Fix the GBM model and the price simulation

[shehio]

Summary

StockHelper.calculate_price() returned NaN, and the geometric Brownian motion behind it was wrong in three independent ways. All four defects sat in a module no test reached.

What Was Broken

1. Arity mismatch — calculate_price() returned NaN. run(sample_number, probability_distribution, estimator_function) calls estimator_function(probability_distribution()), i.e. with one argument, while geometric_brownian(estimators, time, random) takes three. So estimators was bound to the random draw, estimators.mean and estimators.std were undefined, and every term was NaN.

Reproduced on develop:

calculate_price(5) = NaN
miu = undefined, sigma = undefined, drift = NaN, shock = NaN

2. The shock did not scale with √Δt. It was sigma * random * time, so the variance of the log return grew as time² instead of linearly in time.

3. No Itô correction. The drift was mu * time, not (mu - sigma²/2) * time, so E[S_T] overshot S_0·e^{μT} by exp(σ²T/2).

4. Math.random() was used where a standard normal is required. It is uniform on [0, 1) and therefore never negative — the simulated price could only ever be pushed up. Over 400,000 draws, 0 shocks were negative and the minimum shock was exactly 0.0000.

The Fix

• calculate_price(price, estimators, time, sample_size?) closes over the price, estimators and horizon, so the single-argument estimator run() expects receives only the random draw. It now returns S_0 · E[exp(log return)].
• standard_normal() (Box-Muller) supplies the normal draws.
• The log return over Δt is now (μ − σ²/2)Δt + σ√(Δt)·Z, so E[S_T] = S_0·e^{μT}.
• Dropped the per-sample console.log inside geometric_brownian; it printed one line per Monte Carlo path.

Measured Before and After

S_0 = 100, μ = 0.08, σ = 0.25, T = 2, 400,000 paths. Analytical E[S_T] = S_0·e^{μT} = 117.3511.

	E[S_T]	Ratio to analytical
Before	152.2503	1.2974 (+29.7%)
After	117.2575	0.9992

The resulting distribution is lognormal, as it should be — the log returns are normal:

Moment	Simulated	Expected
Mean	0.0976	0.0975 = (μ − σ²/2)T
Variance	0.1249	0.1250 = σ²T
Skewness	−0.0014	~0

Tests

finance/test/models.test.ts is new and is the first test to reach finance/models.ts at all. It covers the standard normal's moments, that it actually produces negative draws, the Itô correction, the √Δt scaling, and the convergence of E[S_T] to S_0·e^{μT}.

Suite: 34 tests / 10 suites before → 40 tests / 11 suites after, all passing.

🤖 Generated with Claude Code

https://claude.ai/code/session_01THEv7BFJd31NjvBRehbZPL