IB Mathematics Analysis and Approaches (AA) SL Extended Essay Example

The research question is clearly stated as an evaluative inquiry and effectively guides the investigation.

The topic and purpose (testing GBM on Apple’s stock over a defined horizon) are communicated accurately and maintained throughout.

The methodology outlines relevant data collection, parameter estimation and Monte-Carlo simulation steps with reasonable clarity.

Background sections contain tangential or repetitive material that does not advance the mathematical focus.

Key methodological assumptions (constant volatility) are acknowledged but no sensitivity analyses or alternative model comparisons are performed.

The choice of a 30-day forecast horizon is not justified or linked to model validity criteria.

Solid application of stochastic calculus in deriving the discrete GBM formula and applying Itô’s lemma.

Key parameters (drift, volatility) are defined and linked to the simulation context.

Terminology such as Wiener process, MSE, RMSE and MAPE is used accurately and consistently in most cases.

An implausibly high annualized drift reveals a scaling error that undermines conceptual rigour.

Use of non-standard terms (e.g. “decreasements”) and occasional language slips reduce precision.

The literature review is narrow and includes questionable academic sources (AI chat prompts).