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Quantitative Methods for Finance

Prof. Sanjiv R. Das

(My main web page)

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• Contents
• Overview
• Software and Data
  
  • Using R and Excel
  • Sources of Financial Data
  • Representing Financial Data
    
• Basic Concepts
  
  • Interest Rates and Exchange Rates
  • Forward Exchange Rates
  • Descriptive Statistics
    
• Stochastic Processes and Dynamics
  
  • Equities
  • Interest Rates
    
• Statistics
  
  • Arithmetic and Geometric Mean
  • Samples and Populations
  • Covariance and Correlation
  • Recap Basic Formulae
  • Difference of Means
    
• Regression Analysis
  
  • Testing the CAPM
    
• Vector Algebra for Portfolios
  
  • Portfolio Moments
  • Generating the portfolio frontier by simulation
  • Regression
  • Regression using Matrices
  • Diversification - Independent Returns
  • Diversification - Dependent Returns
  • Recap: Basic Matrix Operations
    
    • Multidimensional arrays
    • Transpose
    • Inverse and Matrix Multiplication
      
  • Solving Systems of Equations
  • Markov Chains
  • Multiple Period Chains
  • Credit Transition Matrices
  • Input-Output Matrices
    
• Basic Bond Math
  
  • Exponentials
  • Compounding and Discounting
  • The physical world and http://algo.scu.edu/~sanjivdas/q115/img1.png
  • Calculus and http://algo.scu.edu/~sanjivdas/q115/img1.png
  • Pricing discount bonds
  • Logarithms
  • Discounted Cash Flow for Projects
    
• Term Structure of Interest Rates
  
  • Yield-to-Maturity
  • Pricing by Replication
  • Discount Function
  • Zero-Coupon Rate (ZCR)
  • Forward Rate
  • Bootstrapping Yield Curves
  • Duration and Bond Portfolio Risk
  • Smoothing the Yield Curve using the Nelson-Siegel (NS) technique
    
• Bayes' Rule
  
  • The NYSE
  • Application to specialist's Bayesian updating of bid-ask spreads
    
• Revisiting Basic Calculus
  
  • Differentials
  • Integrals
  • Symbolic Math using Mathematical Packages
  • Differential Equations: Simple Concepts
    
• Hypothesis Testing
  
  • Normal Distribution
  • Poisson Distribution
  • Null Hypothesis
  • Type I and Type II Errors
  • Power of a Test
    
• Value-at-Risk (VaR)
  
  • Capital Adequacy
  • Limitations
  • Methods
  • Risk Decomposition
  • Hedging
  • Optimization
  • Coherence
  • Related Measures
    
• CoVaR
• Extending the Regression Framework
  
  • Loading in a file and doing a regression
  • Heteroskedasticity
  • Auto-regressive models
  • Vector Auto-Regression
  • ARCH and GARCH
  • Maximum Likelihood Estimator
  • Logit
  • Probit
    
• Monte Carlo Simulation
  
  • Simulating Normal Random Variables
  • Bivariate Random Variables
  • Cholesky Decomposition
  • Stochastic Processes for Equity Prices
  • ARCH Models
  • Co-integration
  • Interest-rate Processes
  • Estimating Historical Volatility for Equities
  • Estimating Historical Volatility for Interest Rates
  • Path-dependent Options
  • Variance Reduction
  • Antithetic variate Method
  • Control variate techniques
    
• Forwards and Futures
  
  • Arbitrage
  • Forward Contract
  • Pricing Forwards
  • Commodity Forward Prices
  • Replication of a Forward Contract
  • The Need for forwards
  • Futures
  • Futures vs Forwards
    
• Basic Options Concepts
  
  • Option Definitions
  • Call Options
  • Put Options
  • Basic Trading Strategies
  • Covered Call: Long stock, short call
  • Protective Put: Long stock, long put
  • Spreads
  • Bullish Vertical Spread: Gross Payoffs
  • Bearish Vertical Spread: Gross Payoffs
  • Butterfly Spread: Gross Payoffs
  • Combinations:
  • Straddle: Gross Payoffs
  • Strip: Gross Payoffs
    
• No-Arbitrage Restrictions on Option Values
  
  • Restrictions on Call-Option Pricing
  • Relationship between http://algo.scu.edu/~sanjivdas/q115/img2.png and http://algo.scu.edu/~sanjivdas/q115/img3.png
  • Relationship between http://algo.scu.edu/~sanjivdas/q115/img2.png and http://algo.scu.edu/~sanjivdas/q115/img4.png
  • Relationship between http://algo.scu.edu/~sanjivdas/q115/img2.png and http://algo.scu.edu/~sanjivdas/q115/img5.png
  • Restrictions on Put Option Pricing
  • Comparing and Relating Options
  • European Option vs. American Option Prices
  • Put-Call Parity
  • Synthesize forward contracts with options
  • Analogy to valuing assets in a firm
    
• Replication and risk-neutral pricing
• Binomial Model Implementation
  
  • Hedge Ratio
  • The Risk-Neutral Method
  • The Two-Period Binomial Model
  • Method 1
  • Option Deltas
  • Method 2:
  • Illustrative Example
  • The http://algo.scu.edu/~sanjivdas/q115/img6.png-Period Problem
  • European Calls
  • European Put
  • Implementing the Binomial Model
  • Constructing the Binomial Tree
    
• Homework and Solutions
  
  • HW1
  • HW2
  • HW3
  • Quiz 1
    
• About this document ...
  

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Sanjiv Das 2010-02-11