THE VALUE OF BEING LUCKY: OPTION BACKDATING AND NONDIVERSIFIABLE RISK

2021 ◽  
pp. 2150023
Author(s):  
VICKY HENDERSON ◽  
JIA SUN ◽  
A. ELIZABETH WHALLEY
Keyword(s):  
Risk Aversion ◽  
Stock Prices ◽  
Stock Price ◽  
Stock Option ◽  
Risk Averse ◽  
Executive Stock Option ◽  
Early Exercise ◽  
Lookback Option ◽  
Utility Indifference ◽  
Option Compensation

The practice of executives influencing their option compensation by setting a grant date retrospectively is known as backdating. Since executive stock options are usually granted at-the-money, selecting an advantageous grant date to coincide with a low stock price will be valuable to an executive. Empirical evidence shows that backdating of executive stock option grants was prevalent, particularly at firms with highly volatile stock prices. Executives who have the opportunity to backdate should take this into account in their valuation. We quantify the value to a risk averse executive of a lucky option grant with strike chosen to coincide with the lowest stock price of the month. We show the ex ante gain to risk averse executives from the ability to backdate increases with both risk aversion and with volatility, and is significant in magnitude. Our model involves valuing the embedded partial American lookback option in a utility indifference setting with key features of risk aversion, inability to diversify and early exercise.

scholarly journals The Original Management Incentive Schemes

2005 ◽  
Vol 19 (4) ◽  
pp. 135-144 ◽  
Author(s):  
Richard T Holden
Keyword(s):  
Stock Prices ◽  
Stock Price ◽  
Stock Option ◽  
Stock Index ◽  
General Motors ◽  
Executive Stock Option ◽  
Incentive Schemes ◽  
Corporate Executives ◽  
Short Run ◽  
Excessive Risk Taking

During the 1990s, the structure of pay for top corporate executives shifted markedly as the use of stock options greatly expanded. By the early 2000s, as the dot-com boom ended and the Nasdaq stock index melted down, these modern executive incentive schemes were being sharply questioned on many grounds—for encouraging excessive risk-taking and a short-run orientation, for being an overly costly and inefficient method of providing incentives, and even for tempting managers of firms like Enron, WorldCom and Tyco to commit fraud in order to ensure a high stock price at the time of exercise. This article examines executive incentive schemes developed by Du Pont and General Motors in the 1920s —the original incentive schemes linking executive compensation to stock prices. The author argues that these plans were well-designed to pre-empt and address many of the criticisms of modern-day executive stock option plans.

scholarly journals OPTIMAL EXERCISE OF AN EXECUTIVE STOCK OPTION BY AN INSIDER

2011 ◽  
Vol 14 (01) ◽  
pp. 83-106 ◽  
Author(s):  
MICHAEL MONOYIOS ◽  
ANDREW NG
Keyword(s):  
Stock Price ◽  
Stock Option ◽  
Stopping Times ◽  
Inside Information ◽  
Executive Stock Option ◽  
Early Exercise ◽  
Noisy Information ◽  
Exercise Boundary ◽  
Inhomogeneous Diffusion ◽  
The Value Function

We consider an optimal stopping problem arising in connection with the exercise of an executive stock option by an agent with inside information. The agent is assumed to have noisy information on the terminal value of the stock, does not trade the stock or outside securities, and maximises the expected discounted payoff over all stopping times with regard to an enlarged filtration which includes the inside information. This leads to a stopping problem governed by a time-inhomogeneous diffusion and a call-type reward. We establish conditions under which the option value exhibits time decay, and derive the smooth fit condition for the solution to the free boundary problem governing the maximum expected reward, and derive the early exercise decomposition of the value function. The resulting integral equation for the unknown exercise boundary is solved numerically and this shows that the insider may exercise the option before maturity, in situations when an agent without the privileged information may not. Hence we show that early exercise may arise due to the agent having inside information on the future stock price.

Stock option modification under SFAS 123(R)

2014 ◽  
Vol 12 (2) ◽  
pp. 177-195
Author(s):  
Steven Balsam ◽  
Il-woon Kim ◽  
David Ryan ◽  
Hakjoon Song
Keyword(s):  
Financial Reporting ◽  
Stock Prices ◽  
Stock Price ◽  
Stock Option ◽  
Policy Makers ◽  
Content Type ◽  
Economic Determinants ◽  
Political Costs ◽  
Price Performance ◽  
Political Cost

Purpose – The purpose of this paper is to examine the motivations for and variations in terms of stock option modifications under Statement of Financial Accounting Standards (SFAS) 123(R). Stock options are used to motivate and retain employees. Unfortunately, when stock prices decline, existing options lose their incentive value. In response, firms look for ways to re-incentivize their employees. Their choices include issuing additional options and/or modifying existing grants. Design/methodology/approach – We investigate the economic determinants of stock option modification post SFAS 123(R), such as financial reporting cost, shareholder/political cost and employee incentive and retention. Our analysis is based on 67 sample firms that modify their stock option plans from 2005 to 2008 and 67 control firms constructed based on size, industry, year and stock price performance for the prior five years. Findings – The results show that loss firms are more likely to modify their options, which supports the argument that financial reporting costs influence the decision to modify. We find support for the shareholder/political costs hypothesis, as the overhang ratio is positively associated with the decision to modify. However, we find no evidence that modifications substitute for additional option grants. We find that politically sensitive larger firms are more likely to incorporate more shareholder friendly measures such as excluding executives from modification or providing shareholders the opportunity to vote on modification. Originality/value – This is the first paper examining the economic determinants of stock option modification under SFAS 123(R). Our findings provide some insights regarding economic determinants of SFAS 123(R) for accounting policy-makers and investors.

scholarly journals Optimal Exercise Boundary of American Fractional Lookback Option in a Mixed Jump-Diffusion Fractional Brownian Motion Environment

2017 ◽  
Vol 2017 ◽  
pp. 1-17 ◽  
Author(s):  
Zhaoqiang Yang
Keyword(s):  
Brownian Motion ◽  
Stock Price ◽  
Jump Diffusion ◽  
Fundamental Solutions ◽  
Early Exercise ◽  
Optimal Exercise Boundary ◽  
Lookback Options ◽  
Exercise Price ◽  
Lookback Option ◽  
Exercise Boundary

A new framework for pricing the American fractional lookback option is developed in the case where the stock price follows a mixed jump-diffusion fraction Brownian motion. By using Itô formula and Wick-Itô-Skorohod integral a new market pricing model is built. The fundamental solutions of stochastic parabolic partial differential equations are estimated under the condition of Merton assumptions. The explicit integral representation of early exercise premium and the critical exercise price are also given. Numerical simulation illustrates some notable features of American fractional lookback options.

scholarly journals Executive stock options with a rebate: Valuation formula

2006 ◽  
Vol 3 (4) ◽  
pp. 76-79
Author(s):  
P.W.A. Dayananda
Keyword(s):  
Discrete Time ◽  
Continuous Time ◽  
Stock Price ◽  
Stock Options ◽  
Stock Option ◽  
Executive Stock Options ◽  
Exercise Time ◽  
Executive Stock Option ◽  
Exercise Period ◽  
Over Time

We examine the valuation of executive stock option award where there is a rebate at exercise. The rebate depends on the performance of the stock of the corporation over time the period concerned; in particular we consider the situation where the executive can purchase the stock at exercise time at discount proportional to the minimum value of the stock price over the exercise period. Valuation formulae are provided both when assessment is done in discrete time as well as in continuous time. Some numerical illustrations are also presented

scholarly journals OPSI SAHAM PADA PASAR MODAL DI INDONESIA (STUDI PASAR OPSI SAAT PASAR OPSI MASIH BERLANGSUNG DI BURSA EFEK INDONESIA)

2019 ◽  
Vol 2 (2) ◽  
pp. 300
Author(s):  
Syanti Dewi ◽  
Ishak Ramli
Keyword(s):  
Interest Rate ◽  
Stock Prices ◽  
Stock Price ◽  
Stock Exchange ◽  
Option Price ◽  
Stock Option ◽  
Exchange Market ◽  
Strike Price ◽  
Option Trading ◽  
Put Option

Stock option exchange market is not working anymore in the Indonesian Stock Exchange, using the data option exchange market for the running period 2007-2008, we analyzed the effect of stock price, strike price, time to maturity, volatility and risk- free interest rate on the stock option’s price of listed stock call or put option trading at the Indonesian Stock Exchange during 2007-2008. The results found that the stock price, strike price, time to maturity, volatility and risk-free interest rate are positive significantly affecting the stock option price either the buying option price or the selling option price in Indonesia Stock Exchange 2007-2008 period. While there were no variables that significantly affected the call option during the periode 2007-2008, furthermore stock prices and strike prices significantly affected the put option prices. Time to maturity, Volatility, and risk free interest rate did not significantly affect the put option prices.That is why the stock option exchange market stop since the investor were not sure to the stock option price versus the risk of the volatility, time to maturity, and riskfree rate.

scholarly journals Efficient valuation and exercise boundary of American fractional lookback option in a mixed jump-diffusion model

2017 ◽  
Vol 04 (02n03) ◽  
pp. 1750033
Author(s):  
Zhaoqiang Yang
Keyword(s):  
Stock Price ◽  
Jump Diffusion ◽  
Fundamental Solutions ◽  
Market Pricing ◽  
Early Exercise ◽  
Lookback Options ◽  
Exercise Price ◽  
Lookback Option ◽  
Exercise Boundary ◽  
Jump Diffusion Model

This study presents an efficient method for pricing the American fractional lookback option in the case where the stock price follows a mixed jump diffusion fraction Brownian motion. By using It ô formula and Wick–It ô–Skorohod integral, a new market pricing model is built. The fundamental solutions of stochastic parabolic partial differential equations are estimated under the condition of Merton assumptions. The explicit integral representation of early exercise premium and the critical exercise price are also given. Numerical simulation illustrates some notable features of American fractional lookback options.

ENDOGENOUS SHORT-SALE CONSTRAINT, STOCK PRICES AND OUTPUT CYCLES

1997 ◽  
Vol 1 (1) ◽  
pp. 228-254 ◽  
Author(s):  
HAROLD H. ZHANG
Keyword(s):  
Risk Aversion ◽  
Stock Prices ◽  
Stock Price ◽  
Trading Volume ◽  
Time Preference ◽  
Short Sale Constraints ◽  
Short Sale ◽  
Price Movements ◽  
Negative Shock ◽  
Stock Price Movements

This study examines the effect of short-sale constraints on a stock market, in particular, on stock prices, trading volume, and the relationship between stock price movements and output cycles. The economic model features incomplete markets and heterogeneous agents. The short-sale constraint is endogenously determined in the economy and is a function of agents' risk aversion, time preference, and exogenous driving forces. The dynamic model is solved using a policy function iteration algorithm. We find that, for an array of reasonable time-preference parameters and risk-aversion coefficients, the short sale limits range from 27 to 45% of total outstanding shares. Imposing short-sale constraints causes stock prices to move upward. Trading volume is high when some agents have a large amount of stock holdings but incur a negative shock on their nonfinancial income and is low when some agents have few stock holdings and also incur a negative shock to their nonfinancial income. Stock prices are found to be countercyclical and the expected stock returns are procyclical. These countercyclical stock-price movements are shown to be related to the imposition of a short-sale constraint.

A NEW STOPPING PROBLEM AND THE CRITICAL EXERCISE PRICE FOR AMERICAN FRACTIONAL LOOKBACK OPTION IN A SPECIAL MIXED JUMP-DIFFUSION MODEL

2018 ◽  
Vol 34 (1) ◽  
pp. 27-52
Author(s):  
Zhaoqiang Yang
Keyword(s):  
Stock Price ◽  
Jump Diffusion ◽  
Fundamental Solutions ◽  
Market Pricing ◽  
Early Exercise ◽  
Exercise Price ◽  
Lookback Option ◽  
Exercise Boundary ◽  
Critical Boundary ◽  
Jump Diffusion Model

A new stopping problem and the critical exercise price of American fractional lookback option are developed in the case where the stock price follows a special mixed jump diffusion fractional Brownian motion. By using Itô formula and Wick-Itô-Skorohod integral a new market pricing model is built, and the fundamental solutions of stochastic parabolic partial differential equations are deduced under the condition of Merton assumptions. With an optimal stopping problem and the exercise boundary, the explicit integral representation of early exercise premium and the critical exercise price are also derived. Numerical simulation illustrates the asymptotic behavior of this critical boundary.

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