Page 1 of 6

Derivative Pricing and Valuation AFE7507 Coursework 2021-22

The assessment for this module is wholly based on an individually prepared coursework submission. The coursework assignment is composed of TWO questions: Question 1: Application of derivative contracts for hedging an exposure. Maximum possible mark is 50%. Question 2: Binomial lattice pricing of option contracts. Maximum possible mark is 50%.

All EXCEL sheets, and any programming code, used in your analysis must be submitted.

Plagiarism is unacceptable. The University will deal severely with any proven Incidences of plagiarism. The guide on plagiarism is available here: https://unibradfordac.sharepoint.com/sites/academic-skills-advice- intranet/Writing%20%20Study%20Resources/Short%20Guides/Cite%20Ref%20%26%2 0avoid%20Plagiarism%20-%20accompanying%20guide.pdf Submissions with a significantly high “TURNITIN” plagiarism score will be graded with a zero score.

The submitted assignment must comply with the following formatting conventions:

• Maximum word count of the work should be no more than 2500 words, excluding title page, contents page, tables, figure and appendices. • The work should be written in easy-to-read English using an academic style, and without journalistic hyperbole. • Pagination: each page is to be numbered consecutively from 1, except the first. • The first page is the title page including the module title, year of study and student details. • The body of contents is to be sectionalized and numerically ordered. • Minimum font size is Times Roman 12 pt or equivalent, with double or 1.5 line spacing. • Text is to be justified both left and right.

Page 2 of 6

• Tables and figures must have a title and be numerically labeled. If convenient, they should be placed near the relevant text, or if large, exhibited in an appendix at the end. • All external sources of information are to be cited using the normal citation style. Complete details of all citations are to be collected under the “List of References”. • Equations such as formulas should be entered using an equation editor, and numbered. Complex derivations should be assigned to an appendix.

Marks across the 2 questions are awarded according to the following scheme:

20% Formulation and understanding of the financial problem, stating any assumptions clearly as well as reviewing any relevant literature.

40% Computational analysis. Question 1: Deriving the impact of an unhedged and hedged strategy on firm performance. Question 2: Volatility estimation based on historic data and implicit Black-Scholes model; binomial lattice evaluation; examination of non-vanilla options.

40% Justification of your analysis and interpretation of your results; any reservations; improvements for future research; conclusion.

You are always welcome to contact me for advice and guidance. The most effective way of contacting me is through email: r.adkins@bradford.ac.uk

If you are experiencing any irresolvable issues, then you should contact me for advice. All advice given will be made public by posting it on the CANVAS discussion page. If you wish to submit an almost finished draft before submission for comment, then this must be sent to me through email at least 2 weeks before submission date.

Page 3 of 6

Derivative Pricing and Valuation AFE7507 Coursework Assignment 2021-22

QUESTION ONE

Swordfish Energy is a regional energy supplier, which purchases energy at spot market prices to resell to household customers, at a price determined by a 25% mark- up to yield a net profit sales ratio of 5%. Currently, the spot price for energy is £32.00 per unit. Swordfish Energy has 100 thousand household customers on its books.

Annually, each household customer consumes on average 30 energy units, a total of 3 million energy units per year. At a mark-up of 25%, the per unit energy cost for household consumers is £40.00. Its current annual sales revenue is £120 million. Swordfish Energy has negotiated a distribution contract with the network companies to service its household customers. The network companies demand a distribution charge levied at 12% of the annual sales revenue made by Swordfish Energy. The fixed cost of £3.6 million incurred by Swordfish Energy is currently 3% of annual sales revenue and this cost is not expected to change due to any future spot price movements. The annual income statement for Swordfish Energy is presented below:

£ million Sales of energy 120.0 Cost of energy 96.0 Distribution cost 14.4 Fixed cost 3.6 Net profit 6.0 Net Profit/Sales 5.0%

The government energy regulator observes that the profit rate of energy distribution companies increases significantly for increases in per unit energy spot price. The regulator wishes to control this profit rate and stipulates that the per unit energy cost for household consumers is capped at the level of £40.00. This entails that Swordfish Energy and other energy suppliers cannot charge household customers a price higher than £40.00 per unit.

Swordfish Energy management team believe that the energy spot price per unit will rise next year but they are unsure by how much. The management team intend to make a positive net profit and are aware that in the event of a spot price increase, their net profit sales revenue ratio may fall below the current level. An adverse increase in the energy spot price per unit may trigger bankruptcy if Swordfish Energy makes a loss. Further, there is uncertainty regarding next year’s household customer numbers and the annual energy usage per household. Next year, the number of customers is expected to lie between 90 and 110 thousand with equal probability,

Page 4 of 6

and the average usage per household to lie between 29 and 31 units per year, also with equal probability.

Swordfish Energy is considering the use of derivatives to manage its risk exposure. The current energy spot rate per unit is £32.00, the pre-paid one-year forward price is £30.8994, and the one-year forward price is £32.3216. The current premiums for one-year call and put options on 1 unit of energy are reported in the following table:

Exercise Price

Call Premium

Put Premium 22 9.8893 0.0218 23 8.9562 0.0448 24 8.0402 0.0848 25 7.1490 0.1495 26 6.2914 0.2480 27 5.4768 0.3893 28 4.7139 0.5824 29 4.0104 0.8349 30 3.3719 1.1524 31 2.8018 1.5383 32 2.3010 1.9935 33 1.8681 2.5166 34 1.4997 3.1043 35 1.1910 3.7516 36 0.9360 4.4525 37 0.7282 5.2008 38 0.5612 5.9897 39 0.4285 6.8130 40 0.3244 7.6649 41 0.2436 8.5401 42 0.1815 9.4340

The one-year continuous interest rate is 4.5%. Assume all next year’s cash flows occur at the end of the year.

Make recommendations to the management team of Swordfish Energy on how next year’s exposure should be managed. All recommendations must be justified by presenting your accompanying analysis and evaluations.

Page 5 of 6

Derivative Pricing and Valuation AFE7507 Coursework Assignment 2021-22

QUESTION TWO

The assignment task is to numerically evaluate the call and put option prices, both European and American, on an underlying stock index asset by using the lattice framework. Each student is required to select a company listed on a global exchange, which has a five-year history of daily market share price data and at least since January 1st 2022 market data on call and put options. Information on share and option data is accessible through Bloomberg. The selected company and the origination date for evaluating the option value must be registered1. Although it is acceptable that more than one student may select the same company, the origination dates must be different.

You are required to complete the following:

1. Use the daily market data to statistically evaluate the historical volatility for the share price. Collect information on the company’s annual dividend paid and assess its dividend yield. For your chosen origination date, collect data on the annual interest rate for various expiration dates.

2. **Evaluate the option premiums, call and put, European and American, based on a binomial lattice framework.**

Compare your results with the given European option price, examine the effectiveness of your selected method, and make improvements where necessary.

3. Report the Greeks and perform any sensitivity analysis.

4. Derive the American put exercise boundary.

5. Extend your analysis to more complex exotic options.

Calculating the option value requires knowledge of the volatility of the underlying asset. This can be estimated from both the daily (weekly) price data over the past 5 years (or an appropriate period) and the Black-Scholes implied volatility solution. Any material differences between the two methods needs to be explained. Lattice calculated European option values should always be compared with their theoretical equivalent for testing the effectiveness of your adopted framework parameter values. Besides the plain vanilla option, a complex option, such as a barrier, chooser, compound, Asian or other exotic option, should also be analyzed, and the results compared with any analytical solution and the plain vanilla variant. The use of Monte Carlo simulation where relevant may also be applied. Sensitivity analysis on their result by considering pertinent variations in the key parameters of their pricing model

1 Method of registration will be announced subsequently.

Page 6 of 6

should be performed as well as considering alternative ways for determining the periodic up- and down-movements and risk-neutral probabilities. It is important to recognize that this is an academic piece of work, so full and complete referencing of the original articles, rather than citing textbooks, is demanded. Large tables of figures should be confined to the Excel file, and not reported in the text; where there is a need for their inclusion, they should be inserted in an appendix. You need to submit the Excel file of calculations (or other) used in your evaluations, which must be fully documented so the reader can readily understand the structure of calculations.

You may find the following references useful in your binomial lattice evaluations: Black, F. and M. Scholes (1973). “The pricing of options and corporate liabilities.” The Journal of Political Economy 81(3): 637-654. Cox, J. C. and S. A. Ross (1976). “The valuation of options for alternative stochastic processes.” Journal of Financial Economics 3(1-2): 145-166. Cox, J. C., S. A. Ross and M. Rubinstein (1979). “Option pricing: A simplified approach.” Journal of Financial Economics 7(3): 229-263. Rendleman, R. J., Jr. and B. J. Bartter (1979). “Two-state option pricing.” Journal of Finance 34(5): 1093-1110. Smith, C. W. (1976). “Option pricing : A review.” Journal of Financial Economics 3(1- 2): 3-51.