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In this course, you will :
- a review of the fundamental concepts and rules of probability and optimization
- prepare students for the course by teaching them the fundamentals of mathematics
- introduce the computation of present value (PV) on fixed income securities in an arbitrage-free setting, followed by a brief discussion of interest rate term structure.
- Students will work with swaps and options, and they will price them using the 1-period Binomial Model.
- focuses on option pricing over multiple periods using the Binomial and Black-Scholes models
Syllabus :
1. Pre-Requisite Materials
- Discrete Random Variable and Distribution
- Bayes' Theorem, Continuous Random Variable and Distribution
- Conditional Expectation and Variance
- Multivariate Distribution and Independence
- The Multivariate Normal Distribution
- Introduction to Martingale
- Martingales Example
- Introduction to Brownian Motion
- Geometric Brownian Motion
- Vector: Independence and Basis
- Vector: norm and inner Product
- Matrix: Matrix Operations
- Matrix: Linear Functions and Rank
- Linear Optimization: Hedging Problem
- Linear Optimization: Duality
- Nonlinear Optimization: Unconstrained Nonlinear Problem
- Nonlinear Optimization: Largrangian Method
2. Introduction to Basic Fixed Income Securities
- Introduction to No-Arbitrage
- Present Value of Cash Flow
- Fixed Income Instruments
- Floating Rate Bonds
- Term Structure of Interest Rates
- Forward Contracts: Introduction
- Forward Contracts: An Example
3. Introduction to Derivative Securities
- Swaps
- Futures
- Hedging Using Futures
- Futures Excel
- Options
- Properties of Options
- Introduction to Options Pricing
- A Paradox Example
- The 1-Period Binomial Model
- Option Pricing in the 1-Period Binomial Model
- Pricing Derivative Security int he 1-Period Binomial Model
4. Option Pricing in the Multi-Period Binomial Model
- The Multi-Period Binomial Model
- An Example: 3-Period Binimoal Model
- What’s Going On?
- Pricing American Options
- Replicating Strategies and Self-Financing
- Dynamic Replication and Risk-Neutral Price
- Pricing with Dividends with Binomial Model
- Pricing Forwards and Futures with Binomial model
- The Black-Scholes Model
