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,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.
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.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
