Multivariate Random Variables
After completing this reading, you should be able to: Explain how a probability matrix can be used to express a probability mass function (PMF). Compute the marginal and conditional distributions of a discrete bivariate random variable. Explain how the expectation…
Random Variables
After completing this reading, you should be able to: Describe and distinguish a probability mass function from a cumulative distribution function and explain the relationship between these two. Understand and apply the concept of a mathematical expectation of a random…
FRM Part 1 Study Notes
FRM Part I Foundations of Risk Management 1. The Building Blocks of Risk Management 2. How Do Firms Manage Financial Risk? 3. The Governance of Risk Management 4. Credit Risk Transfer Mechanisms 5. Modern Portfolio Theory (MPT) and the Capital Asset…
Regression with a Single Regressor – Hypothesis Tests and Confidence Intervals
After completing this reading you should be able to: Calculate and interpret confidence intervals for regression coefficients. Interpret the \(p-value\). Interpret hypothesis tests about regression coefficients. Evaluate the implications of homoskedasticity and heteroskedasticity. Determine the conditions under which the OLS…
Financial Markets and Products
1. Banks 2. Insurance Companies and Pension Plans 3. Fund Management 4. Introduction to Derivatives 5. Exchanges and OTC Markets 6. Central Clearing 7. Futures Markets 8. Using Futures for Hedging 9. Foreign Exchange Markets 10. Pricing Financial Forwards and Futures 11. Commodity Forwards and Futures 12. Options Markets 13. Properties of Options…
Properties of Options
After completing this reading, you should be able to: Identify the six factors that affect an option’s price. Identify and compute upper and lower bounds for option prices on non-dividend and dividend-paying stocks. Explain put-call parity and apply it to…
Bayesian Analysis
After completing this reading you should be able to: Describe Bayes’ theorem and apply this theorem in the calculation of conditional probabilities. Compare the Bayesian approach to the frequentist approach. Apply Bayes’ theorem to scenarios with more than two possible…
Linear Regression
After completing this reading, you should be able to: Describe the models that can be estimated using linear regression and differentiate them from those which cannot. Interpret the results of an OLS regression with a single explanatory variable. Describe the…
Validating Rating Models
After completing this reading, you should be able to: Explain the process of model validation and describe the best practices for the roles of internal organizational units in the validation process. Compare qualitative and quantitative processes to validate internal ratings…
Default Probability, Credit Spreads and Funding Costs
For credit valuation adjustments (CVA) and debt valuation adjustments (DVA) in the qualification of counterparty risk to be defined comprehensively, default probability and recovery rates associated with those are required. Relevant funding costs that are required when a position is…
