Programming for Financial Engineering

NumPy operations run in optimized C loops on contiguous ndarray memory, avoiding Python's per-element interpreter and boxing overhead — typically 10-100x faster than equivalent Python for loops.

A set of rules that lets NumPy combine arrays of different shapes without copying: dimensions are compared right-to-left, and a dim of size 1 (or missing) is virtually stretched to match the other operand.

Use np.random.default_rng(seed) to get a Generator; it is faster, statistically better (PCG64), and reproducible. Legacy functions like np.random.rand use a global RandomState and should be avoided in new code.

.loc is label-based (uses index labels and column names; endpoints inclusive). .iloc is positional integer-based (0..n-1; endpoints exclusive like Python slicing).

df.groupby('key').agg({'ret': 'mean', 'vol': 'std'}) splits rows by key, applies an aggregator per group, and combines results. Prefer .agg / .transform over .apply for speed (vectorized C path).

df.resample('1D').last() on a DatetimeIndex regroups rows into fixed time buckets ('D','W','M','5min',...). Use .last() for end-of-period prices, .sum() for flows, .ohlc() for bars.