Simulation, Monte Carlo Modeling, and Scenario Analysis

Teaching Problem

Finance is fundamentally about decision-making under uncertainty, but building realistic simulations—Monte Carlo portfolio projections, multi-scenario DCF models, option pricing with stochastic volatility, stress tests—traditionally requires significant programming expertise that most finance faculty and students lack.

How AI Addresses the Problem

AI dramatically lowers the barrier to creating sophisticated financial simulations. Faculty or students describe a scenario in natural language—specifying assumptions, distributions, correlations, and output metrics—and AI generates complete, executable simulation code. The pedagogical value is not in the code generation but in what follows: students must set and defend assumptions, modify parameters, interpret distributional outputs, and make recommendations under genuine uncertainty.

Deployment Details

Courses

Investments/Portfolio Management (UG/MBA), Derivatives (UG/MBA), Risk Management (MBA), Financial Modeling (UG/MBA), Capstone courses

Tools

ChatGPT Code Interpreter/Advanced Data Analysis, Claude with code execution, GitHub Copilot, Python (numpy, scipy, pandas, matplotlib), Google Colab

Student Workflow

1. Receive a modeling scenario with specified requirements.
2. Before using AI, write a 1-page specification document: what assumptions about return distributions, correlations, rebalancing frequency, withdrawal rates, and inflation? Justify each choice.
3. Use AI to generate simulation code based on your specification.
4. Run the simulation and produce required visualizations (terminal wealth distributions, probability of ruin, efficient frontier, convergence plots).
5. Modify at least 2 assumptions and re-run: What happens with fat-tailed return distributions? With regime switching? With higher withdrawal rates?
6. Write a 2-page investment recommendation memo supported by simulation evidence.
7. Present findings to the class (5–7 minutes), defending assumptions under Q&A.

Sample Prompts

Build a Monte Carlo retirement simulation in Python with the following specifications: (1) Simulate 10,000 return paths over 30 years for 3 portfolios: 60/40 stocks/bonds, 80/20 stocks/bonds, and a target-date glide path that starts at 90/10 and linearly shifts to 30/70 over 30 years. (2) Use historical Ibbotson-style parameters: stocks with 10.5% mean annual return and 20% standard deviation; bonds with 5.5% mean and 6% standard deviation; correlation of 0.05. (3) Assume $1M starting balance with $50,000 real annual withdrawals (adjusted for 2.5% inflation). (4) Plot: terminal wealth distributions for all 3 portfolios on one chart, probability of ruin (account hitting $0) over time for each portfolio, and the median and 5th/95th percentile wealth paths. (5) Print a summary table showing median terminal wealth, probability of ruin, and the 5th percentile terminal wealth for each portfolio. (6) Set random seed to 42 for reproducibility.

Implement both the Black-Scholes analytical solution and a Monte Carlo option pricing model in Python. Parameters: S0 = $100, K = $105, r = 5%, sigma = 25%, T = 1 year. For Monte Carlo, simulate with N = [100, 500, 1000, 5000, 10000, 50000] paths. Plot: (1) Monte Carlo price vs. number of paths with the Black-Scholes analytical price as a horizontal reference line, (2) 95% confidence interval around the Monte Carlo estimate at each N, (3) computation time vs. number of paths. Explain in comments why the Monte Carlo price converges to the analytical solution and what drives the width of the confidence interval.

Assessment Approach

• Assumption quality and justification25%
• Code modification sophistication20%
• Output interpretation and memo quality25%
• Presentation and defense under Q&A20%
• Verification against analytical solutions10%

Grade-band guidance — Assumption Quality (25%): Full credit requires citing a specific, verifiable data source for each key parameter — e.g., "I used a 10.5% equity mean return based on Ibbotson Associates' long-run historical series, available through Damodaran's data library." Partial credit for reasonable assumptions stated without sources. Minimal credit for assumptions asserted without justification ("I assumed 7% because that seemed reasonable"). The goal is to develop the professional discipline of defending every parameter choice with evidence.

Skills Developed

Evidence

MIT Sloan’s ‘AI and Money’ course (Gensler, 2025) and ‘AI and Machine Learning Applications in Finance’ (Chen, Kogan, Thesmar, 2025) integrate AI-driven modeling. Wharton provides ChatGPT Enterprise to all MBA students (2024). FinGPT (Yang et al., 2023) and PIXIU (Xie et al., 2023) provide open-source frameworks.

Risks and Safeguards