Pricing Options with Mathematical Models

Go to Course: https://www.coursera.org/learn/pricing-options-with-mathematical-models

Introduction

### Course Review: Pricing Options with Mathematical Models #### Course Overview "Pricing Options with Mathematical Models" is an enlightening course offered through Coursera that introduces students to the complex world of options and other financial derivatives, emphasizing their pivotal role in risk management. With a comprehensive curriculum, this course guides learners through essential concepts, beginning with the definition of derivatives and options before delving into various pricing models. Students will engage with discrete-time frameworks, such as binomial tree models, and progress to continuous-time models featuring Brownian motion. Moreover, a foundational introduction to Stochastic calculus, including Ito calculus, is provided, equipping students with the necessary mathematical tools for understanding sophisticated pricing models like the Black-Scholes-Merton framework. The curriculum also explores more advanced topics such as stochastic volatility models, making it suitable for individuals eager to deepen their understanding of financial instruments. #### Detailed Syllabus Breakdown **Unit 0: Pre-course** Recognizing that this is a quantitative course, this introductory unit invites students to assess their mathematical background to ensure preparedness for the material to come. This step is crucial as it sets the foundation for mastering the course content. **Unit 1: Stocks, Bonds, Derivatives** Students will familiarize themselves with the core securities used in financial markets, including stocks, bonds, and derivatives, establishing a fundamental understanding before diving into more complex topics. **Unit 2: Interest Rates, Forward Rates, Bond Yields** This unit examines the critical role of interest rates in finance, explaining how forward rates and bond yields can influence options pricing. **Unit 3: No-Arbitrage Pricing Relations** Here, students learn about the concept of no-arbitrage, a cornerstone of financial theory that helps in establishing fair pricing of derivatives. **Unit 4: Pricing in Discrete Time Models** The course introduces discrete-time models, prominently featuring binomial trees, which offer a hands-on approach to understanding the mechanics behind options pricing. **Unit 5: Brownian Motion and Ito Calculus** A dive into continuous-time models begins here, with students learning about Brownian motion, a critical concept for modeling stock prices, and an introduction to Ito calculus, providing insights into stochastic processes. **Unit 6: Pricing in the Black-Scholes-Merton Model** Students will engage deeply with the Black-Scholes-Merton pricing model, which revolutionized options trading, gaining insights into its assumptions and applications. **Unit 7: Extensions of Black-Scholes-Merton** This unit expands on the previous one, discussing more complex scenarios that challenge the assumptions of the basic model, enhancing the learner's analytical capabilities. **Unit 8: Hedging** An essential aspect of risk management, this unit covers various hedging strategies that can be employed to mitigate risks associated with options trading. **Unit 9: Beyond Black-Scholes-Merton** Students explore alternative models and theories that have emerged since the introduction of the Black-Scholes-Merton framework, critical for understanding contemporary pricing strategies. **Unit 10: Pricing in Fixed Income Markets** Finally, the course concludes with a broader view of pricing within fixed income markets, rounding out the student’s education on financial instruments. **Final Exam** The course culminates with a final exam, ensuring that students can demonstrate their understanding and mastery of the material covered throughout the course. Note that the number of attempts is limited, adding an element of challenge and focus. #### Recommendation I highly recommend "Pricing Options with Mathematical Models" for anyone looking to enhance their understanding of financial derivatives, particularly students and professionals in finance, economics, and related fields. With its well-structured syllabus, the course is designed to provide a balanced combination of theoretical knowledge and practical application, making it an excellent choice for newcomers as well as those seeking to deepen their expertise. The insights gained from this course will be invaluable for risk management, trading, or any career that involves financial modeling and derivatives. The opportunity to learn from expert instructors and engage with mathematical models through practical examples is a significant advantage that this course offers. Whether you are entering the world of finance or looking to sharpen your skills, "Pricing Options with Mathematical Models" will not only equip you with critical knowledge but also enhance your confidence in navigating the complex landscape of financial derivatives. Enroll today to start your journey into the intricate world of options pricing!

Syllabus

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.