Financial Engineering “Option Valuation Report”

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Employee stock options (ESO) are call options on a company’s stock granted by the company to its employees. ESO have become very popular in the last 20 years. Many companies feel that the only way to attract and keep the best employee is to offer them very attractive stock option packages.” Following this market trend, GlobeTech plc decides to reform its compensation practice and starts to reward its employees with stock options. The company’s stock is listed on a local exchange and trading at £5 per share. Currently at the exchange, no derivatives (futures, options, etc) are traded underlying the company stock. In the past 10 years, the company’s stock has an average annualized volatility of 25%. However, last year the stock has an annualized volatility of 36% due to market uncertainty. WorldTech plc, the major competitor of GlobeTech, has a 10-year average annualized stock volatility of 30%. It is also known that 3-month Government bond currently has a yield of 2%. Additionally, GlobeTech’s stock has a dividend yield of 2% over the past 10 years. It is unlikely that they would change their dividend payout policy in the near future.
Joseph, who started working for GlobeTech 2 years ago, is one of employees that were entitled to receive 10,000 stock options. His options are granted with exercise price of £5. However, he is troubled by the obscurity of options. He does not know how much 10,000 stock options worth in the market. He has no prior knowledge of any financial product. He approached you, advisors at FinancialEngineer Partners, for financial advice.
After a brief discussion with Joseph, you know that his option grants will vest in 5 years. Once options are vested, Joseph can exercise them at any time before maturity, which is 10 years from now. Joseph knows options will be forfeited, if he leaves the firm before options become vested. But he does not want to lose any good opportunities in the job market. Joseph tells you that 2 of his colleagues left GlobeTech after working there for 3 years. However, he also mentions that many employees have worked there for over 10 years. You are also aware that Joseph’s current base salary is £25,000 per annum.
Joseph contracts you for an option valuation report. He wants to know value of his option positions. He also wants to know details of different option valuation methods. Furthermore, Joseph wants to know the competitive salary to leave his current job before options become vested.
1. Value Joseph’s option position based on Black-Scholes (BS) method. You analysis needs cover details behind the standard Black-Scholes method. You are also required to explain detailed adjustment made to the standard BS method, so that the method is ready to value ESO.
2. Value Joseph’s option position based on binomial tree method with a minimum of 50 time steps. Your report needs to cover detailed mechanics underlying the method, and show step-by-step examples and their mathematical rationale. The report should also comment on the advantage and disadvantage of binomial tree method over the BS method.
3. Value Joseph’s option position based on a third method. It can be trinomial tree, finite difference or Monte Carlo. The report needs to show detailed working of the chosen method, and demonstrate its advantage (or disadvantage) over the other 2 methods implemented above.
4. Compare option values obtained from part 1, 2 and 3. The report needs address why option values differ across methods, which option value is the most accurate based on Joseph’s circumstance, and how parameter input affect option values across methods. You need demonstrate understanding of each implemented method.
5. The report needs to advise Joseph the (amount of) competitive salary so that he can quit his current job and forfeit the option position. Your advice should be based on calculations from the first 4 parts.
6. While reading Joseph’s option contract, you discover that his option has a performance condition. The option position will not vest until the company’s stock price is above £7.5, and this condition is in addition to the 5 year vesting period. You realise that this condition is equivalent to a knock-in barrier on Joseph’s option position. Explain how this newly discovered condition impacts value of his options. You may implement this condition in one of your valuation method to support your argument.
When implementing your valuation model, all parameter assumptions should be explicit and reasonably justified. Make sure to use simple language; remember, Joseph does not know anything about financial engineering. You may demonstrate your points using equation, numerical examples, graphs and figures. For non-standard method, e.g. Monte Carle, finite difference with special boundary condition, you need to show workings in detail to demonstrate correctness of your model. The final results may contain a range of possible prices based on different methods and parameters.

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