Module 6 - Fixed Income & Credit

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In the first part of module six, we will review the multitude of interest rate models used within the industry, focusing on the implementation and limitations of each model. In the second part, you will learn about credit and how credit risk models are used in quant finance, including structural, reduced form as well as copula models.

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Sections

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Fixed Income Products and Analysis

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  • Names and Properties of the basic and most important Fixed-income Products
  • Features commonly found in Fixed-income Products
  • Simple ways to Analyze the Market Value of the Instruments: Yield, Duration and Convexity
  • How to construct yield curves and forward rates
  • Swaps
  • The Relationship between Swaps and Zero-coupon Bonds

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Stochastic Interest Rate Modeling

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  • Stochastic models for Interest Rates
  • How to derive the pricing equation for many Fixed-income Products
  • The Structure of many popular one-factor Interest Rate Models
  • The Theoretical Framework for multi-factor Interest Rate Modeling
  • Popular two-factor Models

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Calibration and Data Analysis

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  • How to choose time-dependent parameters in one-factor models so that
  • Today’s yield curve is an output of the model
  • The advantages and disadvantages of yield curve fitting
  • How to analyze short-term interest rates to determine the best model for the volatility and the real drift
  • How to analyze the slope of the yield curve to get information about the market price of risk

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Probabilistic Methods for Interest Rates

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  • The Pricing of Interest Rate Products on a Probabilistic Setting
  • The Equivalent Martingale Measures
  • The Fundamental Asset Pricing Formula for Bonds
  • Application for Popular Interest Rates Models
  • The Dynamics of Bond Prices
  • The Forward Measure
  • The Fundamental Asset Pricing Formula for Derivatives on Bonds
     

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Heath Jarrow and Morton Model

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  • The Heath, Jarrow & Morton (HJM) Forward Rate Model
  • The Relationship between HJM and Spot Rate Models
  • The Advantages and Disadvantages of the HJM Approach
  • How to Decompose the Random Movements of the Forward Rate Curve into its Principal Components

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The Libor Market Model

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  • The Libor Market Model
  • The Market view of the Yield Curve
  • Yield Curve Discretisation
  • Standard Libor Market Model Dynamics
  • Numéraire and Measure
  • The Drift
  • Factor Reduction

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Further Monte Carlo

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  • The Connection to Statistics
  • The Basic Monte Carlo Algorithm, Standard Error and Uniform Variates
  • Non-Uniform Variates, Efficiency Ratio and Yield
  • Co-Dependence in Multiple Dimensions
  • Wiener Path Construction; Poisson Path Construction
  • Numerical Integration for Solving Sdes
  • Variance Reduction Techniques
  • Sensitivity Calculations
  • Weighted Monte Carlo

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Volatility Smiles and the SABR Model

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  • Vanilla options: European Swaptions, Caps, and Floors
  • Arbitrage Free SABR

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Co-Integration for Trading

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  • Multivariate Time Series Analysis
  • Stationary and Unit Root
  • Vector Autoregression Model (VAR)
  • Co-Integrating Relationships and their Rank
  • Vector Error Correction Model (VECM)
  • Reduced Rand Model (Regression) Estimation: Johansen Procedure
  • Stochastic Modeling of Autoregression: Orstein-Uhlenbeck Process
  • Statistical Arbitrage using Mean Reversion
     

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Credit Derivatives & Structural Models

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  • Introduction to Credit Risk 
  • Modelling Credit Risk
  • Basic Structural Models: Merton Model, Black and Cox Model
  • Advanced Structural Models

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Credit Default Swaps

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An Introduction to CDS
Default Modelling Toolkit. Inhomogenous Poisson Process
CDS Pricing: Basic and Advanced Models
Bootstrapping Intensity from CDS Market Quotes
Accruals and Upfront Premium in CDS Pricing

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Intensity Models

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  • Modelling Default by Poisson Process
  • Relationship between Intensity and Arrival Time of Default
  • Risky Bond Pricing: Constant vs. Stochastic Hazard Rate
  • Bond Pricing with Recovery
  • Theory of Affine Models
  • Affine Intensity Models and use of Feynman-Kac
  • Two-factor Affine Intensity Model example: Vasicek
     

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CDO & Correlation Sensitivity

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  • CDO Market Pricing and Risk Management
  • Loss Function and CDO Pricing Equation
  • Motivation from Loss Distribution
  • What Is Copula Function
  • Classification of Copula Functions
  • Simulating Via Gaussian Copula
  • 3 Gaussian Copula Factor Mode
  • The Meaning of Correlation. Intuition and Timescale
  • Linear Correlation and Its Misuse
  • Rank Correlation
  • Correlation in Exotic Options
  • Uncertain Correlation Model for Mezzanine Tranche
  • Compound (Implied) Correlation in Loss Distribution

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X-Valuation Adjustment

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  • Historical Development of OTC Derivatives and Xva
  • Credit and Debt Value Adjustments (CVA and DVA)
  • Funding Value Adjustment (FVA)
  • Margin and Capital Value Adjustments (MVA and KVA)
  • Current Market Practice and Application
  • Implementation of Counterparty Credit Valuation Adjustment (CVA)
  • Review the Numerical Methodologies Currently Used to Quantify CVA in terms of Exposure and Monte Carlo Simulation and the Libor Market Model
  • Illustrate this Methodology as well as DVA, FVA and others

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Lecture order and content may occasionally change due to circumstances beyond our control; however this will never affect the quality of the program.

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Data Science & Machine Learning ll
Advanced Electives