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.