Mathematical Foundations for Quant Finance

Explain the role of the time value of money and calculate present and future values using discount factors.

Represent asset prices and portfolio weights as vectors and perform basic vector operations using NumPy.

Use NumPy to perform matrix operations, including multiplication, transposition, and inversion.

Calculate portfolio returns and volatility using vector and matrix algebra.

Explain the concepts of covariance and correlation matrices and compute them for a set of asset returns.

Define a derivative as a rate of change and relate it to the concept of financial 'Greeks'.

Use a numerical library (e.g., SciPy) to find the roots of a function, as applied in finding implied volatility or yield-to-maturity.