Modifying the Black-Scholes-Merton model to calculate the cost of employee stock options

2014 ◽  
Vol 40 (1) ◽  
pp. 2-32 ◽  
Author(s):  
John D. Finnerty
Keyword(s):  
Utility Maximization ◽  
Design Methodology ◽  
Lattice Models ◽  
Employee Stock Options ◽  
Content Type ◽  
Early Exercise ◽  
Merton Model ◽  
Black Scholes ◽  
Computationally Intensive ◽  
The Cost

Purpose – More than 80 percent of S&P 500 firms that issue ESOs use the Black-Scholes-Merton (BSM) model and substitute the estimated average term for the contractual expiration to calculate ESO expense. This simplification systematically overprices ESOs, which worsens as the stock's volatility increases. The purpose of this paper is to present a modification of the BSM model to explicitly incorporate the rates of forfeiture pre- and post-vesting and the rate of early exercise. Design/methodology/approach – The paper demonstrates the model's usefulness by employing historical exercise and forfeiture data for 127 separate ESO grants and 1.31 billion ESOs to calculate the exercise and forfeiture parameters and value ESOs for nine firms. Findings – The modified BSM model is just as accurate but easier to use than the more computationally intensive utility maximization and trinomial lattice models, and it avoids the ASC 718 BSM model's overpricing bias. Originality/value – If firms prefer the BSM model over more mathematically elegant alternatives, they should at least use a BSM model that is free of overpricing bias.

scholarly journals VALUATION OF EMPLOYEE RELOAD OPTIONS USING UTILITY MAXIMIZATION APPROACH

2005 ◽  
Vol 08 (05) ◽  
pp. 659-674 ◽  
Author(s):  
KA WO LAU ◽  
YUE KUEN KWOK
Keyword(s):  
Risk Aversion ◽  
Stock Options ◽  
Utility Maximization ◽  
Stock Option ◽  
Employee Stock Options ◽  
Employee Stock Option ◽  
General Utility ◽  
Black Scholes ◽  
The Difference ◽  
The Cost

The reload provision in an employee stock option is an option enhancement that allows the employee to pay the strike upon exercising the stock option using his owned stocks and to receive new "reload" stock options. The usual Black–Scholes risk neutral valuation approach may not be appropriate to be adopted as the pricing vehicle for employee stock options, due to the non-transferability of the ownership of the options and the restriction on short selling of the firm's stocks as hedging strategy. In this paper, we present a general utility maximization framework to price non-tradeable employee stock options with reload provision. The risk aversion of the employee enters into the pricing model through the choice of the utility function. We examine how the value of the reload option to the employee is affected by the number of reloads outstanding, the risk aversion level and personal wealth. In particular, we explore how the reload provision may lower the difference between the cost of granting the option and the private option value and improve the compensation incentive of the option award.

Autopilot design for an aircraft by using Luenberger observer design

2018 ◽  
Vol 90 (5) ◽  
pp. 858-868 ◽  
Author(s):  
Muhammad Taimoor ◽  
Li Aijun ◽  
Rooh ul Amin ◽  
Hongshi Lu
Keyword(s):  
Design Methodology ◽  
Research Work ◽  
Linear Quadratic Regulator ◽  
Observer Design ◽  
Linear Quadratic ◽  
Content Type ◽  
Luenberger Observer ◽  
Level Flight ◽  
Aerial Vehicle ◽  
The Cost

Purpose The purpose of this paper is to design linear quadratic regulator (LQR) based Luenberger observer for the estimation of unknown states of aircraft. Design/methodology/approach In this paper, the LQR-based Luenberger observer is deliberated for autonomous level flight of unmanned aerial vehicle (UAV) which has been attained productively. Various modes like phugoid and roll modes are exploited for controlling the rates of UAV. The Luenberger observer is exploited for estimation of the mysterious states of the system. The rates of roll, yaw and pitch are used as an input to the observer, while the remaining states such as velocities and angles have been anticipated. The main advantage of using Luenberger observer was to reduce the cost of the system which has been achieved lucratively. The Luenberger observer proposes sturdiness at the rate of completion to conquest over the turmoil and insecurities to overcome the privileged recital. The FlightGear simulator is exploited for the endorsement of the recital of the Luenberger observer-based autopilot. The level flight has been subjugated lucratively and has been legitimated by exploiting the FlightGear simulator. The authenticated and the validated results are offered in this paper. Microsoft Visual Studio has been engaged as a medium between the MATLAB and FlightGear Simulator. Findings The suggested observer based on LQR ensures the lucrative approximation of the unknown states of the system as well as the successful level flight of the system. The Luenberger observer is used for approximation of states while LQR is used as controller. Originality/value In this research work, not only the estimation of unknown states of both longitudinal and lateral model is made but also the level flight is achieved by using those estimated states and the autopilot is validated by using the FlightGear, while in most of the research work only the estimation is made of only longitudinal or lateral model.

Factors explaining a cost-based pricing essence

2019 ◽  
Vol 34 (8) ◽  
pp. 1850-1865
Author(s):  
Juliana Ventura Amaral ◽  
Reinaldo Guerreiro
Keyword(s):  
Design Methodology ◽  
Empirical Studies ◽  
Pricing Strategy ◽  
Company Size ◽  
Price Setting ◽  
Marketing Theory ◽  
Content Type ◽  
Industrial Companies ◽  
Five Factors ◽  
The Cost

Purpose Empirical studies have found that cost-based pricing remains dominant in pricing practice and suggest that practice conflicts with marketing theory, which recommends value-based prices. However, empirical studies have yet to examine whether cost-plus formulas represent the pricing approach or essence. Design/methodology/approach This study aims to address the factors that explain price setting whereby the cost-plus formula is not just the pricing approach but also the pricing essence. This examination is grounded in a survey conducted on 380 Brazilian industrial companies. Findings The results show that, for price-makers, the cost-based pricing essence is positively associated with four factors (two obstacles to deploying value-based pricing, company size and differentiation), but it is negatively related to one factor (premium pricing strategy). For price-takers, the cost-based pricing essence is positively associated with four factors (two obstacles to deploying value-based pricing, coercive isomorphism and use of full costs), but it is negatively related to five factors (one obstacle to deploying value-based pricing, company size, competitors’ ability to copy, normative isomorphism and experience). Originality/value The key contribution of this paper is demonstrating that cost-plus formulas do not go against the incorporation of competitors and value information. This study reveals that it is possible to set prices based on either value or competitors’ prices while simultaneously preserving the simplicity of the cost-plus formulas. Via the margin, firms may connect costs to information about competition and value. The authors also demonstrate the drawbacks of not segregating companies into price-makers and price-takers and an excessive focus on the pricing approach at the expense of pricing essence.

The two best ways to derive the Black–Scholes PDE

2019 ◽  
Vol 10 (2) ◽  
pp. 168-174
Author(s):  
Paul Wilmott
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Design Methodology ◽  
Content Type ◽  
Technical Requirements ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Business Perspective ◽  
Big Picture ◽  
Complex Methods

Purpose The purpose of this paper is to explain the Black–Scholes model with minimal technical requirements and to illustrate its impact from a business perspective. Design/methodology/approach The paper employs simple accounting concepts and an argument part based on business need. Findings The Black–Scholes partial differential equation can be derived in many ways, some easy to understand, some hard, some useful and others not. The two methods in this paper are extremely insightful. Originality/value The paper takes a big-picture view of derivatives valuation. As such, it is a simple accompaniment to more complex methods and aims to keep modelling grounded in reality.

Stigmatized products: how conflicting laws can influence decisions to proceed

2020 ◽  
Vol 42 (1) ◽  
pp. 41-49
Author(s):  
Stephanie Geiger-Oneto ◽  
Betsy D. Gelb ◽  
Travis Simkins
Keyword(s):  
Design Methodology ◽  
State Legislatures ◽  
Strategic Decisions ◽  
Content Type ◽  
State Laws ◽  
Product Categories ◽  
Plastic Bags ◽  
Single Use ◽  
The Cost ◽  
Different Levels

Purpose The purpose of this paper is to offers the authors’ perspective on a problem rarely considered by those making strategic decisions: conflicting laws at different levels of jurisdiction, specifically those related to stigmatized products. Design/methodology/approach The authors use as examples of product categories from marijuana to single-use plastic bags, describing the conflicting laws that add to costs for marketers and consumers. Findings The authors find that conflicting laws add to the uncertainty, legal expenses, and therefore, the cost of marketing a stigmatized product, whether stigmatized because of its impact on the environment, on health or on moral grounds. Research limitations/implications The examples are not exhaustive, but their implications are significant: that as state legislatures are preempting local bans, Congress may preempt state laws. Originality/value This paper adds one more complexity to decision-making in the area of products to offer and/or merger/acquisition decisions that may bring company products that face conflicting laws.

A deterministic inventory model in reverse supply chain

2019 ◽  
Vol 15 (1) ◽  
pp. 318-338 ◽  
Author(s):  
Sasmita Mohapatra ◽  
Ajay Kumar Behera ◽  
Rabindra Mahapatra ◽  
Harish Das
Keyword(s):  
Design Methodology ◽  
Current Model ◽  
Environmental Damage ◽  
Reverse Supply Chain ◽  
Retail Outlet ◽  
Present Value ◽  
Content Type ◽  
Unique Model ◽  
The Cost ◽  
The Mathematical Model

Purpose The purpose of this paper is to present a unique model for the production–recycling–reuse of aluminium refreshment cans. It is presumed that disposed-off 250-ml aluminium cans are collected from the retail outlet. The cans are thereafter arranged into non-tainted and tainted categories. Design/methodology/approach The current model considers all the factors, i.e. producing, recycling and remanufacturing, whereas the previous models provide emphasis only one factor. Six procedures were considered in the improvement of the mathematical model. Findings In this paper, a recycling–reuse model that remanufactures non-tainted aluminium beverage cans and uses regrind from damaged non-tainted aluminium beverage cans mixed with parent aluminium material in the production of new cans was developed and analysed to reduce the amount of aluminium beverage cans that are disposed off in a scrapyard. The model is assumed to have no shortcomings, and the different percentages regarding the classes of cans are taken to be deterministic. Originality/value The model incorporates several unique aspects, including accounting for the cost of land use and associated environmental damage through the calculation of a present value that is charged to the manufacturer.

Investigating cost efficiency in the branch network of a Greek bank: an empirical study

2008 ◽  
Vol 34 (3) ◽  
pp. 160-171 ◽  
Author(s):  
Athanasios G. Noulas ◽  
Niki Glaveli ◽  
Ioannis Kiriakopoulos
Keyword(s):  
Regression Analysis ◽  
Commercial Bank ◽  
Cost Efficiency ◽  
Comparative Evaluation ◽  
Design Methodology ◽  
Future Research ◽  
Data Envelopment ◽  
Content Type ◽  
Dea Method ◽  
The Cost

PurposeThe purpose of this study is to examine the cost efficiency of 58 branches of a major Greek commercial bank, in six major Greek cities, for the years 2000 and 2001.Design/methodology/approachThe efficiency is measured through the data envelopment analysis (DEA) method. Using regression analysis, the effect of size on cost efficiency is also examined.FindingsThe results indicate that there is a room for substantial efficiency improvements. The average inefficiency is about 30 per cent. It has also been observed that rural branches tend, on average, to be more efficient than urban branches.Research limitations/implicationsA direction of future research would be to extend the analysis of determinants of bank branch efficiency in order to investigate the role that the region and the characteristics of the branch play in relation to efficiency.Originality/valueThe paper provides a comparative evaluation of the efficiency of 58 branches of a major Greek commercial bank using the DEA method.

An efficient reformulation of a multiscale method for the eddy current problem

2017 ◽  
Vol 36 (5) ◽  
pp. 1421-1429
Author(s):  
Markus Schöbinger ◽  
Karl Hollaus ◽  
Joachim Schöberl
Keyword(s):  
Eddy Current ◽  
Design Methodology ◽  
Degrees Of Freedom ◽  
Current Problem ◽  
Multiscale Method ◽  
Content Type ◽  
Eddy Current Problem ◽  
Laminate Thickness ◽  
The Cost ◽  
Laminated Material

Purpose This paper aims to improve the efficiency of a numerical method to treat the eddy current problem on a laminated material, where using a mesh that resolves each individual laminate would be too computationally expensive. Design/methodology/approach The domain is modeled using a coarse mesh that treats the laminated material as a bulk with averaged properties. The fine-structured behavior is recovered by introducing micro-shape functions in the ansatz space. One such method is analyzed to find further model restrictions. Findings By using a special reformulation, it is possible to eliminate the additional degrees of freedom introduced by the multiscale ansatz at the cost of an additional modeling error that decreases with the laminate thickness. Originality/value The paper gives a computationally more efficient approximate variant to a known multiscale method.

A costing study of the document supply service at a Chinese research library: the case of Wuhan University Library

2008 ◽  
Vol 36 (2) ◽  
pp. 86-90 ◽  
Author(s):  
Xia Liu ◽  
Ting Lei
Keyword(s):  
Design Methodology ◽  
Unit Cost ◽  
Research Library ◽  
Cost Study ◽  
Content Type ◽  
University Library ◽  
Costing Study ◽  
The Difference ◽  
The Cost ◽  
The University

PurposeThis paper aims to report on a cost study of document supply at Wuhan University Library, and to investigate the difference in costs over time and the cost‐effectiveness for the university.Design/methodology/approachA quantitative approach is employed.FindingsThe borrowing unit cost and lending unit cost decreased by 27 percent and 60 percent, respectively, between 2002 and 2004, but showed a small increase in 2006.Originality/valueThe paper reveals the cost of document supply in a Chinese research library and proves that the cost could be lowered rapidly by taking effective measures. The paper also demonstrates that document supply is an effective way to resolve the library budgetary crisis as well as satisfying end‐users' needs.

Corporate investment in social responsibility versus dividends?

2012 ◽  
Vol 8 (2) ◽  
pp. 199-207 ◽  
Author(s):  
Michel T.J. Rakotomavo
Keyword(s):  
Corporate Social Responsibility ◽  
Social Responsibility ◽  
Design Methodology ◽  
Corporate Investment ◽  
Cash Flows ◽  
Cost Of Equity ◽  
Content Type ◽  
Corporate Social ◽  
The Cost ◽  
Practical Implications

PurposeThe paper aims to examine whether corporate investment in social responsibility takes away from expected dividends.Design/methodology/approachThe article builds two hypotheses that are tested empirically through the analysis of 17,670 US firm‐year observations covering the period 1991‐2007. The tests are conducted in both univariate and multivariate settings.FindingsThe evidence supports the hypothesis that mature firms tend to invest more in corporate social responsibility (CSR). Specifically, firms investing highly in CSR tend to be larger, more profitable, and with greater earned (rather than contributed) equity. The evidence also supports the hypothesis that CSR investment does not subtract from dividends. Instead, CSR effort and dividend tend to increase together. Thus, CSR investment tends to be effected by companies who can afford it, and it does not lower value by lowering investors' expected payout.Practical implicationsThese results imply that spending resources on CSR does not lower the cash flows paid out to investors. When combined with the finding that CSR lowers the cost of equity, they also mean that CSR increases the value of a company's stock.Originality/valueThis is the first study that explicitly links CSR to the dividend flow.

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