Mathematical Foundations of Risk Measurement
1st Edition
Published on 6. October 2022
231 pages
979-8-9861646-8-7 (ISBN)
Description
Every financial risk manager should be able to assess risks and understand the core mathematics behind these risks. With nuances to the practice of financial risk management that go beyond the quantitative, the chapters in this book are accessible for individuals with little experience in quantitative financial risk management.
Access worksheets to practice your newly gained knowledge, and use the online Excel spreadsheets that accompany the examples in this book to gain invaluable understandings of the mathematical and statistical concepts that form the basis of financial risk assessment.
More details
Content
- Intro
- Foreword
- About PRMIA
- About the Professional Risk Manager (PRM) Designation
- Mathematical Foundations of Risk Measurement
- Chapter 1: Foundations for Algebraic Methods
- Symbols and Rules
- Sequences and Series
- Exponentiation and Logarithms
- Equations and Inequalities
- Functions and Graphs
- Summary
- Chapter 2: Differential and Integral Calculus
- Differential Calculus
- Case Study: Modified Duration of a Bond
- Higher-Order Derivatives
- Financial Applications of Second Derivatives
- Differentiating a Function of More than One Variable
- Optimization
- Integral Calculus or Integration
- Appendix: Calculus
- Chapter 3: Descriptive Statistics
- Introduction
- Data
- The Moments of a Distribution
- Measures of Location or Central Tendency - Averages
- Measures of Dispersion
- Bivariate Data
- Case Study: Interpretation of Statistical Output
- Chapter 4: Numerical Methods
- Solving (Non-differential) Equations
- Numerical Optimization
- Numerical Methods for Valuing Options
- Monte Carlo Simulation
- Summary
- Chapter 5: Matrix Algebra
- Matrix Algebra
- Using Matrix Algebra to Solve Simultaneous Equations
- Applications of Matrix Algebra in Finance
- Checking the Variance-Covariance Matrix
- Eigenvalues and Eigenvectors
- Cholesky Decomposition
- Quadratic Forms
- Principal Components Analysis
- Appendix: Using Microsoft Excel for Matrix Manipulation
- Chapter 6: Probability Theory in Finance
- Definitions and Rules
- Probability Distributions
- Joint Distributions
- Specific Probability Distributions
- Chapter 7: Regression Analysis in Finance
- Univariate Linear Regression
- Multiple Linear Regression
- Evaluating the Regression Model
- Confidence Intervals
- Hypothesis Testing
- Prediction
- Breakdown of OLS Assumptions
- Stationary Data for Time Series Regressions
- Maximum Likelihood Estimation
- Summary
- Chapter 8: Compounding Methods and the Time Value of Money
- Applying Simple Math to a Common Financial Issue: The Time Value of Money
- Appendix A: Greek Letters Frequently Found in Financial Math
- Appendix B: Symbols Frequently Found in Financial Math
- Contributors
- About PRMIA
- Mission and Objectives
- Community and Membership
- Professional Designations
- Certificates in Risk Management
- Certificates of Practice
- Risk Resources
- Learning Programs
- Global Presence
