ito process is a general Gaussian process, one formula for each positive La[0, T]-function. We show that our general model is complete, although the set of equivalent martingale measures is not a singleton. We also demonstrate how to price contingent claims when the underlying process has after-effects in all of its parameters. contingent claims valuation * security market • semi-martingale model * option pricing formulas 1. -
Stock Options and Credit Default Swaps in Risk Management
Stock Options and Credit Default Swaps in Risk Management Bassam Al-Own Faculty of Finance and Business Administration Al al-Bayt University Mafraq 25113, Jordan Email: [email protected] Marizah Minhat* The Business School Edinburgh Napier University Edinburgh EH14 1DJ, United Kingdom Email: [email protected] Simon Gao The Business School Edinburgh Napier University Edinburgh EH14 1DJ, United Kingdom Email: [email protected] Journal of International Financial Markets, Institutions and Money (forthcoming) * Corresponding author. Acknowledgement: This paper was presented at the 2016 Cross Country Perspectives of Finance conferences held in Taiyuan and Pu’er, China. The authors would like to thank Professor Gady Jacoby, Professor Zhenyu Wu, anonymous reviewers, and the conferences’ participants. i Stock Options and Credit Default Swaps in Risk Management 1 ABSTRACT The use of stock options and credit default swaps (CDS) in banks is not uncommon. Stock options can induce risk-taking incentives, while CDS can be used to hedge against credit risk. Building on the existing literature on executive compensation and risk management, our study contributes novel empirical support for the role of stock options in restraining the use of CDS for hedging purposes. Based on data of CEO stock options and CDS held by 60 European banks during the period 2006-2011, we find a negative relationship between option-induced risk- taking incentives (vega) and the proportion of CDS held for hedging. However, the extent of CDS held for hedging is found to be positively related to default risk in the period leading to the financial crisis that erupted in 2007. -
Should We Expense Stock Options
Options Pricing and Accounting Practice Charles W. Calomiris American Enterprise Institute R. Glenn Hubbard Columbia University and the National Bureau of Economic Research AEI WORKING PAPER #103, JANUARY 8, 2004 www.aei.org/workingpapers www.aei.org/publication20882 #17198 I. Introduction In the wake of the recent corporate scandals that have damaged investor confidence, policymakers, academics, and pundits have taken aim at accounting rules as one of the areas in need of reform. Proposals for changing the rules governing the accounting for the granting of stock options has become one of the most hotly contested areas. Advocates of reform argue that options are a form of compensation and that granting options entails real costs to stockholders. They argue that it follows that options should be included as an expense item in the firm’s financial statements. In this article, we consider the potential benefits and costs of requiring the expensing options. First, we show that the potential benefits of developing rules for expensing options would be small, even if the valuation of the options were straightforward. Second, we review practical problems that make it extremely difficult to create a set of accounting conventions that would properly value the options. We conclude that the establishment of new accounting rules for expensing options would likely do more harm than good. II. How Big Are Potential Gains from Establishing a Standard for Expensing Options? At the outset, it may be useful to review the purpose of regulating accounting conventions and to distinguish that regulation from the regulation of the disclosure of information. Financial economists typically argue for the irrelevance of accounting measures of earnings for the purpose of valuing stock prices. -
Employee Stock Options: Tax Treatment and Tax Issues
Employee Stock Options: Tax Treatment and Tax Issues James M. Bickley Specialist in Public Finance June 15, 2012 Congressional Research Service 7-5700 www.crs.gov RL31458 CRS Report for Congress Prepared for Members and Committees of Congress Employee Stock Options: Tax Treatment and Tax Issues Summary The practice of granting a company’s employees options to purchase the company’s stock has become widespread among American businesses. Employee stock options have been praised as innovative compensation plans that help align the interests of the employees with those of the shareholders. They have also been condemned as schemes to enrich insiders and avoid company taxes. The tax code recognizes two general types of employee options, “qualified” and nonqualified. Qualified (or “statutory”) options include “incentive stock options,” which are limited to $100,000 a year for any one employee, and “employee stock purchase plans,” which are limited to $25,000 a year for any employee. Employee stock purchase plans must be offered to all full- time employees with at least two years of service; incentive stock options may be confined to officers and highly paid employees. Qualified options are not taxed to the employee when granted or exercised (under the regular tax); tax is imposed only when the stock is sold. If the stock is held one year from purchase and two years from the granting of the option, the gain is taxed as long-term capital gain. The employer is not allowed a deduction for these options. However, if the stock is not held the required time, the employee is taxed at ordinary income tax rates and the employer is allowed a deduction. -
Employee Stock Option Valuation with an Early Exercise Boundary
Employee Stock Option Valuation with an Early Exercise Boundary Neil Brisley, University of Western Ontario Chris K. Anderson, Cornell University Many companies are recognizing that the Black-Scholes formula is inappropriate for employee stock options (ESOs) and are moving toward lattice models for accounting or decision-making purposes. In the most influential of these models, the assumption is that employees exercise voluntarily when the stock price reaches a fixed multiple of the strike price, effectively introducing a "horizontal" exercise boundary into the lattice. In practice, however, employees make a trade-off between intrinsic value captured and the opportunity cost of time value forgone. The model proposed here explicitly recognizes and accounts for this reality and is intuitively appealing, easily implemented, and compliant with U.S. accounting standards. Another assumption that Lehman made in valuing Mr. Fuld's pay in 2000 was that he would exercise the options two and a half years after receiving them. But Mr. Fuld had a history of holding onto his options until they were about to expire. Indeed, all 2.6 million options that Mr. Fuld has exercised since November 2003 were in the last year of their life when he did so. —Patrick McGeehan (2006) The need to value employee stock options (ESOs) for accounting and economic purposes makes the modeling of employee early exercise behavior relevant for corporate financial officers, security analysts, and those involved in determining option awards. Early exercise by employees reduces the cost of the ESO to the company in relation to an otherwise identical European option (which can be exercised only at the end of its life), so ESO-pricing models must make assumptions to describe in what circumstances an employee will exercise an option before expiration. -
Fair Value Management: a Case Study of Employee Stock Option Pricing Models
Fair Value Management: A Case Study of Employee Stock Option Pricing Models Loïc Belze EMLYON Business School Francois Larmande HEC Paris Lorenz Schneider EMLYON Business School 3 October 2014 ABSTRACT: This paper examines the fair value management of Employee Stock Options (ESOs). Departing from earlier literature focused on input estimates, we study the management of the pricing model itself, which is sometimes freely interpreted by companies. Relaxing certain assumptions of the Black-Scholes-Merton (BSM) model can lead to a range of possible prices. We first show that when estimating the ESO cost for the company, only prices equal to or above the BSM model price should be considered, whereas discounts are in fact observed at issuance. Second, based on a specific class of listed ESO in an IFRS context, our empirical study finds an overall average discount of 64% on our model price after controlling for ESO-specific characteristics. The discount results mainly from model management. These results provide interesting insights into the scope for model management under different accounting standards, and are also relevant for authorities in charge of enforcement. Keywords: Fair value – ESO – Transaction costs – IFRS 2 – SFAS 123R Data: All data are available from public sources 1 I. INTRODUCTION Implementing fair value principles is not a straightforward task. Standard setters have progressively refined the notion of fair value, as evidenced by the recent efforts of the FASB1 (e.g. the update of Topic 820 for US GAAP2) and the IASB3 (e.g. the recent implementation of IFRS 134) to produce new guidance on this issue. In the specific case of share-based compensation both standard setters (SFAS 123R5 for US GAAP and IFRS 26 for IFRS) determined in 2004 that, in order to improve accountability and transparency towards shareholders, share-based compensation instruments should be recognized as a cost by firms and expensed in the income statement at their fair value. -
Employee Stock Options and Equity Valuation
DOI: 10.1111/j.1475-679x.2005.00164.x Journal of Accounting Research Vol. 43 No. 1 March 2005 Printed in U.S.A. Employee Stock Options, Equity Valuation, and the Valuation of Option Grants Using aWarrant-Pricing Model ∗ FENG LI AND M.H.FRANCOWONG† Received 5 January 2004; accepted 11 July 2004 ABSTRACT We investigate the use of a warrant-pricing approach to incorporate em- ployee stock options (ESOs) into equity valuation and to account for the di- lutive effect of ESOs in the valuation of option grants for financial reporting purposes. Our valuation approach accounts for the jointly determined nature of ESO and shareholder values. The empirical results show that our stock price estimate exhibits lower prediction errors and higher explanatory powers for actual share price than does the traditional stock price estimate. We use our valuation approach to assess the implications of dilution on the fair-value es- timates of ESO grants. We find that the fair value is overstated by 6% if we ignore the dilutive feature of ESOs. Furthermore, this bias is larger for firms that are heavy users of ESOs, small, and R&D intensive, and for firms that have a broad-based ESO compensation plan. ∗ University of Michigan; †University of Chicago. We thank Ray Ball, Dan Bens, Phil Berger, Clement Har, Steve Kaplan, Doron Kliger, S. P. Kothari, Susan Krische, Richard Leftwich, Thomas Lys, James Myers, Dennis Oswald, Joe Piotroski, Doug Skinner, Abbie Smith, K. R. Subramanyam, Shyam V. Sunder, Brett Trueman, Martin Wu, Peter Wysocki, an anonymous referee, and workshop participants at Chicago, MIT, Northwestern, University of Illinois at Urbana-Champaign, and the London Business School 2004 Accounting Symposium for their comments and suggestions. -
Financial Mathematics
Financial Mathematics Rudiger¨ Kiesel February, 2005 0-0 1 Financial Mathematics Lecture 1 by Rudiger¨ Kiesel Department of Financial Mathematics, University of Ulm Department of Statistics, LSE RSITÄT V E U I L N M U · · S O C I D E N N A D R O U · C · D O O C D E c Rudiger¨ Kiesel N 2 Aims and Objectives • Review basic concepts of probability theory; • Discuss random variables, their distribution and the notion of independence; • Calculate functionals and transforms; • Review basic limit theorems. RSITÄT V E U I L N M U · · S O C I D E N N A D R O U · C · D O O C D E c Rudiger¨ Kiesel N 3 Probability theory To describe a random experiment we use sample space Ω, the set of all possible outcomes. Each point ω of Ω, or sample point, represents a possible random outcome of performing the random experiment. For a set A ⊆ Ω we want to know the probability IP (A). The class F of subsets of Ω whose probabilities IP (A) are defined (call such A events) should be be a σ-algebra , i.e. closed under countable, disjoint unions and complements, and contain the empty set ∅ and the whole space Ω. Examples. Flip coins, Roll two dice. RSITÄT V E U I L N M U · · S O C I D E N N A D R O U · C · D O O C D E c Rudiger¨ Kiesel N 4 Probability theory We want (i) IP (∅) = 0, IP (Ω) = 1, (ii) IP (A) ≥ 0 for all A, (iii) If A1,A2,..., are disjoint, S P IP ( i Ai) = i IP (Ai) countable additivity. -
The Effect of Employee Stock Options on Bank Investment Choice, Borrowing, and Capital
Federal Reserve Bank of New York Staff Reports The Effect of Employee Stock Options on Bank Investment Choice, Borrowing, and Capital Hamid Mehran Joshua Rosenberg Staff Report no. 305 October 2007 Revised June 2008 This paper presents preliminary findings and is being distributed to economists and other interested readers solely to stimulate discussion and elicit comments. The views expressed in the paper are those of the authors and are not necessarily reflective of views at the Federal Reserve Bank of New York or the Federal Reserve System. Any errors or omissions are the responsibility of the authors. The Effect of Employee Stock Options on Bank Investment Choice, Borrowing, and Capital Hamid Mehran and Joshua Rosenberg Federal Reserve Bank of New York Staff Reports, no. 305 October 2007; revised June 2008 JEL classification: G21, G28, G32, J33, M41 Abstract In this paper, we assess the effects of CEO stock options on three key corporate policies for banks: investment choice, amount of borrowing, and level of capital. Using a sample of 549 bank-years for publicly traded banks from 1992 to 2002, we find that stock option grants lead CEOs to undertake riskier investments. In particular, higher levels of option grants are associated with higher levels of equity and asset volatility. Consistent with the role of options as a nondebt tax shield, we also show that option grants reduce the banks’ incentive to borrow as evidenced by lower levels of interest expense and federal funds borrowing. Furthermore, we demonstrate that increases in CEO and employee stock option grants result in increased bank capital levels, perhaps because option grants create a contingent liability for the firm that needs to be funded in advance.