Week 1. A Brief Introduction to Derivatives and Financial Markets
    A.    Derivative Securities: A Brief Introduction
    B.    Financial Securities, Instruments and Markets: A Brief Review
      Securities and Instruments
      Financial Markets
      Market Efficiency
    C.    Introduction to Commodities, Forward and Futures Markets
      Commodities
      Forward and Futures Contracts
      Futures Contracts and Business Risk
    D.    Introduction to Options Contracts and Markets
      European and American Options
      Options Markets
    E.    Introduction to Swaps and Other Derivative Instruments
      Swap Contracts
      Collateralized Debt Obligations
    F.    The Dark Side of Derivatives

Week 2. Pricing, Returns, Arbitrage and No Arbitrage Models (Will overlap into Week 3)
    A.    Brief Review of Time Value
      Yield Curves
      The Term Structure of Interest Rates
    B.    Arbitrage and No-Arbitrage
    C.    Probability and Risk
      Sets and Measures
      Probability Spaces
      Random Variables
      Conditional Probability
    D.    Discrete State Models
      Outcomes, Payoffs and Pure Securities
      Spanning and Complete Markets
      Arbitrage and No Arbitrage Revisited
      The Equivalent Martingale: Synthetic Probabilities
      The Risk Neutrality Argument
      Binomial Option Pricing: One Time Period
      Put-Call Parity: One Time Period
      Completing the State Space
    E.    Discrete Time-Space Models
      Discrete Time Models
      Multiple Time Periods and States: Illustration

Week 3. Continuous Time and Continuous State Models (Will overlap into Week 4)
    A.    Continuous Time Payment Models
      Single Payment Model
      Pricing a Bond with a Deterministic Continuous Rate
    B.    Differential Equations in Financial Modeling: An Introduction
      Separable Differential Equations and Growth Models
      Security Returns in Continuous Time
      Mean Reverting Interest Rates
    C.    Continuous State Models
      Option Pricing: The Elements
      Expected Values of European Options
      Call Options and Uniformly Distributed Stock Prices

Week 4. Structure and Mechanics of Forward and Futures Markets
    A.    Forward Contracts and Markets
      Forward Market Risks
      Forward Market Regulation
    B.    Futures Contracts and Markets
      Futures Market Risks
      Currency and Interest Rate Futures Markets
    C.    Order Types and Liquidity
      Orders
      Liquidity
    D.    Futures Clearing and Settlement
      Trade Confirmation and Comparison
      Novation and Netting
      Trade Settlement
    E.    Regulation of Futures Markets
      Major Legislation
      The Commodity Futures Trading Commission
    F.    Prediction Markets

Week 4. Pricing and Hedging with Forward and Futures Contracts (Will overlap into Week 5)
    A.    Pricing Forward Contracts
      The Expectations Hypothesis
      Contango
      Backwardation
      The Net Hedging Hypothesis
    B.    Forward and Futures Market Complications
      Dividends
      Carry Costs
      FX and Interest Rates: Interest Rate Parity

Week 5. Structure and Mechanics of Options Markets (Will also include Section 7.A from Week 6 following)
    A.    Option Contract Fundamentals
      Option Payoff Functions
      Minimum Option Market Values
    B.    Options Exchanges
      Options Technology
      Options Clearing

Week 6. Stochastic Processes: Introduction for Option Pricing
    A.    Random Walks and Martingales
      Stochastic Processes: A Brief Introduction
      Random Walks and Markov Processes
      Martingales and Submartingales
      Equivalent Probabilities and Equivalent Martingale Measures
    B.    Binomial Processes: Characteristics and Modeling
      Binomial Processes
      Binomial Returns Process
      Illustration: Binomial Outcome and Event Spaces
      Pure Security Prices
      Physical Probabilities, the Equivalent Martingale Measure and Change of Numeraire
      Binomial Pricing, Change of Numeraire and Martingales
    C.    Brownian Motion and Itô Processes
      Brownian Motion Processes
      Brownian Motion Processes with Drift
    Itô Processes
    D.    Option Pricing: A Heuristic Derivation of Black-Scholes
      Estimating Exercise Probability in a Black-Scholes Environment
      The Expected Expiry Date Call Value
      Observations Concerning N(d1), N(d2) and c0

Week 7: QUIZ

Week 8. Binomial Option Pricing
    A.    Binomial Option Pricing: One Period Case
      The Hedge Ratio
      Pricing the Call in the One Period Case
      Risk-Neutral Setting: One-Period Case
      Illustration: Binomial Option Pricing - One Period Case
    B.    Multi-Period Framework
      Extending the Binomial Model to Two Periods
    C.    Multiplicative Upward and Downward Movements in Practice
      The Binomial Model in Practice: An Illustration
      Dividing an Interval Into Sub-Intervals

Week 9. Fundamentals of Stochastic Calculus
    A.    Stochastic Calculus: An Introduction
      Differentials of Stochastic Processes
      Stochastic Integration
      Elementary Properties of Stochastic Integrals
    B.    A digression on Taylor Series Expansions
      Taylor Series and Two Independent Variables
      Taylor Series and the Differential Notation
    C.    Itô's Lemma
      The Itô Process
    Itô's formula
    Itô's Lemma
      Applying Itô's Lemma
      Application: Geometric Brownian Motion

Week 10. The Black-Scholes Model
    A.    Preliminaries
      Self-Financing Strategies and Portfolios
      Pricing a European Call Option and the Black-Scholes Formula
    B.    Deriving the Black-Scholes Model
      Black-Scholes Assumptions
      The Self-Financing Replicating Portfolio and Black-Scholes
      The Black-Scholes Model
      Put-Call Parity
      The Black-Scholes Model: Simple Numerical Illustrations
    B.    Simple Numerical Illustrations
    C.    Implied Volatility
      The Method of Bisection
      The Newton Raphson Method
      Smiles, Smirks and Aggregating Procedures
    D.    Empirical Evidence
      The Black-Scholes Study
      The Galai and Bhattacharya Studies
      Smiles and Smirks
      Put-Call Parity

Week 11. The Greeks, Dividend Adjustments and Early Exercise
    A.    The Greeks
      Greeks Calculations for Calls
      Greeks Calculations for Puts
    B.    The Black-Scholes Model and Dividend Adjustments
      The European Known Dividend Model
      Modeling American Calls
      Black's Pseudo-American Call Model
    C.    Merton's Continuous Leakage Formula

Week 12. Beyond Plain Vanilla Options on Stock
    A.    Compound Options
      Estimating Exercise Probabilities
      Valuing the Compound Call
      The Roll-Geske-Whaley Compound Option Formula
      Put-Call Parity for Compound Options
    B.    Changing the Pricing Numeraire
    C.    Exchange Options
      The Margrabe Model
      The Garman- Köhlagen Model
    D.    Hedging Exchange Exposure with Currency Options
    E.    Exotic Options
      Locking in Profits
      Path Dependent Options
      Other Exotic Options

Week 13. Other Derivatives and Markets
    A.    Swap Contracts
      Equity Swaps
      Total Return Swaps
      Regulation of Swap Markets
    B.    Structured Finance and Derivative Instruments
      Securitized Instruments
      Pass-through Securities
      Collateralized Debt Obligations
      Credit Derivatives
      Interest Rate Derivatives
    C.    ADRs
    D.    Hybrids
      Warrants
      Convertible and Callable Bonds
    E.    Index Contracts
      Index Options
      Index Construction
      Portfolio Insurance and Program Trading
    F.    Volatility Index Contracts

 
Week 15: EXAM, May