Maths. In order.

The distributions, roots and matrices every model above stands on.

9 problems~3h5 easy2 medium2 hard

paper only · educational · not advice

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30Normal CDF, Abramowitz–Stegun
Φ(x) to six decimals with one polynomial — no libraries.
easy15 minstart →
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31Log vs simple returns
Convert a price path into both, and show where they diverge.
easy10 min
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32GBM path
Simulate geometric Brownian motion from a drift, a vol and a seed.
easy15 min
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33Cholesky for correlated shocks
Decompose a covariance matrix and generate correlated normals.
hard40 min
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34Newton's method root
Iterate x − f(x)/f′(x) to tolerance and report the iteration count.
medium20 min
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35Portfolio variance
wᵀΣw for a weight vector and a covariance matrix.
easy10 min
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36Barrier-touch probabilityPro
The chance a GBM path touches a level before expiry.
hard35 min
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37Expected value of a bet
Probabilities times payoffs — and why a positive EV can still ruin you.
easy10 min
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38Autocorrelation at lag k
Does today's return remember yesterday's? Measure it.
medium20 min