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Practical Methods of Financial Engineering and Risk Management

Book Description

Risk control, capital allocation, and realistic derivative pricing and hedging are critical concerns for major financial institutions and individual traders alike. Events from the collapse of Lehman Brothers to the Greek sovereign debt crisis demonstrate the urgent and abiding need for statistical tools adequate to measure and anticipate the amplitude of potential swings in the financial market's from ordinary stock price and interest rate moves, to defaults, to those increasingly frequent "rare events" fashionably called black swan events. Yet many on Wall Street continue to rely on standard models based on artificially simplified assumptions that can lead to systematic (and sometimes catastrophic) underestimation of real risks.

In Practical Methods of Financial Engineering and Risk Management, Dr. Rupak Chatterjee former director of the multi-asset quantitative research group at Citiintroduces finance professionals and advanced students to the latest concepts, tools, valuation techniques, and analytic measures being deployed by the more discerning and responsive Wall Street practitioners, on all operational scales from day trading to institutional strategy, to model and analyze more faithfully the real behavior and risk exposure of financial markets in the cold light of the post-2008 realities. Until one masters this modern skill set, one cannot allocate risk capital properly, price and hedge derivative securities realistically, or risk-manage positions from the multiple perspectives of market risk, credit risk, counterparty risk, and systemic risk.

The book assumes a working knowledge of calculus, statistics, and Excel, but it teaches techniques from statistical analysis, probability, and stochastic processes sufficient to enable the reader to calibrate probability distributions and create the simulations that are used on Wall Street to valuate various financial instruments correctly, model the risk dimensions of trading strategies, and perform the numerically intensive analysis of risk measures required by various regulatory agencies.

Table of Contents

  1. Cover
  2. Title
  3. Copyright
  4. Dedication
  5. Contents at a Glance
  6. Contents
  7. Series Editor’s Foreword
  8. About the Author
  9. About the Technical Reviewers
  10. Acknowledgments
  11. Introduction
  12. Chapter 1: Financial Instruments
    1. Bloomberg Market Data Screens
    2. Cash Instruments
      1. Fed Funds
      2. Eurodollar Deposits
      3. US Treasury Bills, Notes, and Bonds
      4. Repo and Reverse Repo
      5. Equity Indices
      6. Commercial Paper
      7. LIBOR
      8. Spot Forex
      9. Key Rates
      10. Gold
    3. Futures and Swaps
      1. Crude Oil
      2. Fed Funds Futures
      3. 90-Day Eurodollar Futures
      4. 10-Year Treasury Note Futures
      5. Swaps
      6. Swap Valuation
      7. Swap Spreads
      8. Swap Futures
    4. Derivatives and Structured Products
      1. Dynamic Hedging and Replication
      2. Implied Volatility
      3. Caps and Floors
      4. Market Implied Volatility Quotes for Caps and Floors
      5. Swaptions
      6. Mortgage-Backed Securities
    5. Appendix: Daycount Conventions
    6. Problems
    7. Further Reading
  13. Chapter 2: Building a Yield Curve
    1. Overview of Yield Curve Construction
    2. Cash LIBOR Rates
    3. 90D Eurodollar Futures
    4. Swaps
    5. Generic Discount Factors
    6. Problems
      1. Problem 2.1: Build a Simple Yield Curve
    7. Further Reading
  14. Chapter 3: Statistical Analysis of Financial Data
    1. Tools in Probability Theory
      1. Moments of a Distribution
    2. Creating Random Variables and Distributions
      1. The Inverse Transform Method
      2. Creating a Density Function: Histograms and Frequencies
      3. Mixture of Gaussians: Creating a Distribution with High Kurtosis
      4. Skew Normal Distribution: Creating a Distribution with Skewness
    3. Calibrating Distributions through Moment Matching
      1. Calibrating a Mixed Gaussian Distribution to Equity Returns
      2. Calibrating a Generalized Student’s-t Distribution to Equity Returns
      3. Calibrating a Beta Distribution to Recovery Rates of Defaulted Bonds
    4. Basic Risk Measures
      1. Calculating VaR and CVaR from Financial Return Data
    5. The Term Structure of Statistics
      1. The Term Structure of the Mean
      2. The Term Structure of Skew
      3. The Term Structure of Kurtosis
      4. The Term Structure of Volatility
      5. The Term Structure of “Up” Volatility
      6. The Term Structure of “Down” Volatility
      7. Autocorrelation
    6. Dynamic Portfolio Allocation
      1. Modern Portfolio Theory
      2. Generic Rules to Dynamic Portfolio Allocation with Volatility Targets
    7. Appendix. Joint Distributions and Correlation
      1. Joint Distribution Function
      2. Joint Density Function
      3. Marginal Distribution Function
      4. Independence
      5. Covariance and Correlation
      6. Cauchy-Schwarz Inequality
      7. Conditional Distribution and Density Functions
      8. Conditional Expectation
      9. Convolution
    8. Problems
      1. Problem 3-1. Create a Gaussian Random Number Generator in Excel
      2. Problem 3-2. Create a Mixture of Gaussians in Excel
      3. Problem 3-3. Calibrate S&P 500 Returns to a Mixed Normal in Excel
      4. Problem 3-4. Calibrate SX5E Returns to a Student’s-t distribution in Excel
      5. Problem 3-5. Create a Skew Normal Distribution in Excel
      6. Problem 3-6. VaR and CVaR
      7. Problem 3-7. Term Structure of Statistics
    9. References
  15. Chapter 4: Stochastic Processes
    1. Stochastic Calculus
      1. Wiener Stochastic Process
      2. Quadratic Variation
      3. Stochastic Integrals
    2. Geometric Brownian Motion and Monte Carlo Simulations
      1. Creating Random Stock Paths in Excel
    3. GARCH Process for Stock Returns
      1. GARCH(1,1)
      2. The GARCH(1,1) Model for the “Traditional” Term Structure of Volatility
    4. Statistical Modeling of Trading Strategies
      1. Pairs Trading
      2. Models for Residuals: Mean Reverting Ornstein-Uhlenbeck Process
      3. Equilibrium Statistics
      4. ETF Factor-Neutral Calibration and Trading Strategy
      5. Including the Drift Term
      6. Hints for Constructing Market-Neutral Portfolios
      7. The Rolling NAV Equation
    5. Appendix A. Black-Scholes with Holes
    6. Appendix B. Moment Matching and Binomial Trees
    7. Problems
      1. Problem 4-1. Create a Brownian Motion Process for Stock Returns Using Monte Carlo Simulations in Excel
      2. Problem 4-2. Ito’s Lemma
      3. Problem 4-3. Calibrate a GARCH(1,1) Process for SX5E
      4. Problem 4-4. Create a GARCH(1,1) Simulator in Excel
      5. Problem 4-5. Volume Adjustment for Pairs Trading for MCD versus XLY
    8. References
  16. Chapter 5: Optimal Hedging Monte Carlo Methods
    1. Dynamic Hedging and Replication
    2. Wealth Change Equations: Spot, Forwards, and Options
      1. Forward Contracts
      2. European Options
    3. The OHMC Optimization Problem and Solution Methodology
      1. The OHMC Optimization Problem
      2. The OHMC Technique
      3. Basis Function Expansions and the Lagrange Multiplier Technique
    4. Risk Capital
    5. The OHMC Examples
      1. Hedge Fund Index: GARCH Calibration to Daily Returns
      2. Option Pricing: Hedge Fund Index: 1.20Yr 110% Strike Call, 2 Day Liquidity
      3. Option Pricing: Hedge Fund Index: 1.20Yr 99% Strike Put, 2 Day Liquidity
      4. Dynamic Portfolio Allocation Index: GARCH Calibration to Daily Returns
      5. Option Pricing: Dynamic Portfolio Allocation: 2.00Yr 110% Strike Call, 5 Day Liquidity
      6. Option Pricing: Dynamic Portfolio Allocation: 2.00Yr 95% Strike Put, 5 Day Liquidity
      7. Hedge Fund Index: GARCH Calibration to Monthly Returns
      8. Option Pricing: Hedge Fund Index: 3.00Yr 100% Strike Put, 3-Month Liquidity
      9. Option Pricing: Hedge Fund Index: 3.00-Yr 110% Strike Call, 3-Month Liquidity
      10. Cliquet Contracts
      11. Knockout Cliquet Sellers Wealth Change Equation
    6. Problems
      1. Problem 5-1. Linear Basis Function Expansion
      2. Problem 5-2. Hermite Cubic Basis Function Expansion
      3. Problem 5-3. One-Time-Step OHMC Problem
    7. References and Further Reading
  17. Chapter 6: Introduction to Credit Derivatives
    1. The CDS Contract: Overview
    2. The CDS Contract: Pricing
    3. Intensity-Based Reduced-Form Default Models
    4. Bootstrapping a Survival Curve with Piecewise Constant Hazard Rates
    5. Credit Triangle
    6. Quotation Conventions for Standard Contracts
    7. Par Asset Swaps
    8. Collateralization
      1. CDO2
      2. Standard CDS Indices and Tranches
    9. Correlation and Copulas
      1. Density Method
      2. Variable Method
      3. Factor Models
      4. Copulas
      5. Large Homogeneous Portfolio Approximation
      6. One-Factor Gaussian Model
      7. Implied Compound and Base Correlations
    10. Stochastic Hazard Rates
      1. Case 1: Risky Zero Coupon Discount Bond B(t) Maturing at T with No Recovery
      2. Case 2: Continuous Coupon Payment Ct until Default
      3. Case 3: Recovery Payment Rt at Default
    11. OHMC and the Static Hedging of a Risky Bond with a CDS
    12. OHMC and CDS Swaptions
    13. Appendix. Bloomberg Functionality
    14. Problems
      1. Problem 6-1. Calculate Hazard Rates from Par CDS Spreads
      2. Problem 6-2. Standard Convention Upfront Payment
      3. Problem 6-3. Generating Correlated Bivariate Normal Variables
    15. References
  18. Chapter 7: Risk Types, CVA, Basel III, and OIS Discounting
    1. Risk Types
      1. Market Risk
      2. Credit Risk
      3. Operational Risk
      4. Liquidity Risk
      5. Systemic Risk
    2. Coherent Risk Measures
    3. Regulation and Its Effects
    4. Accounting Credit Valuation Adjustment (CVA)
      1. Wrong-Way Risk
    5. Basel I
    6. Basel II
      1. CCR RWA
      2. Market Risk RWA
      3. Operational Risk RWA
    7. Basel III
      1. Capital Requirements under Basel III
    8. EAD and EPE Profiles
    9. Portfolio CCR Aggregation, Netting Sets, and Collateral Margin
      1. Initial Margin
      2. Variation Margin
      3. Margin Period of Risk
      4. Margin Threshold
      5. Minimum Transfer Amount
    10. OIS Discounting
      1. Calculating “Adjusted” Forward LIBOR Rates from OIS Curves and Basis Swaps
    11. References
  19. Chapter 8: Power Laws and Extreme Value Theory
    1. Power Laws and Scaling
      1. Moments
      2. Extrapolation
      3. Power-Law Monte Carlo Simulation
      4. Maximum Likelihood Calibration
    2. Extreme Value Theory
      1. Maximum Likelihood Calibration for the GPD
      2. The Power-Law Equivalence of the GPD
    3. VaR and CVaR
    4. Problems
      1. Problem 8-1. Power-Law MC Simulation in Excel
      2. Problem 8-2. The Power-Law Nature of the GPD
    5. References
  20. Chapter 9: Hedge Fund Replication
    1. Overview of Hedge Fund Styles
    2. Replicating Methodologies
    3. A Heuristic Example
    4. Replication through Kalman Filtering
      1. Process Model
      2. Measurement Model
      3. Kalman Filter
      4. Time Update with an Initial Prediction
      5. Measurement (Observation) Update with Kalman Filter Correction
    5. References
  21. Index