Advanced Topics in Derivative Pricing

Go to Course: https://www.coursera.org/learn/financial-engineering-advancedtopics

Introduction

**Course Review: Advanced Topics in Derivative Pricing on Coursera** In the ever-evolving world of finance, understanding derivatives and their pricing is paramount for anyone looking to delve into quantitative finance or risk management. Coursera's course titled **"Advanced Topics in Derivative Pricing"** offers a comprehensive exploration of these essential subjects, making it a valuable addition for both students and practitioners in the finance sector. ### Course Overview "Advanced Topics in Derivative Pricing" equips learners with a deep understanding of various derivative pricing models and risk management techniques. The course is meticulously structured, beginning with the foundational Black-Scholes model, which serves as the cornerstone for further discussions on Greeks, a set of metrics crucial for evaluating options' sensitivities. ### Syllabus Breakdown 1. **Equity Derivatives in Practice: Part I** This introductory module guides learners through the binomial model before transitioning into the Black-Scholes framework. The spotlight is on the Greeks — Delta, Gamma, Theta, Vega, and Rho — which offer insights into how derivative values react to changes in market conditions. The module importantly connects these theories to practical risk management and hedging strategies, emphasizing their relevance in constructing and adjusting portfolios. An introduction to implied volatility and volatility smiles provides further depth, setting the stage for subsequent discussions. 2. **Equity Derivatives in Practice: Part II** Continuing from the foundational knowledge, this module dives deeper into implied volatility and addresses concepts such as volatility skew, risk aversion, and the leverage effect. It offers practical insights into pricing derivatives using the volatility surface and introduces complex products like digital options and range accruals. A hands-on assignment encourages learners to think outside the Black-Scholes model, fostering a model-free approach that is increasingly relevant in today’s dynamic markets. 3. **Review and Assignment for Equity Derivatives** This segment allows learners to synthesize their knowledge through targeted assignments, reinforcing the crucial concepts learned in the earlier modules. 4. **Credit Derivatives and Structured Products** In this forward-looking section, the course tackles credit derivatives and structured products, shedding light on critical financial instruments like Credit Default Obligations (CDOs) and the Gaussian Copula model. Given the prominence of these topics in light of the 2008 financial crisis, understanding the risk-return profiles and valuations of various tranches is essential for effective risk management and investment strategies. 5. **Other Applications of Financial Engineering** This final module explores real options, linking financial theory to real-world assets like natural gas and electricity. The focus on dynamic programming for valuation in uncertain environments underpins the necessity of adaptable financial strategies. ### Course Highlights - **Expert Instructors**: The course is presented by seasoned professionals who provide insights drawn from real-world applications. - **Hands-On Learning**: Real-world assignments and case studies enhance understanding, encouraging learners to apply theoretical knowledge practically. - **Flexible Learning**: As an online course, it accommodates various schedules, making it accessible to a broad audience. ### Recommendations For finance enthusiasts looking to advance their knowledge in derivatives, this course is highly recommended. It strikes a good balance between theory and practice, making complex topics approachable for learners. The structured progression from basic models to advanced applications ensures that participants not only grasp essential concepts but can also apply them in real-world scenarios. However, prospective learners should have a foundational understanding of financial concepts and mathematics to fully benefit from this course. If you're eager to deepen your expertise in derivative pricing and risk management, "Advanced Topics in Derivative Pricing" on Coursera is a compelling choice that will equip you with the necessary skills and insights to excel in the finance industry.

Syllabus

Course Overview

This module contains the first part of equity derivatives. After a brief review on the binomial model, we introduce Black-Scholes model and how to utilize this model to derive so-called "Greeks." Greeks are very important indices in options, which measure the sensitivity of option value to a wide range of variables such as stock price and volatility. We are also covering risk management and hedging. Greeks play an important role in risk management and hedging, as traders and quants often use Greeks approach to hedge and construct their portfolios. Moreover, we will introduce scenario analysis and how Greeks are used to measure portfolio value change. In the end, we are covering an introduction to implied volatility and volatility smile. Implied volatility is a key link between market option prices and options prices under the framework of Black-Scholes model. We'll be covering more about this topic in the next module.

This module contains the second part of equity derivatives. Following past module, we'll continue discussing implied volatility and volatility smile. We introduce two main explanations about volatility skew: risk aversion and leverage effect. Next, we will cover how to utilize volatility surface to price derivatives, including digital options and range accruals. Meanwhile, we will introduce a method to obtain risk-neutral density of terminal stock price distribution from option prices. We will also cover two additional topics about joint distribution of two securities and dynamic replication in practice. In module 3, you will have a real-world assignment where you will use all the knowledge from previous modules to solve the problems about equity derivatives. In this assignment, you will be exposed to many think-about questions where you can jump out of the Black-Scholes framework and think in a model-free world.

This module involves topics in credit derivatives and structured products. Firstly, we will cover the definition of Credit Debit Obligation (CDO) and Gaussian Copula model, where Gaussian Copula can be used to compute the portfolio loss function. CDO plays an important part in the past financial crisis starting from 2008, and it is an important part of working for traders and quants in Securitized Products Group (SPG). Next, we will introduce a simple version of 1-period CDO, where you can learn how to get the expected tranche losses and understand CDO from observations about equity, mezzanine and senior tranches. In the end, we will cover the mechanism about synthetic CDO and the method to calculate the fair value of premium lag, default lag, and CDO tranche. We will also cover CDO portfolios, including pricing and risk management of CDO portfolios and higher-order CDO products.

This module involves topics in real options. Real options are based on highly volatile underlying assets with many uncertainties including market, industrial, technical, organizational, and political issues. We take natural gas and electricity related options as an example to introduce valuation methods such as dynamic programming in real options.