A Linear Algebra Primer for Financial Engineering: Covariance Matrices, Eigenvectors, OLS, and more (Financial Engineering Advanced Background Series)

This book covers linear algebra methods for financial engineering applications from a numerical point of view. The book contains many such applications, as well as pseudocodes, numerical examples, and questions often asked in interviews for quantitative positions.

Financial Applications

· The Arrow—Debreu one period market model

· One period index options arbitrage

· Covariance and correlation matrix estimation from time series data

· Ordinary least squares for implied volatility computation

· Minimum variance portfolios and maximum return portfolios

· Value at Risk and portfolio VaR

Linear Algebra Topics

· LU and Cholesky decompositions and linear solvers

· Optimal solvers for tridiagonal symmetric positive matrices

· Ordinary least squares and linear regression

· Linear Transformation Property

· Efficient cubic spline interpolation

· Multivariate normal random variables

The book is written in a similar spirit as the best selling ``A Primer for the Mathematics of Financial Engineering" by the same author, and should accordingly be useful to a similarly large audience:

· Prospective students for financial engineering or mathematical finance programs will be able to self-study material that will prove very important in their future studies

· Finance practitioners will find mathematical underpinnings for many methods used in practice, furthering the ability to expand upon these methods

· Academics teaching financial engineering courses will be able to use this book as textbook, or as reference book for numerical linear algebra methods with financial applications.