Introduction
Management is an important practice in the business environment. Different functions of management must be effectively coordinated to ensure that the respective individual or organization achieves the intended goals and objectives. Management is an important practice to individuals in the working and investment environment too. Finance is one of the essential sections or departments of an organization. Individuals must also manage their finances effectively to ensure achieving the set goals and objectives. Employees must be aware of the principles of finance to bargain on salaries and their future benefits.
Options valuation is an important element in a working environment, especially in companies where employees are offered stock options (Swanson, Marshall, Lokey, & Norley 2008). This is because inadequate information and understanding of the concept have caused several employees financial strains despite working for several years for such organizations. Stock options tie employees to a certain organization for a long time in case they are not in a position to determine the value of the respective stock option. Generally, valuation is the process that is applied to determine the actual worth of an item or property.
Although several assets can be valued, the most common are assets and liabilities. The bonds offered by a company or stock options are considered liabilities. They require valuations due to several reasons, for instance, investment analysis, financial reporting, litigation, and tax liability among others (Pratt 1999). Several valuation methods are used by financial experts and organizations; they include Monte Carlo, binomial, finite difference, Black-Scholes, and trinomial among others. This is a financial advice paper to address the valuation needs of Joseph who is an employee in an organization that offers option stock to its employees.
He needs a better understanding to enhance operation in the working environment and ensure safety and guarantee of his finances despite leaving the company prematurely. This paper presents advice to Joseph using the Monte Carlo and Black-Scholes method. It will discuss the advantages and disadvantages of using the two methods in the valuation process. Moreover, it will advise Joseph on when to leave the organization and the number of his earnings in the organization (Anderson 2005).
Valuation methods
Several methods can be used to determine the worth of an asset or liability. However, the application of the respective method depends on the nature of the asset of liability that requires a valuation. These methods are important in determining the worth of an asset or liability, which is important in investment analysis among others. Furthermore, the application of a valuation method should consider the person and capability of using and understanding the respective methods (Kroese, Taimre, & Botev 2011). This is because certain methods are complicated and require financial experts for explanations.
Moreover, most people who require valuation services are not well versed with financial management and terms, which requires financial experts and analysts to use terms that can be easily understood without further or extensive explanations. Considering the nature and procedures of the valuation methods, it is advisable to present financial advice to Joseph based on Mote Carlo and Black-Scholes (Gaugham 2004).
Monte Carlo Methods
The Monte Carlo methods are also referred to as the Monte Carlo experiments. Monte Carlo methods are computational algorithms that utilize random sampling in the valuation of assets and liabilities. It is a method used by financial experts to obtain numerical results. This is a valuation method that uses the random sampling method to determine the worth of a liability or asset. The method is suitable for solving mathematical and physical problems (Caflisch 2001).
The problem presented by Joseph is a mathematical problem; therefore, Monte Carlo is an appropriate method that can be used to determine the worth of Joseph’s liability. This method is however effective when used in solving problems with specific nature or characteristics. The problems that Monte Carlo can solve effectively are integrated, optimized, and numerical (Binder 1995).
Monte Carlo is one of the oldest valuation methods that have been used in the determination of the worth of assets and liabilities. The business environment is constantly changing. Therefore, this led to the advancement of the Monte Carlo method. Monte Carlo advanced to the modern Monte Carlo in the 1940s. The modern version was invented by Stanislaw Ulam, but named by Nicholas Metropolis after the gambling venue of Ulam’s uncle, Monte Carlo Casino (Hammersley & Handscomb 1975). Ulam developed or invented the modern version of Monte Carlo while carrying out his duties at Los Alamos National Laboratory. During this period, the Ulam was working on a nuclear weapon project. After the invention of the modern version, John Von Neumann hijacked it and developed a computer program to conduct Monte Carlo calculations. This is because Von Neumann was the first person to realize the importance of the Monte Carlo method (Hubbard 2007).
Advantages and disadvantages of Monte Carlo Methods
Monte Carlo is one of the valuation methods that are frequently used by financial experts to determine the worth of assets and liabilities. I prefer using Monte Carlo to assist Joseph to determine the worth of option stock offered by his company. There are several reasons why I chose Monte Carlo as the most appropriate method to assist Joseph understands the value of the liability being offered by his employer, for instance, graphical results. Using Monte Carlo to determine the worth of an asset or liability enables the analyzer to generate different graphs depending on the outcome of each simulation (Kloeden & Platen 1992).
Joseph expects to determine the value of his liability, which will be easily determined and explained using a graphical representation. Graphical representation is easy to understand. Moreover, this will enable representation of the offer that Joseph may accept and leave the organization, but not lose much of his earnings accrued on the stock option. Additionally, this enables a clear representation of findings to Joseph (Hall 2000).
Monte Carlo enables sensitivity analysis. It is easier to determine the inputs that had the biggest effect on bottom-line results. This will enable us to explain to Joseph the factors or inputs that affect the value of the liability offered by the company. It will be easy to make realistic recommendations and decisions based on the value determination using this method (Pachamanova & Fabozzi 2010). Furthermore, the Monte Carlo method is important in explaining scenarios. It is easier to identify the value of inputs using the Monte Carlo method. This is important because the determination of the worth of an asset or liability depends on the values of the inputs. However, this is a trait that hinders pursuing further analysis. The worth of an asset or liability may appreciate or depreciate due to several factors that affect assets and liabilities. Inability to pursue further analysis is disadvantageous because it might not allow a person or organization to address uncertainties effectively (Jaekel 2002).
Monte Carlo use to determine the worth of the liability of Joseph in the company is important because modeling the relationship between input variables is possible. Monte Carlo allows individuals to determine the effect of each input on the other, especially interdependent variables. Through Monte Carlo, it is easy to determine the results of the decrease or increase of input on the other dependent variable (Duffy & Kienitz 2009).
Therefore, this will be important in explaining and understanding the effects of factors such as leaving a job with the organization prematurely or maturely among other factors that affect the value of the stock option offered by the company. Moreover, this will enable Joseph to understand the right time to quit working with the organization or the reasons that should compel him to maintain working for the company (Brigo & Mercurio 2001).
Finally, the Monte Carlo method will be useful and important in explaining the worth of the liability to Joseph because it is easy to understand. The results presentation through Monte Carlo is easy to understand and anyone can interpret. This is because Monte Carlo leads to the presentation of results that reveals how individual outcome occurred in the process (Brigo & Mercurio, 2001). Furthermore, it also reveals what can happen in the process of determining the value of the liability. The worth of assets and liabilities can be affected. Clients interested in investment must know what could happen, and how each outcome is.
This enables investors and other interested parties to decide on the right and the most appropriate investments to engage in or establish (Glasserman 2003). Therefore, using Monte Carlo to explain to Joseph the worth of his stock option, when to leave the company in case another company offers him employment, and when not to leave the company and maintain the worth of his stock option will be easy through Monte Carlo method. Considering the nature of the stock option offered to Joseph, the value is likely to increase by around 5% annually, which is a good deal that should keep him in the company as long as there is no other company offering him more than the current stock option or salary (Brigo & Mercurio 2001).
Black-Scholes model
The Black-Scholes model is also popularly known as Black-Scholes Merton. It is one of the mathematical models used in the financial market to determine the worth of assets and liabilities. It is also one of the frequently used models by financial experts to explain and illustrate the worth or value of an asset or liability to investors to encourage them to decide on the right decisions to take while initiating an investment plan (Haug 2007).
This method enables financial experts to deduce the European-style option. This is one of the methods that have contributed greatly to the development and performance of several investments in the global market, for instance, the Chicago Board Options Exchange. This is one of the most successful ventures and investments in the globe. It was improved through the input of the Black-Scholes model (McKenzie 2006).
The black – Scholes model was articulated by Myron Scholes and Fischer Black, which led to the coining of the name, Black-Scholes. It is also one of the earliest valuation methods in the modern financial analysis arena. This model was developed and introduced in 1973 by Myron Scholes and Fischer Black (Triana 2009). The name of the model was later modified to Black-Scholes-Merton due to the contributions of Merton in the development and improvement of the model in the global financial economy. Merton was the first person to discover the importance of the Black-Scholes model and published it discussing and highlighting its use and importance in a financial journal.
This earned Merton global respect in the World of economics. The efforts of Merton and Scholes towards the development and establishment of this model were recognized in 1997 when they received the Nobel Prize in Economics (Bernstein 1992). The prize was received by the two due to the death of Black. Black died before the model was globally accepted by the financial experts as one of the most important methods that can be used to determine the value or worth of liabilities and assets. Black died in 1995, two years before the model was recognized by a group of economists in the globe (Brigo & Mercurio 2001).
Advantages and disadvantages of Black-Scholes
Although the model was initially developed by Scholes and Black, Merton later contributed to the development and establishment of the model. It is through the efforts of Merton that the model is currently widely used around the globe by financial experts to determine the worth or value of liabilities and assets. Merton contributed to the establishment of the model by providing an explanation of the mathematical concepts and publishing the model for others to view and make suggestions after testing (Swanson, Marshall, Lokey, & Norley 2008).
Considering the nature and the characteristics of the model, it is essential and appropriate in explaining to Joseph the worth and value of his liability in the organization. Several factors make this model appropriate for use to explain to individuals who do not have financial knowledge about the worth or value of assets or liabilities that they are attached to or interested in (Gaugham 2004).
The black – Scholes model is one of the simplest valuation models that can be used to determine and explain the worth or value of an asset or liability. Generally, the Back-Scholes model has a formula that is used in determining the value or worth of an asset or liability. This enables financial experts to easily determine worth and explain to clients, for example, Joseph the worth of their interest. The formula of the Black-Scholes model only requires the appropriate substitution of the inputs to determine the actual worth of a liability or asset (Brigo & Mercurio 2001).
Therefore, it is advisable to use the Black – Scholes model to explain to Joseph the worth of the stock option because it will be easy to illustrate to him how the final worth is determined because it involves substituting values with the formula provided. Secondly, the model incorporates the use of the equation, which can be used to explain to clients how the value of their liability or asset is affected by the different factors that determine its final worth. Moreover, this model enables financial experts to determine factors that may affect the worth or value of an asset or a liability (Hubbard 2007).
The model saves time. Determining the value of an asset or liability consumes a lot of time because it requires adequate research on the factors that might affect the value of the respective asset or liability in the future. However, the equation and formula provided for use in the determination of the value of an asset or liability using Black-Scholes enable experts to easily determine the factors because they are included in the equation (Brigo & Mercurio 2001).
The long process involved in the determination of the value of an asset or liability may not enable a person or organization to determine the exact value due to the external factors that may lead to the appreciation or depreciation of the value of the respective asset or liability. Therefore, since Black-Scholes uses a formula and equation to determine the value or worth of an asset or liability, it is essential and appropriate to use in determining the value of the liability offered to Joseph by the company because it may enable the determination of the exact value. This reduces or minimizes chances or wrong valuation (Swanson, Marshall, Lokey, & Norley 2008).
Conclusion
Considering Joseph’s situation, he must understand the value of the liability offered by the company. This will enable him to make the right decisions whether to leave or stay in the organization. Several methods can be used to determine the value of an asset or liability. However, the choice of the method to use depends on the knowledge of the client on financial terms and situations. However, Joseph is not well versed with financial terms, which makes the Black-Scholes model and Monte Carlo methods the most appropriate methods to use in explaining and advising him on his situation because they can be used to simplify valuation.
List of References
Anderson, P. L 2005, New Developments in Business Valuation: Developments in Litigation Economics. Elsevier, New York.
Bernstein, P 1992, Capital Ideas: The Improbable Origins of Modern Wall Street. The Free Press, New York.
Binder, K 1995, The Monte Carlo Method in condensed Matter Physics. Springer, New York.
Brigo, D., & Mercurio, F 2001, Interest Rate Models: Theory and Practice with Smile, inflation and credit. Springer, Verlag.
Caflisch, R. E 2001, Monte Carlo and Quasi-Monte Carlo Methods. Springer, New York.
Duffy, D. J., & Kienitz, J 2009, Monte Carlo Frameworks: Building Customisable High Performance Applications. John Wiley & Sons, New York.
Gaugham, P. A 2004, Measuring Business Interruption and Losses. John Wiley & Sons, Inc, London.
Glasserman, P 2003, Monte Carlo Financial Methods in Engineering. Springer, Verlag.
Hall, J. C 2000, Options, Futures and other derivatives. Prentice Hall, London.
Hammersley, J. M., & Handscomb, D. C 1975, Monte Carlo Methods. Methuen, London.
Haug, E. G 2007, Option Pricing and Hedging from Theory to practice; Derivatives: Models on models. John Wiley & sons, London.
Hubbard, D 2007, How to Measure anything: Finding the value of Intangibles in Business. John Wiley & Sons, New York.
Jaekel, P 2002, Monte Carlo Methods in Finance. John Wiley & Sons, New York.
Kloeden, P. E., & Platen, E 1992, Numerical solution of Stochastic Differential Equations. Springer, Verlag.
Kroese, D. P., Taimre, T., & Botev, Z. I 2011, Handbook of Monte Carlo Methods. John Wiley & Sons, New York.
McKenzie, D 2006, An Engine, not a camera: How Financial Models Shape Markets. MIT Press, New York.
Pachamanova, D., & Fabozzi, F. J 2010, Simulation and optimization in Finance: Modelling with MATLAB. John Wiley & Sons, London.
Pratt, S. H 1999, Valuing Small Businesses and Professional Practice. McGraw-Hill, New York.
Swanson, J., Marshall, P., Lokey, H., & Norley, L 2008, A practitioner’s guide to CorRestructuring. Cengage Learning, London.
Triana, P 2009, Lecturing Birds on Flying: Can Mathematical Theories Destroy the Financial Markets? John Wiley & Sons, New York.