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Market Risk Measurement And Management

Credit Risk Measurement And Management

Operational Risk And Resilience

Liquidity And Treasury Risk Measurement And Management

Risk Management And Investment Management

Current Issues In Financial Markets

1. Estimating Market Risk Measures-An Introduction and Overview

  • a. Estimate VaR using a historical simulation approach
  • b. Estimate VaR using a parametric approach for both normal and lognormal return distributions
  • c. Estimate the expected shortfall given profit and loss (P&L) or return data
  • d. Estimate risk measures by estimating quantiles
  • e. Evaluate estimators of risk measures by estimating their standard errors
  • f. Interpret quantile-quantile (QQ) plots to identify the characteristics of a distribution

2. Non-Parametric Approaches

  • a. Apply the bootstrap historical simulation approach to estimate coherent risk measures
  • b. Describe historical simulation using non-parametric density estimation
  • c. Compare and contrast the age-weighted, the volatility-weighted, the correlation-weighted, and the filtered historical simulation approaches
  • d. Identify advantages and disadvantages of non-parametric estimation methods

3. Parametric Approaches II-Extreme Value

  • a. Explain the importance and challenges of extreme values in risk management
  • b. Describe extreme value theory (EVT) and its use in risk management
  • c. Describe the peaks-over-threshold (POT) approach
  • d. Compare and contrast the generalized extreme value (GEV) and POT approaches to estimating extreme risks
  • e. Discuss the application of the generalized Pareto (GP) distribution in the POT approach
  • f. Explain the multivariate EVT for risk management

4. Backtesting VaR

  • a. Describe backtesting and exceptions and explain the importance of backtesting VaR models
  • b. Explain the significant difficulties in backtesting a VaR model
  • c. Evaluate the accuracy of a VaR model based on exceptions or failure rates by using a model verification test
  • d. Identify and describe Type I and Type II errors in the context of a backtesting process
  • e. Explain the need to consider conditional coverage in the backtesting framework
  • f. Describe the Basel rules for backtesting

5. VaR Mapping

  • a. Explain the principles underlying VaR mapping and describe the mapping process
  • b. Explain how the mapping process captures general and specific risks, and calculate these risks in a portfolio given a set of primitive risk factors
  • c. Differentiate among the three methods for mapping portfolios of fixed-income securities
  • d. Summarize how to map a fixed-income portfolio into positions of standard instruments
  • e. Describe how mapping of risk factors can support stress testing
  • f. Explain how VaR can be calculated and used relative to a performance benchmark
  • g. Describe the method of mapping forwards, forward rate agreements, interest rate swaps, and options

6. Validation of Risk Management Models for Financial Institutions

  • a. Describe some important considerations for a bank in assessing the conceptual soundness of a VaR model during the validation process
  • b. Explain how to conduct sensitivity analysis for a VaR model, and describe the potential benefits and challenges of performing such an analysis
  • c. Describe the challenges a financial institution could face when calculating confidence intervals for VaR
  • d. Discuss the challenges in benchmarking VaR models and various approaches proposed to overcome them

7. Beyond Exceedance-Based Backtesting of Value-at-Risk Models

  • a. Identify the properties of an exceedance-based backtest that indicate a VaR model is accurate, and describe how these properties are reflected in a PIT-based backtest
  • b. Explain how to derive probability integral transforms (PITs) in the context of validating a VaR model
  • c. Describe how the shape of the distribution of PITs can be used as an indicator of the quality of a VaR model
  • d. Describe backtesting using PITs, and compare the various goodness-of-fit tests that can be used to evaluate the distribution of PITs: the Kolmogorov-Smirnov test, the Anderson-Darling test, and the Cram�r-von Mises test

8. Correlation Basics-Definitions, Applications, and Terminology

  • a. Describe financial correlation risk and the areas in which it appears in finance
  • b. Explain how correlation contributed to the global financial crisis of 2007-2009
  • c. Describe how correlation impacts the price of quanto options as well as other multi-asset exotic options
  • d. Describe the structure, uses, and payoffs of a correlation swap
  • e. Estimate the impact of different correlations between assets in the trading book on the VaR capital charge
  • f. Explain the role of correlation risk in market risk and credit risk
  • g. Explain how correlation risk relates to systemic and concentration risk

9. Empirical Properties of Correlation-How Do Correlations Behave in the Real World

  • a. Describe how equity correlations and correlation volatilities behave throughout various economic states
  • b. Calculate a mean reversion rate using standard regression and calculate the corresponding autocorrelation
  • c. Identify the best-fit distribution for equity, bond, and default correlations

10. Financial Correlation Modeling-Bottom-Up Approaches

  • a. Explain the purpose of copula functions and how they are applied in finance
  • b. Describe the Gaussian copula and explain how to use it to derive the joint probability of default of two assets
  • c. Summarize the process of finding the default time of an asset correlated to all other assets in a portfolio using the Gaussian copula

11. Regression Hedging and Principal Component Analysis

  • a. Explain the drawbacks to using a DV01-neutral hedge for a bond position
  • b. Describe a regression hedge and explain how it can improve a standard DV01-neutral hedge
  • c. Calculate the regression hedge adjustment factor, beta
  • d. Calculate the face value of an offsetting position needed to carry out a regression hedge
  • e. Calculate the face value of multiple offsetting swap positions needed to carry out a two-variable regression hedge
  • f. Compare and contrast level and change regressions
  • g. Explain why and how a regression hedge differs from a hedge based on a reverse regression
  • h. Describe principal component analysis and explain how it is applied to constructing a hedging portfolio

12. Arbitrage Pricing with Term Structure Models

  • a. Calculate the expected discounted value of a zero-coupon security using a binomial tree
  • b. Construct and apply an arbitrage argument to price a call option on a zero-coupon security using replicating portfolios
  • c. Define risk-neutral pricing and apply it to option pricing
  • d. Explain the difference between true and risk-neutral probabilities and apply this difference to interest rate drift
  • e. Explain how the principles of arbitrage pricing of derivatives on fixed-income securities can be extended over multiple periods
  • f. Define option-adjusted spread (OAS) and apply it to security pricing
  • g. Describe the rationale behind the use of recombining trees in option pricing
  • h. Calculate the value of a constant-maturity Treasury swap, given an interest rate tree and the risk-neutral probabilities
  • i. Evaluate the advantages and disadvantages of reducing the size of the time steps on the pricing of derivatives on fixed-income securities
  • j. Evaluate the appropriateness of the Black-Scholes-Merton model when valuing derivatives on fixed-income securities

13. Expectations, Risk Premium, Convexity, and the Shape of the Term Structure

  • a. Explain the role of interest rate expectations in determining the shape of the term structure
  • b. Apply a risk-neutral interest rate tree to assess the effect of volatility on the shape of the term structure
  • c. Estimate the convexity effect using Jensen�s inequality
  • d. Identify the components into which the return on a bond can be decomposed, and calculate the expected return on a bond for a risk-averse investor

14. The Art of Term Structure Models-Drift

  • a. Construct and describe the effectiveness of a short-term interest rate tree assuming normally distributed rates, both with and without drift
  • b. Calculate the short-term rate change and standard deviation of the rate change using a model with normally distributed rates and no drift
  • c. Describe methods for addressing the possibility of negative short-term rates in term structure models
  • d. Construct a short-term rate tree under the Ho-Lee Model with time-dependent drift
  • e. Describe uses and benefits of the arbitrage-free models and assess the issue of fitting models to market prices
  • f. Describe the process of constructing a simple and recombining tree for a short-term rate under the Vasicek Model with mean reversion
  • g. Calculate the Vasicek Model rate change, standard deviation of the rate change, expected rate in T years, and half-life
  • h. Describe the effectiveness of the Vasicek Model

15. The Art of Term Structure Models-Volatility and Distribution

  • a. Describe the short-term rate process under a model with time-dependent volatility
  • b. Calculate the short-term rate change and determine the behavior of the standard deviation of the rate change using a model with time-dependent volatility
  • c. Assess the efficacy of time-dependent volatility models
  • d. Describe the short-term rate process under the Cox-Ingersoll-Ross (CIR) and lognormal models
  • e. Calculate the short-term rate change and describe the basis point volatility using the CIR and lognormal models
  • f. Describe lognormal models with deterministic drift and mean reversion

16. The Vasicek and Gauss Models

  • a. Describe the structure of the Gauss+ model and discuss the implications of this structure for the model�s ability to replicate empirically observed interest rate dynamics
  • b. Compare and contrast the dynamics, features, and applications of the Vasicek model and the Gauss+ model
  • c. Calculate changes in the short-term, medium-term, and long-term interest rate factors under the Gauss+ model
  • d. Explain how the parameters of the Gauss+ model can be estimated from empirical data

17. Volatility Smiles

  • a. Describe a volatility smile and volatility skew
  • b. Explain the implications of put-call parity on the implied volatility of call and put options
  • c. Compare the shape of the volatility smile (or skew) to the shape of the implied distribution of the underlying asset price and to the pricing of options on the underlying asset
  • d. Describe characteristics of foreign exchange rate distributions and their implications on option prices and implied volatility
  • e. Describe the volatility smile for equity options and foreign currency options and provide possible explanations for its shape
  • f. Describe alternative ways of characterizing the volatility smile
  • g. Describe volatility term structures and volatility surfaces and how they may be used to price options
  • h. Explain the impact of the volatility smile on the calculation of an option�s Greek letter risk measures
  • i. Explain the impact of a single asset price jump on a volatility smile

18. Fundamental Review of the Trading Book

  • a. Describe the changes to the Basel framework for calculating market risk capital under the Fundamental Review of the Trading Book (FRTB) and the motivations for these changes
  • b. Compare the various liquidity horizons proposed by the FRTB for different asset classes and explain how a bank can calculate its expected shortfall using the various horizons
  • c. Explain the FRTB revisions to Basel regulations in the following areas: - Classification of positions in the trading book compared to the banking book - Backtesting, profit and loss attribution, credit risk, and securitizations