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
nding 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.
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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
| Today s stock price S0 | = | 100 |
| Strike E | = | 100 |
| Time to expiry (T t) | = | 1 year |
| volatility | = | 20% |
| constant risk-free interest rate r | = | 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 nance 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 nance 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 (writeup, code, results).
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Score key
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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