This is an introductory course on options and other financial derivatives, and their applications to risk management. We will start with defining derivatives and options, continue with discrete-time, binomial tree models, and then develop continuous-time, Brownian Motion models. A basic introduction to Stochastic, Ito Calculus will be given. The benchmark model will be the Black-Scholes-Merton pricing model, but we will also discuss more general models, such as stochastic volatility models. We will discuss both the Partial Differential Equations approach, and the probabilistic, martingale approach. We will also cover an introduction to modeling of interest rates and fixed income derivatives.

Offered By

## Pricing Options with Mathematical Models

Caltech## About this Course

Prior experience with calculus based probability/statistics. Some exposure to stochastic processes and partial differential equations is helpful.

## Instructor

Prior experience with calculus based probability/statistics. Some exposure to stochastic processes and partial differential equations is helpful.

## Offered by

### Caltech

Caltech is a world-renowned science and engineering research and education institution, where extraordinary faculty and students seek answers to complex questions, discover new knowledge, lead innovation, and transform our future. Caltech's mission is to expand human knowledge and benefit society through research integrated with education. We investigate the most challenging, fundamental problems in science and technology in a singularly collegial, interdisciplinary atmosphere, while educating outstanding students to become creative members of society.

## Syllabus - What you will learn from this course

**2 hours to complete**

## Unit 0: Pre-course

Since this is a quantitative course, a certain level of mathematical background is necessary for a student to master the course material. In this unit, I would like to invite you to take the prerequisites assessment.

**2 hours to complete**

**6 hours to complete**

## Unit 1. Stocks, Bonds, Derivatives

**6 hours to complete**

**5 hours to complete**

## Unit 2. Interest Rates, Forward Rates, Bond Yields

**5 hours to complete**

**8 hours to complete**

## Unit 3. No-Arbitrage Pricing Relations

**8 hours to complete**

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