Advanced Options and Financial Derivatives Course

Course Description

This advanced course on options and financial derivatives offers a comprehensive exploration of risk management applications in finance. Taught by a Caltech professor, it provides an in-depth understanding of option pricing models and equips students with the knowledge to further their studies in this field independently.

The course begins with discrete-time, binomial trees models before delving into continuous-time, Brownian Motion driven models. Students will receive a foundational introduction to Stochastic and Ito Calculus, crucial components in understanding modern financial theory. The Black-Scholes-Merton pricing model serves as the benchmark, but the course also covers more advanced concepts like stochastic volatility models.

Throughout the course, students will explore both Partial Differential Equations and probabilistic, martingale approaches to financial modeling. The curriculum also includes an introduction to interest rate modeling and fixed income derivatives, providing a well-rounded understanding of financial instruments and their pricing mechanisms.

What Students Will Learn

• Option pricing and risk-hedging methods in binomial tree and Black-Scholes-Merton models
• Advanced techniques for pricing options and other financial derivatives beyond Black-Scholes-Merton
• Interest rate models and the pricing of interest rate derivatives
• Evaluation of the economic and mathematical principles underlying financial models
• Application of Stochastic and Ito Calculus in financial modeling
• Understanding of continuous-time, Brownian Motion driven models
• Proficiency in both Partial Differential Equations and martingale approaches

Prerequisites

• Working knowledge of basic calculus
• Solid understanding of statistics and probability
• Interest in mathematical modeling
• Willingness to engage in challenging coursework and dedicate serious effort

Course Content

• Discrete-time, binomial trees models
• Continuous-time, Brownian Motion driven models
• Introduction to Stochastic and Ito Calculus
• Black-Scholes-Merton pricing model
• Stochastic volatility models
• Partial Differential Equations approach
• Probabilistic, martingale approach
• Interest rate modeling
• Fixed income derivatives

Who This Course Is For

This course is ideal for advanced undergraduate students, graduate students, or professionals in finance, economics, or related fields who want to deepen their understanding of options and financial derivatives. It's particularly suitable for those who enjoy mathematical challenges and are interested in the intersection of finance and advanced mathematics.

Real-World Applications

The skills acquired in this course are highly valuable in various financial sector roles, including:

• Risk management in banks, hedge funds, and other financial institutions
• Derivatives trading and pricing
• Financial product development
• Quantitative analysis and modeling
• Investment strategy formulation
• Economic forecasting and policy analysis
• Academic research in financial economics

These skills enable professionals to make informed decisions about complex financial instruments, develop sophisticated risk management strategies, and contribute to the ongoing evolution of financial markets.

Syllabus Overview

A detailed syllabus is not provided, but based on the course description, the syllabus likely includes sections on:

1. Introduction to options and financial derivatives
2. Discrete-time models and binomial trees
3. Continuous-time models and Brownian Motion
4. Stochastic and Ito Calculus
5. Black-Scholes-Merton model
6. Advanced option pricing models
7. Partial Differential Equations approach
8. Martingale approach
9. Interest rate modeling
10. Fixed income derivatives

Students are encouraged to refer to Unit 0 in the Course Outline for a prerequisites assessment and potentially more detailed syllabus information.