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Caltech

Pricing Options with Mathematical Models

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. I teach the same class at Caltech, as an advanced undergraduate class. This means that the class may be challenging, and demand serious effort. On the other hand, successful completion of the class will provide you with a full understanding of the standard option pricing models, and will enable you to study the subject further on your own, or otherwise. Prerequisites. A basic knowledge of calculus based probability/statistics. Some exposure to stochastic processes and partial differential equations is helpful, but not mandatory. It is strongly recommended you take the prerequisites test available in Unit 0, to see if your mathematical background is strong enough for successfully completing the course. If you get less than 70% on the test, it may be more useful to work further on your math skills before taking this course. Or you can just do a part of the course.

Status: Finance
Status: Financial Modeling
IntermediateCourse69 hours

Featured reviews

GC

5.0Reviewed Sep 10, 2023

Great learning process, great videos, and great notes, but really, really hard work,

YW

4.0Reviewed Dec 20, 2021

nice course and nice professor. More examples, would be better.

AB

5.0Reviewed Jul 6, 2022

i​t was fantastic course with useful curriculum. Moreover, the problem sets were challenging and shed light on some dark issues. I really appriciate the professor Cvitanic as well!

PL

5.0Reviewed Sep 14, 2024

highly informational on option pricing models and highly recommend

SR

5.0Reviewed Oct 3, 2024

Really good foundational coverage of key option pricing concepts. Good additional industry knowledge + other relevant information such as implementation, history and context

AB

5.0Reviewed Nov 20, 2023

Great course! I just felt it went a bit too quickly towards the end, but its a great course nevertheless.

JC

5.0Reviewed Oct 14, 2024

Great course! Detailed, step by step instructions!

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