Derivatives Pricing and Valuation

Derivative Pricing and Valuation AFE7507 Coursework 2020-21

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 used in your analysis must be submitted.

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.

· 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”.

( Page 1 of 8 )

· 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.

Derivative Pricing and Valuation AFE7507 Coursework 2020-21

QUESTION ONE

REM (UK) is a robotic engineering and manufacturing UK based company with annual sales of £20 million that makes customized high-specification medical equipment. It is about to submit a bid for 4 biomedical machines for Kingston State Hospital Network (KSAN), USA. KSAN stipulate a non-negotiable bid price of $0.25 million for each of the 4 machines. Although REM has submitted a bid for 4 machines, the company recognizes that it may not be awarded a contract to supply all 4 machines, it may be required to supply less than 4 machines, even none. The results of the bidding process are due to be announced after 6 months. Successful bidders are obliged and contracted to deliver 1, 2, 3, or 4 machines in line with the bid announcement. Delivery is expected to be 12 months after the date of announcement. Full payment for the machines is to be made on the delivery date.

The software design and manufacturing operations undertaken by REM in fulfilling the contract will be performed entirely in the UK without the need for any imported products or services. The company is expecting a profit rate of 12.5% on the possible sale to KSAN, the same rate as for sales to other similar buyers.

As a UK firm, REM will be facing foreign exchange risk if they are awarded any of the 4 individual contracts. If REM is contracted to supply one or more machines, then the payment date is known but the spot exchange rate on that date is unknown. REM is intending to manage any foreign exchange risk exposure through using currency derivative contracts. However, REM is unclear whether the derivative contracts should be arranged immediately or whether the decision should be deferred until the bid announcement date. By adopting the former policy, the company runs the potential risk of selecting the wrong $ amount to exchange, but by adopting the latter policy, the company suffers possible currency risk between now and the announcement date.

For your calculations, assume that the $ annual continuously compounded interest rate at all dates and for all maturities is 4.5%, and the corresponding

£ interest rate is 3.5%. Information on derivative prices to be used in your analysis is exhibited in the Appendix. Ignore any cost inflationary price rises.

a) REM decides to arrange the derivative contracts immediately at the time of making the bid submission. Based on its previous bidding history, the company expects to be awarded a contract to supply 2 machines to KSAN. Make a recommendation on the most effective arrangement of derivative contracts for managing the currency exposure. Test your recommendation against the possible bid outcomes of being awarded 0, 2 or 4 machines.

b) REM decides to wait until the time of the bid announcement for arranging the derivative contracts. The company is awarded a contract to supply 2 machines. Make a recommendation on the most effective arrangement of derivative contracts for managing the currency exposure. Show whether your recommendation is indeed effective.

c) Discuss your results obtained from parts (a) and (b) above.

QUESTION ONE: APPENDIX

Bid Submission Date

Spot exchange rate is £0.800/$.

18-month forward exchange rate is £0.8121/$.

Premiums for the 18-month call and put £/$ currency options for various exercise prices:

Exercise Price	Call Premium	Put Premium
0.74	0.07870	0.01131
0.75	0.07392	0.01588
0.76	0.06914	0.02045
0.77	0.06436	0.02501
0.78	0.05958	0.02958
0.79	0.05480	0.03415
0.80	0.05002	0.03871
0.81	0.04524	0.04328
0.82	0.04046	0.04785
0.83	0.03568	0.05242
0.84	0.03089	0.05698
0.85	0.02611	0.06155
0.86	0.02133	0.06612

Bid Announcement Date

Spot exchange rate is £0.760/$.

12- month forward exchange rate is £0.7676/$.

Premiums for the 12-month call and put £/$ currency options for various exercise prices:

Exercise Price	Call Premium	Put Premium
0.70	0.07858	0.01392
0.71	0.07387	0.01877
0.72	0.06915	0.02361
0.73	0.06444	0.02846
0.74	0.05973	0.03331
0.75	0.05502	0.03815
0.76	0.05030	0.04300
0.77	0.04559	0.04785
0.78	0.04088	0.05269
0.79	0.03616	0.05754
0.80	0.03145	0.06239
0.81	0.02674	0.06723
0.82	0.02202	0.07208

Derivative Pricing and Valuation AFE7507 Coursework 2020-21

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 assigned a single dedicated asset identifying number. Historical daily asset prices over a 5-year period, estimated annual continuous dividend yield and the European option price for each of these assets are available in an EXCEL sheet posted on CANVAS.

You are required to complete the following:

1. 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.

2. Report the Greeks and perform any sensitivity analysis.

3. Derive the American put exercise boundary.

4. 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 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 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.