Introduction to Derivative Pricing

SI 527 (Spring 2026) Course Details

Study Material

Chapter 1: Overview of Financial Systems (Included in Quiz 1 and Midsem Exam)
Financial System: An Overview
Financial Market Framework
Financial Instruments
Securities
Market Levels
Market Segments
Trading Mechanism
Market Participants
Market Makers
Investors
Speculators
Hedgers
Arbitrageurs
Overview of Derivatives
Essential Market Terms
Purpose of Derivatives
Need for Pricing Models and Analysis
Non-Contingent Claims: Forwards, Futures, and Swaps
Forwards and Futures
Swaps
Contingent Claims: Options
Chapter 2: Price Dynamics (Included in Quiz 1 and Midsem Exam) (Section Interest-rate Models is included in Quiz 2)
Price Dynamics
Deterministic Interest-rate Models
Discrete Time Models
Continuous Time Model
Non-constant Interest Rate
Present Value
Cash Flow Stream
Stochastic Models
Stochastic Processes
Stock Price Model
Wiener Process
Itô Formula
Parameter Calibration
Interest-rate Models
Wiener Integral
Numerical Simulation
Distribution of the stochastic increment
Exact simulation scheme
Chapter 3: Portfolio And Arbitrage (Included in Quiz 2 and Midsem Exam)
Portfolio and Arbitrage
Portfolio Concepts
Value and Gain Processes
Market Model
Predictable Strategy
Self-financing Strategy
Arbitrage Opportunity
Arbitrage Portfolio
Application: Forward Pricing
Law of One Price
Arbitrage Strategy
Application: Future Contracts
Marking to Market
Pricing Model
Chapter 4: Basic Concepts of Options (Included in Quiz 2 and Midsem Exam)
Basic Concepts of Options
Basic Terminology
Defining Parameters
Payoff and Gain
Time Value in an Option Price
Premium Bounds and Arbitrage Opportunities
European Options
American Options
Put-Call Parity Estimates
Premium Valuation
Chapter 5: Discrete Time Models (Included in Quiz 3 and Endsem Exam)
Discrete Time Models
Single-Step Binomial Model
Underlying Model
Risk-neutral Probability
European Option Pricing Model
Multi-step Binomial Model
Stock Price Model
European Option Pricing Model
Generalization to Multi-step Method
Logarithmic Return Model
Application to Binomial Model
Hedge Strategy
Pricing for American Options
Exotic Options
Chapter 6: Discrete Martingale Theory (Included in Quiz 3 and Endsem Exam)
Discrete Martingale Theory
Basic Concepts
Normalized Market and Numéraire
Characterization of Self-financing condition
Conditional Expectation
Martingale Process and Measure
Discrete Martingale Process
Fundamental Theorem of Asset Pricing
General Pricing Model
Chapter 7: Continuous Time Model (Included in Quiz 4 and Endsem Exam)
Continuous Time Models
Stock Price Models
Lognormal Model
Brownian Motion
Option Pricing Model
Black-Scholes Formula
Black-Scholes Differential Equation
Continuous-Time Martingale Pricing
Martingale Representation Theorem
Girsanov's Theorem
Feynman-Kac
Chapter 8: Hedging With Options (Included in Quiz 4 and Endsem Exam)
Hedging and Trading Strategies
Greeks and Hedging
Delta
Delta Hedge
Gamma
Theta
Vega
Rho
Option Trading Strategies
Spreads
Bull Spread
Bear Spread
Butterfly Spread
Volatility Speculation
Straddle
Strangle

References

General Instructions