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.
• 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.
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