# Question 1 – Simulation a Stochastic Process Using MCS,

Question 1 – Simulation a Stochastic Process Using MCS, 150 150 Affordable Capstone Projects Written from Scratch

Financial Derivatives
Coursework Assignment
Notes:
This coursework carries 100% of the overall mark for the Financial Derivatives module and should be
completed by groups of four students maximum. Students are free to choose their partners. Any attempt
of copying or replicating other peoples’ work will be considered as plagiarism and will result in the failure of
both parties.
Answers, including tables and figures, should not exceed 8 pages (please use an A4 format and a font
size of at least 12). Therefore, answer each question briefly and precisely without omitting relevant points.
You can answer all questions just using Excel; some of you may also want to use other statistical software,
such as Eviews, Matlab, @Risk, R etc., which is also acceptable. Please do not submit any Excel
Objectives:
The aim of this coursework is to familiarize the students with the different types of derivative instrument and
their pricing, covered in the Financial Derivatives module. In particular, students will learn how to: price
options using Monte Carlo simulation methods; how to calculate, interpret and apply the option Greeks for
hedging short option positions; how to evaluate total-return swaps; and, how to calculate minimum variance
hedge ratios for futures contracts.
Question 1 – Simulation a Stochastic Process Using MCS
EUR/USD FX spot is currently trading at 1.22 (expressed as number of US Dollars required for 1 Euro).
The 1Y realized volatility is 10% p.a., the 1Y US\$ and the € risk free rates are at 4.00% and 2.00% p.a.
respectively.
[a] Simulate the price paths for EUR/USD FX over a period of twelve months using Monte Carlo Simulation
(MCS). Assume that there are 252 trading days in a year and that each time step corresponds to one
trading day. Paths must be simulated 1,000 times.
[5 marks]
[b] Given the simulated paths in [a] above, construct 95% confidence intervals for the premia of a six-month
European call and put options with strike price of 1.30 (expressed as the number of US Dollars required for
1 Euro). Please also show the level of the implied forward rate used in your calculations, and comment your
results.
[5 marks]
[c] Given the simulated option prices, calculate the values of Delta, Gamma and Vega. How do these
compare with the same estimates from the Black-Scholes model? Comment and discuss on your findings.
[10 marks]
[d] Suppose now that you are using FX options to hedge the currency risk of a long US\$ denominated real
estate exposure. Which option strategy would you employ? Please select at least 2 and illustrate the
different payoff structures and associated costs. Please also show the hedge effectiveness using any one
of the simulated paths calculated in (a) and comment your results. You can calculate the value of the option
and the value of the delta using the Black-Scholes model.
[15 marks]
* * *
Question 2 – Exotic Options
Consider again EUR/USD FX spot, details of which were given in Question 1.
[a] Use MCS to price a six-month American Knock-Out call and put option on EUR/USD FX with a strike
price of 1.30 and a continuously monitored Knock-Out barrier at 1.40. As before, assume that there are 252
trading days in a year and that each time step corresponds to one trading day. Paths must be simulated
1,000 times. Compare the option premia with the corresponding premia of the European options calculated
in Question 1. Comment your results.
[5 marks]
[b] Given the simulated option prices, calculate the values of Delta, Gamma and Vega. How do these
compare with the same estimates for the equivalent European options? How would these value change
[15 marks]
* * *
Question 3 – Total Return Swaps
Consider an Egyptian T-bill with a maturity of 3 months trading in the local market at a price of 95.6. An
Investor is looking to establish a long position in the T-bill through a fully unfunded US\$ Total Return swap
(“TRS”) for an amount of \$100MM. Under the terms of the TRS, the Investor would receive the economic
performance of the T-bill and pay a rate of \$Libor + a spread of 125bps. The TRS will settle in US\$ at
maturity. The Initial Margin required on the TRS is 10% of the invested Notional.
The USD/EGP FX spot rate is 17.70 and the relevant non-deliverable forward (“NDF”) rate is 18.03. The
\$Libor is currently trading at 2.35%.
Given the information above:
[a] Please calculate: (1) the implied yield of the T-bill and (2) the total funding costs in US\$ of the facility.
[5 marks]
[b] Please provide an illustrative scenario analysis of the estimated returns (on a p.a. basis) of the fully
unfunded TRS assuming the Investor decides to leave the currency exposure of the investment un-hedged.
How would the scenario change in the situation where the Investor decides to fully hedge the currency risk
[10 marks]
* * *
Question 4 – Stock Futures
You are an Asset Manager and have invested in an equally weighted portfolio of 4 stocks of your choice.
You are now looking to establish a macro hedge to your portfolio using an appropriate Stock Index Future.
[a] Download monthly futures and spot prices for the contracts in question for the period January 2007 and
May 2016. Calculate the descriptive statistics and comment on your results. Do you observe any structural
break in the time series considered?
[5 marks]
[b] Using the historical data for the period January 2007 to December 2013, calculate the historical (expost)
minimum variance hedge ratio (MVHR). Estimate the degree of hedging effectiveness that a hedging
counterparty would have achieved if he had used the estimated MVHR. Compare this to the hedging
effectiveness that would have been achieved if the hedging counterparty had used a one-to-one hedge.
[10 marks]
[c] Use the historical (ex-post) minimum variance hedge ratio estimated above, to hedge a position
between January 2014 and May 2016. Assess the effectiveness of this strategy.
[10 marks]
[d] One criticism for the estimate of the MVHR in [c] is that it assumes a constant risk metric in the spot and
futures markets. Please comment and discuss alternative methods that could be used for the calculation of
the hedge ratio.
[5 marks]

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