The topics to be covered under this subject are as follows:

After completion of this topic you will be able to

- Explain how asset return distributions tend to deviate from the normal distribution
- Explain reasons for fat tails in a return distribution and describe the implications
- Distinguish between conditional and unconditional distribution
- Describe the implications of regime switching on quantifying volatility
- Explain the various approaches for estimating VaR
- Compare and contrast different parametric and non-parametric approaches for estimating conditional volatility
- Calculate conditional volatility using parametric and non-parametric
- Explain the process of return aggregation in the context of volatility forecasting methods
- Evaluate implied volatility as a predictor of future volatility and its
- Explain long horizon volatility/VaR and the process of mean reversion according to an AR(1) model
- Calculate conditional volatility with and without mean reversion
- Describe the impact of mean reversion on long horizon conditional volatility estimation.

After completion of this topic you will be able to

- Explain and give examples of linear and non-linear derivatives
- Describe and calculate VaR for linear derivatives
- Describe the delta-normal approach for calculating VaR for non-linear derivatives
- Describe the limitations of the delta-normal method
- Explain the full revaluation method for computing VaR
- Compare delta-normal and full revaluation approaches for computing VaR
- Explain structured Monte Carlo, stress testing, and scenario analysis methods for computing VaR, and identify strengths and weaknesses of each approach
- Describe the implications of correlation breakdown for scenario analysis
- Describe worst-case scenario (WCS) analysis and compare WCS to VaR

After completion of this topic you will be able to

- Describe the mean-variance framework and the efficient frontier
- Explain the limitations of the mean-variance framework with respect to assumptions about the return distributions
- Define the Value-at-Risk (VaR) measure of risk, describe assumptions about return distributions and holding period, and explain the limitations of VaR
- Define the properties of a coherent risk measure and explain the meaning of each property
- Explain why VaR is not a coherent risk measure
- Explain and calculate expected shortfall (ES)
- Describe spectral risk measures
- Describe how the rule of certio analysis can be interpreted as coherent uk measures

After completion of this topic you will be able to

- Calculate the value of an American and European call or put option using step and two-step binomial model
- Describe how volatility is captured in the binomial model
- Describe how the value calculated using a binomial model conveyed as time p are added
- Explain how the binomial model can be altered to price options on: stocks wi dividends, stock indices, currencies, and futures

After completion of this topic you will be able to

- Explain the lognormal property of stock prices, the distribution of rates of te and the calculation of expected return
- Compute the realized return and historical volatility of a stock
- Describe the assumptions underlying the Black-Scholes Merton option pricing model
- Compute the value of a European option using the Black-Scholes-Merton m non-dividend-paying stock
- Compute the value of a warrant and identify the complications involving th valuation of warrants
- Define implied volatilities and describe how to compute implied volatilities market prices of options using the Black-Scholes-Merton model
- Explain how dividends affect the decision to exercise carly for American call put options
- Compute the value of a European option using the Black-Scholes-Merton n a dividend-paying stock

After completion of this topic you will be able to

- Describe and assess the risks associated with naked and covered option
- Explain how naked and covered option positions generate a stop loss trading strategy
- Describe delta hedging for an option, forward, and futures contracts
- Compute the delta of an option
- Describe the dynamic aspects of delta hedging and distinguish between dy hedging and hedge-and-forget strategy
- Define the delta of a portfolio
- Define and describe theta, gamma, vega, and rho for option positions
- Explain how to implement and maintain a delta-neutral and a gamma-net position
- Describe the relationship between delta, theta, gamma, and vega

After completion of this topic you will be able to

- Define discount factor and a discount function to compute present and future values
- Define the "law of one price, explain it using an arbitrage argument, and describe how it can be applied to bond pricing
- Identify the components of a U.S. Treasury coupon bond, and compare and contrast the structure to Treasury STRIPS, including the difference between P-STRIPS and C-STRIPS
- Construct a replicating portfolio using multiple fixed income securities to match the cash flows of a given fixed income security
- Identify arbitrage opportunities for fixed Income securities with certain cash Rows
- Differentiate between clean" and "dirty" bond pricing and explain the implications of accrued interest with respect to bond pricing.
- Describe the common day-count conventions used in bond pricing

After completion of this topic you will be able to

- Calculate and interpret the impact of different compounding frequencies on a bond's value
- Calculate discount factors given interest rate swap rates
- Compute spot rates given discount factors
- Interpret the forward rate, and compute forward rates given spot rates
- Define par rate and describe the equation for the par rate of a bond
- Interpret the relationship between spot, forward and par rates
- Assess the impact of maturity on the price of a bond and the returns generated by bonds
- Define the "flattening" and "steepening of rate curves and describe a trade to reflect expectations that a curve will flatten or steepen

After completion of this topic you will be able to

- Distinguish between gross and net realized returns, and calculate the realized return for a bond over a holding period including reinvestments
- Define and interpret the spread of a bond, and explain how a spread is derived from a bond price and a term structure of rates
- Define, interpret, and apply a bond's yield-to-maturity (YTM) to bond pricing
- Compute a bond's YTM given a bond structure and price
- Calculate the price of an annuity and a perpetuity
- Explain the relationship between spot rates and YTM
- Define the coupon effect and explain the relationship berween coupon rate, YTM and bond prices
- Explain the decomposition of P&L for a bond into separate factors including carry roll-down, rate change, and spread change effects
- Identify the most common assumption in any roll down scenarios, including called forward, unchanged term structure, and unchanged yields

After completion of this topic you will be able to

- Describe an interest rate factor and Identify common examples of interest rate factors
- Define and compute the DV01 of a fixed Income security viven change in yield and the resulting change in price
- Calculate the face amount of bonds required to hedge an option position given the DVOI of each
- Define, compute, and interpret the effective duration of a fixed income security given a change in yield and the resulting change in price
- Compare and contrast DV01 and effective duration as measures of price sensitivity
- Define, compute, and interpret the convexity of a fixed income security given a change in yield and the resulting change in price
- Explain the process of calculating the effective duration and convexity of a portfolio of fixed income securities
- Explain the impact of negative convexity on the hedging of fixed income securities
- Construct a barbell portfolio to match the cost and duration of a given bullet investment, and explain the advantages and disadvantages of bullet vs barbell portfolios

After completion of this topic you will be able to

- Describe and assess the major weakness attributable to single-factor approaches when hedging portfolios or implementing asset liability techniques
- Define key rate exposures and know the characteristics of key rate exposure factors including partial ‘01s and forward-bucket ‘01s
- Describe key-rate shift analysis
- Define, calculate, and interpret key rate '01 and key rate duration
- Describe the key rate exposure technique in multi-factor hedging applications summarize its advantages and disadvantages
- Calculate the key rate exposure for a given security, and compute the appropriate hedging positions given a specific key rate exposure profile
- Relate key rates, partial ‘01s and forward-bucker '01s, and calculate the forward bucket '01 for a shift in rates in one or more buckets
- Construct an appropriate hedge for a position across its entire range of forward bucket exposures
- Apply key rate and multi-factor analysis to estimating portfolio volatility

After completion of this topic you will be able to

- Identify sources of country risk
- Explain how a country's position in the economic growth life cycle, political risk legal risk, and economic structure affect its risk exposure
- Evaluate composite measures of risk that Incorporate all types of country risk and explain limitations of the risk services
- Compare instances of sovereign default in both foreign currency debt and local currency debt, and explain common causes of sovereign default page
- Describe the consequences of sovereign default
- Describe factors that influence the level of sovereign default risk; explain and ICS how rating agencies measure sovereign default risks
- Describe the advantages and disadvantages of using the sovereign default spread as a predictor of defaults

After completion of this topic you will be able to

- Describe external rating scales, the rating process, and the link between ratings and default
- Describe the impact of time horizon, economic cycle, industry, and geography on external rating
- Explain the potential impact of ratings changes on bond and stock prices
- Compare external and internal ratings approaches
- Explain and compare the through-the-cycle and at-the-point internal ratings approaches
- Describe a ratings transition matrix and explain its uses
- Describe the process for and issues with building, calibrating and backtesting an internal rating system
- Identify and describe the biases that may affect a rating system

After completion of this topic you will be able to

- Evaluate a bank's economic capital relative to its level of credit risk
- Identify and describe important factors used to calculate economic capital for credit risk: probability of default, exposure, and loss rate
- Define and calculate expected loss (EL)
- Define and calculate unexpected loss (UL)
- Estimate the variance of default probability assuming a binomial distribution
- Calculate UL for a portfolio and the risk contribution of each asset
- Describe how economic capital is derived
- Explain how the credit loss distribution is modeled
- Describe challenges to quantifying credit risk

After completion of this topic you will be able to

- Compare three approaches for calculating regulatory capital
- Describe the Basel Committee's seven categories of operational risk
- Derive a loss distribution from the loss frequency distribution and loss severity distribution using Monte Carlo simulations
- Describe the common data issues that can introduce inaccuracies and biases in the estimation of loss frequency and severity distributions
- Describe how to use scenario analysis in instances when data is scarce
- Describe how to identify anal relationships and how to use risk and control sell assessment (RCSA) and key risk indicators (KR) to measure and manage operational risks
- Describe the allocation of operational risk capital to business units,(page 242) to use the power law to measure operational risk
- Explain the risks of moral hazard and adverse selection when using insurance to mitigate operational risks

After completion of this topic you will be able to

- Describe the key elements of effective governance over stress testing
- Describe the responsibilities of the board of directors and senior management in stress testing activities
- Identify elements of clear and comprehensive policies, procedures, and documentations on stress testing
- Identify areas of validation and independent review for stress tests that require attention from a governance perspective
- Describe the important role of the internal audit in stress testing governance and control
- Identify key aspects of stress testing governance, including stress testing coverage stress testing types and approaches, and capital and liquidity stress testing

After completion of this topic you will be able to

- Describe the relationship between stress testing and other risk measures, particularly in enterprise-wide stress testing
- Describe the various approaches to using VaR models in stress tests
- Explain the importance of stressed inputs and their importance in stressed VaR
- Identify the advantages and disadvantages of stressed risk metrics

After completion of this topic you will be able to

Describe the rationale for the use of stress testing as a risk management tool

Describe weaknesses identified and recommendations for improvement in

The use of stress testing and integration in risk governance

Stress testing methodologies

Stress testing scenarios

Stress testing handling of specific risks and products

- Describe stress testing principles for banks regarding the use of stress testing and integration in risk governance, stress testing methodology and scenario selection and principles for supervisors