Are you minding your risk?

This course provides an in-depth introduction to credit derivatives modeling. Techniques for calibrating the LIBOR curve are introduced. Alternative approaches to modeling default probabilities are considered, including Merton’s model, reduced-form models and the hazard rate model. The basic properties of credit derivatives are covered in detail, along with pricing models. Strategies for hedging credit risk with these derivatives are discussed in detail. Correlation products are covered, including Collateralized Debt Obligations (CDOs) and single-tranche CDOs. These are priced with Monte Carlo simulation while hedging strategies are developed. All models are implemented in Excel/VBA.

Learning Objectives

• Excel - Learn several of Excel's specialized bond pricing functions. Understand how to use Excel's add-in tools to implement advanced statistical techniques, such as regression analysis and random number generation.
• Visual Basic for Applications (VBA) - Learn the fundamental programming structures of the VBA language, and how it can be used to extend Excel's capabilities.
• Statistical foundations - Learn how to implement Monte Carlo simulation using Excel/VBA. Learn techniques for improving the speed of convergence, including importance sampling and low-discrepancy sequences.
• Calibrating the LIBOR curve - Understand how the LIBOR curve may be estimated from market data in order to price credit derivatives.
• Default rate modeling - Understand how Merton's structural model may be used to estimate default probabilities. Understand alternative approaches to default rate modeling, including reduced-form models and the hazard rate model.
• Credit spread derivatives - understand how credit spread forwards, swaps and options are structured and how they are priced. Understand how credit spread options can be priced with an extension of the Black-Scholes model.
• Credit Default Swaps (CDS) - Understand the properties of a CDS and how it can be priced. Learn how a CDS can be used to create a synthetic position in a risky asset, such as a corporate bond. Understand how CDS expose investors to changes in the credit spread curve, LIBOR curve and recovery rates and how these risks may be measured and hedged. Understand how credit DV01, spread convexity and theta are defined for a CDS.
• Correlation products - Understand the properties of credit derivatives whose value depends on the behavior of two or more underlying assets. Understand the structure of Collateralized Debt Obligations (CDOs) and the motivations for issuing them. Learn how to price CDO tranches using Monte Carlo simulation and other alternative approaches. Understand how to measure the risk associated with a CDO tranche. Understand how nth-to-Default Swaps are structured and how they may be used to enhance returns through the use of leverage.

This course provides a detailed overview of volatility and correlation models. First, estimate volatility from historical data then, implied volatility is defined and derived from option prices using root-finding methods. Dive deeper into the term structure of volatilities and volatility surface are analyzed in great detail. Learn how to price exotic options and the corresponding Greeks from the volatility surface. An overview of hedging and trading strategies using volatility derivatives is given; these include VIX options and futures and OTC derivatives, such as variance and volatility swaps. Several techniques for estimating correlation are covered, along with an overview of correlation derivatives. Trading and hedging strategies with correlation products are explored in detail. All models are implemented using Excel and the Visual Basic for Applications (VBA) programming language.

Learning Objectives

• Excel - Understand how to use Excel's optimization package Solver to estimate volatility models.
• Visual Basic for Applications (VBA) - Learn how to extend the capabilities of Excel with the VBA programming language. Understand the basic programming structures of VBA, such as arrays, objects, properties, methods, and branching and looping statements. Learn how to write user-defined functions and macros.
• Historical volatility - Understand how to estimate volatility from historical data. Implement the simple moving average approach, the Exponentially-Weighted Moving Average (EWMA) approach and the GARCH methodology using Excel. Understand the advantages and disadvantages of each approach.
• Implied volatility - Understand how implied volatility can be computed from the Black-Scholes model using root-finding techniques such as Newton-Raphson. Understand the properties of the volatility skew and how the term structure of volatilities is calculated. Learn how the implied volatility surface is constructed from the volatility skew and the term structure of volatilities.
• Implied trees - Understand the methodology used to generate implied binomial and trinomial trees from the volatility surface. Learn how to implement the Derman-Kani implied tree model in order to price exotic options and calculate the Greeks for these options. Understand how the Greeks may be used for hedging.
• Stochastic volatility models - Learn how volatility can be modeled as a two-factor stochastic process. Understand how the Heston model may be implemented with Monte Carlo simulation and as a closed-form solution using numerical methods. Use Heston model to calculate implied volatility surface and use this information to price exotic options.
• Volatility derivatives - Understand the properties of several volatility derivatives, including VIX options and futures, variance and volatility swaps. Understand how the VIX index is constructed and how VIX options and futures may be used to hedge volatility. Understand several trading strategies using VIX options and futures to speculate on future direction of volatility, including bull / bear spreads, calendar spreads, diagonal spreads, butterfly spreads & condors.
• Correlation models - Understand how correlation can be estimated from historical data using simple moving averages, Exponentially-Weighted Moving Averages and GARCH. Be able to extract implied correlations from the prices of currency options. Understand the properties of the correlation skew. Learn how default correlations may be estimated from structural models such as Merton.
• Correlation derivatives - Learn key properties of correlation derivatives, such as covariance & correlation swaps, nth-to-default swaps and Collateralized Debt Obligations (CDOs.) Understand different types of risk carried by correlation products, such as default risk, spread risk, implied correlation risk and time decay and how these risks may be managed using delta and gamma. Learn how a position in correlation may be taken with CDS or CDO tranches.
• Copulas - Understand how several types of copulas are constructed, including the Gaussian copula. Learn how these may be used to price correlation products, such as CDS and CDOs.

This course is designed to provide an intensive introduction to fixed income markets and interest rate derivatives. The course presents several alternative measures of interest rates: yield to maturity, spot rates, forward rates and discount factors; techniques for pricing bonds with these measures are covered. The measurement and management of interest rate risk is then explored in depth.

Learning Objectives

• Excel - Learn how Excel can be used to implement several sophisticated models of interest rates and interest rate risk. Understand how interest rate derivative securities can be priced based on these models.
• Visual Basic for Applications (VBA) - Learn how to extend the capabilities of Excel with the VBA programming language. Understand the basic programming structures of VBA, such as arrays, objects, properties, methods, and branching and looping statements. Learn how to write user-defined functions and macros.
• Interest rate modeling - Understand the definitions of yield to maturity, spot rates, forward rates and discount factors. Learn how these measures relate to each other and how they can be used to price fixed-income securities, including bonds. Understand different types of compounding conventions.
• Measuring interest rate risk - Understand the properties of duration and convexity and how they are derived. Learn how duration and convexity are used to measure and manage interest rate risk. Understand how duration hedging is implemented and the drawbacks to this approach. Gain insight into how convexity can be used to increase the effectiveness of duration hedging.
• Principal components analysis (PCA) - Understand how PCA is used to identify the factors that explain the behavior of the yield curve. Learn how PCA can be used to derive more realistic versions of duration, known as level, slope and curvature duration, and how these may be used to hedge interest rate risk.
• Modeling interest rates - Understand how the term structure of interest rates can be modeled as a binomial tree and implemented in Excel. Understand how the binomial tree can be used to price callable and puttable bonds, floating rate bonds and inverse floaters. Learn how the tree is used to compute analytics such as effective duration, effective convexity and option-adjusted spread (OAS.) Understand how OAS is used in rich-cheap analysis to identify the relative value of different fixed income securities.
• Monte Carlo simulation - Understand how Monte Carlo simulation can be used to price fixed income securities and compute effective duration, effective convexity and OAS.
• Interest rate derivatives - Understand basic properties of interest rate futures, forwards, swaps and options. Learn how interest rate options can be priced using modified Black-Scholes model and the binomial interest rate tree.
• Hedging with interest rate derivatives - Understand basic strategies for hedging interest rate risk with interest rate futures, such as Eurodollar futures and Treasury bill futures. Understand the concept of basis risk. Learn how hedging strategies can be implemented with interest rate swaps and options.
• Passive fixed income portfolio management strategies - Understand how passive strategies are used to replicate the returns to an index, such as the Barclays Capital Aggregate Bond Index. Learn different approaches to replication, such as stratified sampling, tracking-error minimization, factor-based replication, and derivatives-based replication. Understand how immunization strategies can be implemented; these include cash-flow matching and duration matching. Learn how derivatives can be used to implement passive strategies.
• Active fixed income portfolio management strategies - learn how market timing strategies are implemented based on anticipated yield curve changes. These include "riding the yield curve" and bullet, barbell, ladder and butterfly strategies. Understand how trading strategies can be based on exploiting market inefficiencies, such as spread and convergence trades. Learn how derivatives can be used to implement active strategies.

This course provides an analysis of the term structure of interest rates and interest rate derivatives pricing models. Several different types of interest rate derivatives are covered, including interest rate futures and forwards, interest rate swaps and interest rate options. The uses of these derivatives for hedging and trading purposes is explored in depth. Black’s model is applied to the pricing of European interest rate options. Equilibrium models of the term structure of interest rates are introduced and implemented in Excel. These models are used to price zero-coupon bonds and coupon bonds.

The drawbacks of equilibrium term structure models are considered. No-arbitrage models of the term structure are explored in depth, including the lognormal model, Black-Derman-Toy (BDT) and Hull-White. The comparative strengths and weaknesses of these models are considered. The BDT model is implemented in VBA as a binomial interest rate tree. The model is then used to price European, American and Exotic interest rate options.

Learning Objectives

• Excel - Learn how Excel can be used to implement several sophisticated pricing models for interest rate derivatives. Understand how simple models of the term structure of interest rates can be implemented in Excel.
• Visual Basic for Applications (VBA) - Learn how to extend the capabilities of Excel with the VBA programming language. Understand the basic programming structures of VBA, such as arrays, objects, properties, methods, and branching and looping statements. Learn how to write user-defined functions and macros.
• Stochastic processes - Learn the statistical properties of key stochastic processes and how they may be used to model the evolution of interest rates over time.
• Interest rate forwards and futures - Understand the properties of interest rate forward contracts, such as forward rate agreements (FRAs), and how they are priced. Learn how FRAs are used to lock in a borrowing or a lending rate. Learn how interest rate futures, such as Eurodollar futures, are used for hedging fluctuations in interest rates. Understand how basis risk arises when hedging with futures contracts. Learn how to implement duration-based hedges with futures contracts. Learn how and why cross-hedging is implemented, and how to measure its effectiveness with regression analysis. Understand the convexity adjustment that relates forward rates of interest to futures rates.
• Interest rate swaps - Learn how interest rate swaps are structured. Understand how swap rates are determined from the term structure of interest rates, and how interest rate swaps are priced. Learn how interest rate swaps may be used to hedge risk by transforming floating rate assets/liabilities to fixed rate and vice versa. Learn how the risk of a negative or positive GAP can be hedged with an appropriate position in an interest rate swap. Understand how a synthetic position in a security can be created with an interest rate swap.
• Interest rate options - Become familiar with the properties of interest rate options, such as caps, floors, collars, swaptions and futures options. Understand how European interest rate options can be priced with Black's model, how Greeks can be calculated for these options, and how the prices of caps, floors and swaps are related. Understand how the Greeks can be used to implement hedging strategies. Analyze the strengths and weaknesses of Black's model. Understand the properties of American and exotic interest rate options. Learn how caps can be used to hedge floating rate liabilities, floors can be used to protect the returns to floating rate assets and collars are used to set upper and lower boundaries on interest rates. Understand how swaptions can be used to lock in a maximum rate for floating rate debt, and how they can be used to transform fixed-rate assets into floating rate assets to benefit from rising rates.
• Equilibrium term structure models - Understand the key features of two key equilibrium models: Vasicek and Cox-Ingersoll-Ross. Understand how these models can be used to price coupon bonds and zero coupon bonds. Understand how these models are derived and why they are not appropriate for pricing interest rate derivatives.
• No-arbitrage term structure models - Learn the key properties of no-arbitrage term structure models, such as the lognormal model, Black-Derman-Toy (BDT) and Hull-White. Gain insights into the stochastic processes that underlie these models. Understand how to implement the Black-Derman-Toy model using VBA. Learn how to use the Black-Derman-Toy model to price European interest rate options, such as caps, floors and collars, and compare the results with Black's model. Use BDT to price American and exotic interest rate options, such as barrier caps and floors, bounded caps and floors, cancelable swaps and captions and floortions.

The course presents an overview of exchange rates, foreign exchange risk and strategies for pricing and hedging with foreign exchange derivatives. The basic features of the foreign exchange markets are introduced, along with several international parity conditions. The key properties of foreign exchanges forwards, futures, swaps and options are covered in detail; pricing models are introduced for each type of derivative along with hedging strategies.

Several models are introduced for pricing foreign exchange options and are implemented in VBA. These models are used to compute the Greeks and implement sophisticated hedging strategies. The properties of exotic foreign exchange options are covered; these are priced with stochastic volatility option pricing models.

Learning Objectives

• Excel - Understand how to use Excel's optimization package Solver for applications such as computing implied volatility. Learn how to implement regression analysis using Excel's Data Analysis Tool-Pak add-in.
• Visual Basic for Applications (VBA) - Learn how to extend the capabilities of Excel with the VBA programming language. Understand the basic programming structures of VBA, such as arrays, objects, properties, methods, and branching and looping statements. Learn how to write user-defined functions and macros.
• The foreign exchange markets - Understand the meaning of spot, forward and cross-exchange rates. Learn how real exchange rates are determined from nominal exchange rates, and how both are calculated.
• International parity relations - Understand how exchange rates are affected by interest rates and inflation rates through purchasing power parity and the International Fisher Effect. Learn how interest rate parity ties together the values of spot and forward exchange rates, and how violations of IRP lead to arbitrage profits. Understand how uncovered interest rate parity "carry trade," can be used to increase returns.
• Foreign exchange forwards and futures - Understand the properties of foreign exchange forwards and futures; understand how FX forward contracts are priced. Learn how marking-to-market affects the relationship between futures and forward prices. Understand how FX forwards can be used to lock in the exchange rate at which future transactions will take place. Learn different approaches to futures hedging and how the optimal hedge ratio can be determined with regression analysis. Understand how basis risk arises with FX futures hedging and how cross hedges are implemented and their effectiveness.
• Foreign exchange swaps - Learn how FX swaps can be priced as a sequence of FX forward contracts or as a portfolio of bonds. Understand how FX swaps can be used to convert the denomination of assets and liabilities from one currency into another in order to hedge FX risk or increase rates of return.
• FX options - Understand the basic features of FX options and several hedging strategies, including bull spreads, bear spreads, butterfly spreads, straddles and strangles. Learn the properties of several exotic FX options, including barrier options, digital options and quantos. Understand the properties of the standard Greeks: delta, gamma, theta, vega and rho, as well as the higher-order Greeks, such as vanna and volga.
• Implied volatility - Understand how implied volatility can be computed from the Black-Scholes model using root-finding techniques such as Newton-Raphson. Understand the properties of the volatility skew and how the term structure of volatilities is calculated. Learn how the implied volatility surface is constructed from the volatility skew and the term structure of volatility.
• Foreign exchange option pricing models - Learn how plain vanilla FX options can be priced with an extension of the Black-Scholes model, known as the Garman-Kohlhagen model, and how the Greeks may be derived from the model. Understand how the Greeks are used for hedging strategies. Learn how exotic FX options can be priced with the stochastic volatility SABR (stochastic alpha beta rho) model and how the Greeks can be determined with the model. Understand the vanna-volga approach to pricing exotic FX options and computing the Greeks. Learn strategies for hedging delta, vega, vanna and volga risk.

This course is an intensive introduction to option trading strategies and the Greeks. Several examples of spreads and combinations are covered in detail; strategies that combine options with other types of assets are also explained in depth. These include covered calls, protective puts and collars. In addition to these strategies, the use of options to synthetically replicate other types of positions is also explored.

Several option risk measures, known as the Greeks, are covered in detail: delta, gamma, theta, vega and rho. The properties of the Greeks are analyzed, while models for computing the Greeks are derived from the Black-Scholes model using Excel. The importance of the Greeks in trading strategies is shown with numerous examples.

Learning Objectives

• Excel - Understand how to implement several key mathematical and statistical Excel functions, such as variance, standard deviation, covariance, correlation, the normal probability distribution and the cumulative normal probability distribution.
• Visual Basic for Applications (VBA) - Learn how to extend the capabilities of Excel with the VBA programming language. Understand the basic programming structures of VBA, such as arrays, objects, properties, methods, and branching and looping statements. Learn how to write user-defined functions and macros.
• Options - Review basic options terminology and understand how options are priced with the Black-Scholes model. Understand the statistical foundations of the Black-Scholes option pricing model and how to implement the Black-Scholes model in Excel. Learn how the put-call parity condition enables Black-Scholes to price puts and calls.
• Option trading strategies - Understand the basic types of trading strategies, including spreads and combinations. Understand the payoff profile and the break-even point of each strategy. Understand which strategies are appropriate when the market outlook is bullish, bearish or neutral. Learn the potential rewards and risk associated with each strategy. Understand how changes in volatility affect each strategy, and how the passage of time affects the profitability of each strategy. Learn how to synthetically reproduce various payoff profiles with the use of options.
• Black-Scholes - Learn how European options may be priced with the Black-Scholes model. Understand the statistical foundations of the Black-Scholes option pricing model and the concept of risk-neutral pricing. Be able to implement the Black-Scholes model in Excel and VBA. Learn how to extend the Black-Scholes model to price European puts with the put-call parity condition. Learn how the Greeks may be calculated with the Black-Scholes model. Understand how the assumptions underlying the Black-Scholes model may be violated in practice.
• Option Volatility - Understand how to calculation implied volatility and the implications volatility has in pricing options. Connect the "smile" of volatility to implied volatility and strike price and validate / negate the assumptions of Black-Scholes. Internalize the impact of volatility skew on in-the-money calls and out-of-the-money puts which all relate to the term structure of volatility and how mispricing arises.
• The Greeks - Understand five of the most important Greeks: delta, gamma, theta, vega and rho. Understand how delta and gamma can be used to measure the sensitivity of an option's price to changes in the price of the underlying variable. Learn how theta measures the impact of the passage of time on an option's price. Understand the relationship between option prices and volatility, as measured by vega. Gain insight into how interest rates impact option prices, as measured by rho. Learn how to compute these measures in Excel and understand their role in measuring and managing risk. Understand the role of the Greeks in trading strategies.

This course introduces the Monte Carlo simulation approach to pricing derivative securities. Several different techniques for simulating random numbers are described; the risk-neutral framework for pricing derivative securities is covered in detail. The properties of Brownian Motion and Geometric Brownian Motion are explored, along with alternative stochastic processes that may be used to price derivatives. The simulation of European option prices and the Greeks is implemented in the VBA programming language.

The Longstaff-Schwartz approach to pricing American options is covered in depth. The properties of several types of exotic derivatives are explained in detail. The prices of these derivatives are obtained from Monte Carlo simulation and compared with the results obtained from closed-form models. Several techniques for reducing the computational time of Monte Carlo simulation are explored, such as low-discrepancy sequences, control variates and antithetic variables.

Learning Objectives

• Excel - Understand how to use Excel's add-in tools to implement advanced statistical techniques, such as regression analysis and random number generation.
• Visual Basic for Applications (VBA) - Learn how to extend the capabilities of Excel with the VBA programming language. Understand the basic programming structures of VBA, such as arrays, objects, properties, methods, and branching and looping statements. Learn how to write user-defined functions and macros.
• Risk-neutral pricing - Understand how derivative securities are priced with the risk-neutral framework of Black and Scholes. Learn the statistical properties of Brownian Motion. Understand how a stochastic process such as Geometric Brownian Motion can be used to model the behavior of financial assets.
• Monte Carlo simulation - Understand how the statistical properties of traded assets can be used to generate simulated prices, and how option prices can be derived from these results. Learn several techniques for simulating random numbers from a probability distribution, and be able to evaluate their relative strengths and weaknesses. Learn how to implement a Monte Carlo simulation in VBA.
• The Longstaff-Schwartz model - Understand how American options may be priced using the Longstaff-Schwartz approach, which combines regression analysis and Monte Carlo simulation.
• Variance reduction techniques - Understand several techniques that may be used to reduce the computational time required for a Monte Carlo simulation. Learn how random number sequences are generated and how deterministic sequences may be used to speed up the convergence of a Monte Carlo simulation. Understand how the use of control variates and antithetic variables can reduce the standard error associated with a Monte Carlo simulation.
• VIX options - Understand how the Chicago Board Option Exchange Volatility Index (VIX) is constructed. Learn how VIX options are priced, and how they may be used to implement volatility trading strategies.
• Exotic options - Understand the properties of these highly complex options and how they may be priced with Monte Carlo simulation. Understand the concept of path-dependence. Learn how exotic options may be used to hedge market risk. The options to be covered include:
• Barrier options - Understand the properties of the different types of barrier options: up-and-in, up-and-out, down-and-in, down-and-out. Learn how these options may be used to hedge risk at a lower cost than plain vanilla options.
• Binary (digital) options - Understand the properties of the two basic types of binary options: cash-or-nothing and asset-or-nothing. Understand how the behavior of the Greeks for a binary option differs from plain vanilla options, and how this affects hedging strategies.
• Lookback options - Understand the path-dependent behavior of lookback options. Understand how lookback options are priced and why they are a more expensive alternative to plain vanilla options.
• Asian options - Learn the properties of the different types of Asian options: average price and average strike. Understand the path-dependent nature of Asian options, and the types of situations that can be successfully hedged with Asian options. Understand why Asian options are cheaper than the corresponding plain vanilla options.
• Rainbow options - Understand the features of the different types of rainbow options: maximum options, minimum options, better-of options, worst-of options, two-asset correlation options and spread options. Learn how these options may be used for hedging strategies and how they can be priced with Monte Carlo simulation. Understand how Monte Carlo simulation can be extended to price options written on two or more assets through the use of Cholesky Decomposition.

Course Sections

• Learn the properties of several types of exotic derivatives and the concept of path-dependence; then model and price the exotics.
• Specific options strategies covered include: barrier options, binary (digital) options, Peroni options, rainbow options, lookback options, Asian options, multiple-asset options and others.
• Understand how the Chicago Board Option Exchange Volatility Index (VIX) is constructed, how VIX options are priced, and how they may be used to implement volatility trading strategies.
• Utilize Monte Carlo simulation approach to pricing derivative securities, from the risk-neutral framework to Brownian Motion to Longstaff-Schwartz and alternative stochastic processes.
• Simulate and model European option prices and implement the Greeks in Excel & VBA.
• Utilize VBA for arrays, objects, properties, methods, branching & looping statements and user-defined functions and macros.

Economics - if not dismal, the “science” can certainly be frustrating. Ask yourself, do weak employment figures portend a decline in corporate profits and falling equity prices, or does it signal potential intervention from the central bank and rising equity prices? Exasperating, right?

The application of economic data to real world investment decisions often requires a secondary and even tertiary analysis of its meaning. Said differently, using economic data in the real world is more a “sentiment game” than a mathematical formula. What is a sentiment game? Keynes would describe it as a newspaper beauty contest, but more technically it’s a strategic interaction between multiple players seeking to ascertain not necessarily their interpretation of a given set of information, but the interpretation and reaction of the other players in the game.

This Global Macroeconomics course examines the practice of interpreting economic information in a way that is helpful to decision makers. We address key theoretical concepts including basic macroeconomics, the business and debt cycles, monetary and fiscal policy, and international trade; but also leave the ivory tower to examine actual economic releases and discuss not what “should” happen but what does or can happen.

The course is broadly divided into two sections: Core Concepts and Key Economic Indicators & Data Series. The Core Concepts section of the course covers introductory economic theories and models that are required background information for economic analysis. This is done through an explanation of content followed by a real world example taken from a leading financial news source. The second portion of the course looks at key economic data series including among others, employment figures, price levels, monetary policy measures, and business/consumer activity measures. We use recent economic data to make it more applicable to current investment decisions and avoid the obfuscation that often accompanies older data sets.

Students should walk away with a better understanding of basic economic theory, how it translates into real world application, and knowledge about the distribution of and meaning behind important economic indicators. This is perfect for investment decision makers looking to integrate economic analysis into their decision making process or more experienced “economists” looking for a review of key concepts.

Core Concepts

• Basic Macro: fundamental understanding of the global economy; aggregate supply/demand, gaps, stagflation, etc.
• Business & Debt Cycles: determinants of economic growth, Neoclassical vs. Keynesian economics and implications
• Monetary and Fiscal Policy: monetary vs. fiscal policy impacts and trading implications for rates trading desks
• International Trade: comparative advantage and impact of trade treaties on trading strategy
• Balance of Payments and FX: impact of balance of payments and foreign exchange trade strategies

Key Economic Indicators & Data Series:

• Understand what each indicator is, importance of and strengths and limitations of each of the following:
• Business Activity: business outlook, durable goods & factory orders report, production, capacity utilization and others
• Employment: employment cost index, employment situation, jobless claims report and related employment figures
• Real Estate: existing home sales, housing starts, new residential sales
• Prices: consumer price index, headline vs. core, producer price index
• Monetary: Federal Reserve Beige Book, Fed communications and signaling, money supply, commercial banks
• Consumer: consumer confidence index, consumer sentiment index, consumer credit report, personal income
• International and Output: international transactions, GDP, productivity and costs
• Other: commodities, 10-year government bonds, currencies, other miscellaneous indicators

This course provides an in-depth introduction to credit risk. Techniques for modeling credit transition matrices are covered in great detail, while several statistical techniques for modeling default probabilities and correlations are explored in depth. Methodologies for modeling credit portfolio risk are covered, including the asset value approach and the structural approach. Prepayment models are developed for Mortgage-Backed Securities (MBS). All models are developed in Excel/VBA.

Learning Objectives

• Excel - Learn several of Excel's specialized functions. Understand how to use Excel's add-in tools to implement advanced statistical techniques, such as regression analysis. Learn how to use Solver, Excel's optimization package.
• Visual Basic for Applications (VBA) - Learn the fundamental programming structures of the VBA language, and how it can be used to extend Excel's capabilities.
• Statistical foundations - Learn to implement Monte Carlo simulation using Excel/VBA. Learn techniques for improving the speed of convergence, including importance sampling and low-discrepancy sequences. Understand the binomial and Poisson distributions. Learn the fundamental principles of linear regression analysis, as well as Poisson regression. Understand the maximum likelihood and method of moments approaches to statistical estimation.
• Merton's model - Understand Merton's model of credit risk; learn how it is related to the Black-Scholes model and how it can be used to compute default probabilities.
• Credit ratings transition matrices - Understand the structure of a transition matrix. Learn how to estimate a transition matrix with the cohort approach and the hazard rate approach.
• Estimating default probabilities and correlations - Understand how to use linear regression analysis to estimate default probabilities. Learn how to apply Poisson regression to estimate default probabilities. Understand how the asset value approach can be used to estimate default correlations using the method of moments approach and maximum likelihood approach.
• Credit portfolio risk models - Understand different approaches to modeling credit portfolio risk. Learn how to use Monte Carlo and Quasi-Monte Carlo simulation to implement the asset value approach. Learn how the structural approach is used to explain the sources of credit risk, and how it can be implemented as an extension of the Black-Scholes option pricing model.
• Prepayment modeling - Understand the structure of Mortgage-Backed Securities (MBS) and MBS derivatives, such as Interest-Only (IO) strips and Principal-Only (PO) strips. Understand different measures of prepayment speed, such as Single Monthly Mortality (SMM), Conditional Prepayment Rate (CPR) and Absolute Prepayment Speed (ABS). Learn how to implement these measures in Excel.

Course Sections

• Implement statistical foundations, including Monte Carlo simulation using built-in native Excel functions and tools
• Understand the structure of a credit ratings transition matrix and estimate using the cohort approach and the hazard rate approach
• Estimate default probabilities and correlations, using Merton's model of credit risk, linear & Poisson regression analysis, the asset value approach (method of moments and maximum likelihood approaches)
• Simulate and model prepayment rates, incorporating the structure of MBS & related derivatives, including IO and PO strips
• Model different measures of prepayment speed, such as Single Monthly Mortality (SMM), Conditional Prepayment Rate (CPR) and Absolute Prepayment Speed (ABS)
• Utilize Excel's specialized functions, including advanced statistical techniques, and Excel's built-in optimization tools
• Code in Excel VBA: learn the fundamental programming structures and how it can be used to extend Excel's capabilities in Credit Risk Modeling

This course provides an overview of Value at Risk (VaR) modeling for a wide array of financial assets, including stocks, bonds, forward contracts, futures contracts, swaps and options. The key statistical assumptions underlying the VaR methodology are explored; several different models for computing VaR are implemented in Excel. The Delta-Normal approach is used to compute VaR for bonds, stocks and linear derivative securities, such as forwards, futures and swaps, as well as calls and puts. The Delta-Gamma approach is introduced as an alternative to computing VaR for options; this approach can capture the non-linear behavior of an option but at the cost of greater computational complexity.

Full valuation approaches to computing VaR are covered in great detail; these have the advantage of being independent of any distributional assumptions about financial assets. These approaches include Historical Simulation, Weighted Historical Simulation and Monte Carlo Simulation. Several portfolio VaR measures are demonstrated; these are designed to measure the impact of a potential trade on portfolio VaR. These measures are known as Marginal VaR, Incremental VaR and Component VaR.

The course concludes with a discussion of the strengths and weaknesses of the VaR methodology, with a consideration of several alternative possible approaches.

Learning Objectives

• Excel - Learn several advanced statistical and mathematical functions in Excel. Understand how random numbers can be generated in Excel. Understand how to implement probability distributions in Excel, including the normal distribution. Learn how Excel's add-in tools can be used to implement advanced statistical techniques. Understand Excel's specialized matrix algebra operations.
• Statistical properties of financial assets - gain an in-depth understanding of the statistical concepts that form the foundation for all risk management models, including volatility, covariance and correlation and the normal distribution.
• The Value at Risk methodology - understand the statistical foundations of the Value at Risk framework. Gain insight into how the assumptions of Value at Risk are violated in practice. Understand how to interpret the output of a Value at Risk model.
• Delta-Normal approach to VaR - understand how VaR can be computed from the volatilities and correlations among the assets in a portfolio. Understand how VaR mapping is used to measure the exposure of financial assets to various risk factors. Learn how VaR can be computed for more complex assets, including fixed income products and derivative securities.
• Delta-Gamma approach to VaR - understand how the Delta-Normal approach can be extended to capture the behavior of non-linear assets, such as options.
• Full-valuation approach to VaR - understand how VaR can be computed directly from historical data or from simulated market prices. Gain an in-depth understanding of the Historical Simulation approach, which is used to compute VaR directly from past market returns. Understand how the Weighted Historical Simulation approach more realistically allows for the decay in the impact of past prices over time. Learn how Monte Carlo simulation uses assumptions about the statistical properties of asset returns to compute VaR. Understand how Monte Carlo simulation can be extended to multiple assets through the use of Cholesky Decomposition. Understand the advantages and disadvantages of the full-valuation approaches relative to the delta-normal and delta-gamma approaches.
• Portfolio VaR measures - understand how changes in the composition of a portfolio affect VaR. Be able to implement three important measures of the sensitivity of VaR to changes in a portfolio: marginal VaR, incremental VaR and component VaR and understand how to interpret these measures.
• Extensions of VaR - understand how to compute the Expected Shortfall (ES) measure and be able to interpret it. Understand how VaR may be implemented with non-normal distributions, such as the Generalized Pareto Distribution (GPD), which can better capture the tail behavior of financial returns.

Course Sections

• Explore the statistical foundations and methodology of the VaR framework in Excel and gain insight into how the assumptions of VaR are violated in practice
• Learn the Delta-Normal, Delta-Gamma & Full Valuation approaches to compute VaR for bonds, stocks and linear and non-linear derivative securities, such as forwards, futures and swaps, as well as calls and puts
• Understand how changes in the composition of a portfolio affect VaR and implement VaR sensitivities in a portfolio: marginal, incremental and component VaR
• Comprehend extensions of VaR and how VaR may be implemented with non-normal distributions, such as the Generalized Pareto Distribution (GPD), which can better capture the tail behavior of financial returns
• Utilize Excel's advanced statistical and mathematical functions, from basics of random numbers to implementing probability distributions (including normal distribution) to Excel's specialized matrix algebra operations

This course provides an overview of portfolio modeling. The course reviews several key components of portfolio math, such as standard deviation, correlation and covariance, as well as optimization techniques. Markowitz’ formula for measuring portfolio risk is covered in detail. The equivalent matrix representation is introduced, along with Excel’s matrix algebra functions.

The Capital Asset Pricing Model (CAPM) framework is used to introduce several key concepts, such as beta and the efficient frontier. Excel Solver is used to derive the efficient frontier from a portfolio of stocks. Beta is estimated using linear regression analysis. The Capital Market Line and Security Market Line are derived, showing the relationship between risk and return in equity markets. The Sharpe Ratio is introduced as a measure of relative risk.

Learning Objectives

• Excel - Learn several advanced statistical and mathematical functions in Excel. Understand how Excel's add-in tools can be used for regression analysis. Learn how to use Excel's specialized matrix algebra operations. Understand how to optimize functions using Excel's Solver add-in.
• Portfolio math - Gain an in-depth understanding of the statistical concepts that form the foundation of portfolio theory, including expected return, standard deviation, covariance and correlation. Learn how to calculate these measures in Excel, and understand their economic significance. Learn how the inputs to a portfolio model can be estimated from historical data using Excel.
• Optimization - Learn the basic principles of constrained and unconstrained optimization using Excel's matrix algebra functions and Solver.
• Markowitz's model - Understand how Markowitz's model is used to measure the risk of a portfolio. Understand the concept of diversification and how it relates to correlation and covariance. Learn how to implement Markowitz's formula for multiple assets using Excel's built-in matrix algebra functions.
• The Capital Asset Pricing Model (CAPM) - Understand the statistical foundations of the CAPM model. Understand how beta is derived and how it is interpreted. Understand the significance of the Capital Market Line and the Security Market Line and how they may be implemented in Excel. Learn how to compute and interpret Jensen's alpha.
• The Efficient Frontier - Understand the properties of the efficient frontier and how it can be implemented using optimization techniques. Learn how to construct the efficient frontier using Excel Solver. Understand how the minimum variance portfolio and the market portfolio are constructed. Learn how to optimize the weights of the assets in a portfolio to earn a target return given any constraints on the risk of the portfolio. Learn how the ability to sell stocks short affects the efficient frontier. Understand how the availability of a risk-free asset impacts the efficient frontier. Understand how portfolio rebalancing may be used to preserve a portfolio's risk and return characteristics over time.

Course Sections

• Extend the fundamentals of CAPM to the foundations of portfolio math, such as standard deviation, correlation and covariance, as well as optimization techniques
• Learn how to easily implement Markowitz's efficient frontier methodology using Excel's matrix algebra functions and array tools to quickly calculate correlations amongst almost infinite set of securities
• Understand and quantify the concept and benefits of diversification and how risk can be reduced with a portfolio of assets
• Start with raw return data for equity securities and construct optimal stock portfolio in Excel; then layer on different asset classes including cash, fixed income and options
• Sensitize and quantify the effect of specific securities in the context of the overall portfolio: for instance, a stock may optimize the stock portfolio but not the overall diversified portfolio
• Utilize Excel to optimize portfolio construction based on maximizing returns and minimum variance mix of securities, using advanced statistical and mathematical functions

This course presents an overview of the Basel Accords and how they have evolved since their debut in 1988. The three-pillar structure is explained in great detail, with a focus on the measurement of capital requirements under Pillar 1. The Value at Risk methodology is covered in depth as a technique for computing market risk capital requirements. The key features of the approaches to computing credit risk capital are covered: the Standardized Approach, the Foundation Internal Ratings Based Approach and the Advanced Internal Ratings Based Approach.

The three approaches to computing operational risk capital are explored in detail: the Basic Indicator Approach, the Standardized Approach and the Advanced Measurement Approach. The new features of Basel III are explained, including changes to the measurement of Tier 1 and Tier 2 capital, updates to the calculation of credit risk capital and a more advanced approach to measuring liquidity risk.

Learning Objectives

• Overview of the Basel Accords - understand how the Basel Accords have evolved since being introduced in 1988. Learn how Basel II improves risk measurement and how it is organized into three pillars: determining regulatory capital for market, credit and operational risk; supervisory review and market discipline. Gain a broad understanding of the different methods that are used to compute capital requirements for market risk, credit risk and operational risk under Pillar 1. Understand the four key principles of supervisory review under Pillar 2: having a process for assessing overall capital adequacy, evaluation of banks' internal capital adequacy strategies, expecting banks to hold more capital than required, and early intervention. Understand that Pillar 3 is designed to impose market discipline on banks by requiring them to disclose key information about risk and capital holdings.
• Modeling capital requirements for market risk - understand the Value at Risk methodology and how it is used to calculate capital requirements under the Basel Accords.
• Modeling capital requirements for credit risk - learn how the Standardized Approach assigns risk weights to different types of assets, such as claims against corporations, loans to individuals and small businesses, residential and commercial real estate loans and claims against sovereign governments and central banks. Understand how the Standardized Approach incorporates several risk mitigating techniques, such as collateral, netting and credit derivatives. Understand how the Foundation Internal Ratings Based (IRB) Approach enables banks to use their own estimates of default probabilities, while the Advanced Internal Ratings Based Approach allows banks to estimate their own default probabilities, loss given default, exposure at default and effective maturity for each exposure.
• Measuring capital requirements for operational risk - understand how the Basic Indicator Approach computes the operational capital charge as 15% of a bank's average gross income. Learn how the Standardized Approach divides a bank's activities into eight business lines, and weights each with a risk factor. Learn how the Advanced Measurement Approach enables a bank to use internal data to determine the appropriate operational risk capital charge.
• Basel III - understand the changes that will occur under Basel III. These include updated definitions for Tier 1 and Tier 2 capital, the risk-based capital ratio, countercyclical capital buffers, changes to the Standardized and IRB approaches to credit risk and the measurement of liquidity risk.