Assignment for Module 3
April 2025
Instructions: This is a mini project on the use of the Monte Carlo scheme to price various call 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
● finding 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 to Riaz Ahmad at zendesk
Task
Use the expected value of the discounted payo§ under the risk-neutral density Q
V (S, t) = e-r(T-t)EQ [Payof]
for the appropriate form. of payo§, to consider European and binary options.
Use the Euler-Maruyama scheme, Milstein scheme and closed form solution for simulating the underlying stock price. As an initial example you may use the following set of sample data
Todayís stock price S0 = 100
Strike E = 100
Time to expiry (T — t) = 1 year
volatility σ = 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:
● Introduction - outline of the Önance problem and numerical procedure used. [20%]
● Results - appropriate tables, error analysis and comparisons. [40%]
● Any interesting observations and problems encountered. [15%]
● Conclusion. [20%]
● References. [5%]
For a Python Jupyter Notebook, a detailed notebook will become the complete report (write- up, code, results). No other format of Python will be accepted.
Note: There is no additional credit for calculating the greeks.
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.