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.