MODULE 01
Institutional Problem Bank
25+ curated challenge problems across 5 disciplines. From stochastic calculus proofs to real-time factor alphas, complete with automated unit tests and mathematical rigor.
solution.py
Python 3.11 WASM
In-Memory Exec
import numpy as np
class KalmanPairsArbitrage:
# Dynamic state estimation: Jane Street / Citadel QR Desk
def __init__(self, delta=1e-4, vt=1e-3):
self.theta = np.zeros(2) # [slope, intercept]
self.P = np.eye(2) * 1.0; self.R = vt
def step(self, px_a, px_b):
F = np.array([px_b, 1.0]); y_hat = np.dot(F, self.theta)
e = px_a - y_hat; K = np.dot(self.P, F) / (np.dot(F, np.dot(self.P, F)) + self.R)
self.theta += K * e; return float(e)
SPREAD Z-SCORE: -2.34σ
LONG SPREAD ARBITRAGE
SPREAD SIGNAL TRIGGERED (-2.0σ)