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

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

<p>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.</p> <p><b>Financial Applications</b></p> <p>• The Arrow—Debreu one period market model</p> <p>• One period index options arbitrage</p> <p>• Covariance and correlation matrix estimation from time series data</p> <p>• Ordinary least squares for implied volatility computation</p> <p>• Minimum variance portfolios and maximum return portfolios</p> <p>• Value at Risk and portfolio VaR</p> <p><b>Linear Algebra Topics</b></p> <p>• LU and Cholesky decompositions and linear solvers</p> <p>• Optimal solvers for tridiagonal symmetric positive matrices</p> <p>• Ordinary least squares and linear regression</p> <p>• Linear Transformation Property</p> <p>• Efficient cubic spline interpolation</p> <p>• Multivariate normal random variables</p> <p>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:</p> <p>• 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</p> <p>• Finance practitioners will find mathematical underpinnings for many methods used in practice, furthering the ability to expand upon these methods</p> <p>• 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.</p>