Exam 2 (Module 3) January 2024
Instructions: This is a mini project on the use of the Monte Carlo scheme to price exotic options to be completed using Python. C++ is also allowed, but Excel/VBA is not permitted. As this is the half way point of the CQF, this assessment is designed for delegates to show independence and maturity in interpretation of a slightly open ended problem. It will test
Önding and understanding the relevant lectures, Python labs and tutorials in module 3; as well as the Python primer.
ability to experiment and demonstrate initiative in mathematical and numerical methods.
willingness to work outside narrow instruction that are typical of maths based tests/exams.
Queries FAO Riaz Ahmad on zendesk Task
Use the expected value of the discounted payo§ under the risk-neutral density Q V(S;t)=e r(T t)EQ[Payo (ST)]
for the appropriate form of payo§, to consider Asian and lookback options.
Use the Euler-Maruyama (only) scheme for initially simulating the underlying stock price. As an initial
example you may use the following set of sample data
Todayís stock price S0 Strike E Time to expiry (T t) volatility constant risk-free interest rate r
= 1 year = 20% = 5%
Then vary the data to see the a§ect on the option price. Your completed assignment should centre on a report to include:
Mark Scheme
Outline of the Önance problem and numerical procedure used 20% Results – appropriate tables and comparisons 35% Any interesting observations and problems encountered 25% Conclusion 15% References 5%
Outline of the Önance problem and numerical procedure used. Results – appropriate tables and comparisons.
Any interesting observations and problems encountered.
Conclusion and references
For a Python Jupyter Notebook, a detailed notebook will become the complete report (write- up, code, results).
Programming Help
60-65 Pass
66-70 Good
71-79 Very Good
80-89 Excellent
90-95 Outstanding
96+ Exceptional
Note: An assessment of this form di§ers from mathematical exercises that can attract full marks. The key above is provided for this reason.
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