Greeks, American Options and Volatility from edX

In this course, three methods are presented for pricing an option.

1. The first method is an analytical one whereby the Black Scholes formula is used to price a call or a put. The drawback of the analytical approach is that it only works for European options.
1. The second method presented is the binomial tree, which is illustrated in the pricing of an American option to facilitate early exercise.
1. The third method presented is the Monte Carlo simulation.

Then the assumption of constant volatility is challenged, due to the presence of the volatility smile, which is formally defined and shown to be empirically observed in all derivatives markets. Monte Carlo simulations are run to generate a distribution with kurtosis -- a mixture of normal distributions.

Finally, the Heston Model, which relaxes the assumption of constant volatility is presented.

- - First, the Heston Model is shown to incorporate kurtosis by allowing volatility.
- Second, the Heston model includes an additional Brownian motion that allows volatility to mean-revert.
- Third, these Brownian motions are linked by a correlation.

Sample code is provided to run the Heston model. The corresponding implied volatilities are graphed and shown to replicate the volatility smile.

What you'll learn

Define and discuss the Greek sensitivities of the option price to underlying variables.
Price European and American options, and compare their methods and values.
Identify weaknesses within the assumptions of Black Sholes, particularly constant volatility.
To implement and price the Heston model to address the limitation of constant volatility.
To define the volatility smile, and illustrate how the output from the Heston Model can replicate it.

What's inside

Syllabus

Module 01: Greeks

Lesson 01: Delta and Gamma

Lesson 02: Theta

Lesson 03: Vega

Lesson 04: Stock Pinning

Module 02: American Options

Lesson 01: Introduction

Lesson 02: Monte Carlo Simulation

Lesson 03: Books to Read

Module 03: Volatility

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Demonstrates how to price European and American options, which is essential for derivatives traders

Examines the limitations of the Black-Scholes model and introduces the Heston model, which is more realistic and accurate

Provides a solid understanding of the Greeks, which are key sensitivities used in option pricing

Teaches how to implement and price the Heston model, which is an important skill for quantitative analysts and risk managers

Requires some background in probability and statistics

Activities

Be better prepared before your course. Deepen your understanding during and after it. Supplement your coursework and achieve mastery of the topics covered in Greeks, American Options and Volatility with these activities:

Review basic probability and statistics

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This will help you strengthen your foundation in probability and statistics, which are essential for understanding option pricing.

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Review your notes from a previous probability and statistics course.
Take practice problems.
Watch online tutorials.

Create a study guide

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This will help you organize and retain the information covered in the course.

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Organize your notes, assignments, and quizzes.
Identify the key concepts.
Summarize the key concepts.

Review Hull's Options, Futures, and Derivatives

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This book provides a comprehensive overview of the topics covered in the course and can help you reinforce your understanding.

View Options, Futures, and Other Derivatives on Amazon

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Read the relevant chapters in the book.
Take notes and highlight important concepts.
Complete the end-of-chapter exercises.

Five other activities

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Practice solving option pricing problems

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Solving practice problems will reinforce the concepts learned in the course and improve your problem-solving skills.

Browse courses on Black-Scholes Model

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Find practice problems online or in textbooks.
Solve the problems using the methods learned in the course.
Check your answers against the provided solutions.

Follow tutorials on pricing options with Python

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These tutorials will provide hands-on experience with pricing options using Python, which can help you apply the concepts learned in the course.

Browse courses on Option Pricing

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Find tutorials online or in online courses.
Follow the tutorials step-by-step.
Implement the code and test it on your own data.

Attend a workshop on option pricing

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This workshop will provide an opportunity to learn from experts in the field and ask questions about specific topics.

Browse courses on Option Pricing

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Find a workshop that aligns with your interests.
Register for the workshop.
Attend the workshop.

Create a presentation on the Heston Model

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This will challenge you to synthesize your knowledge of the Heston Model and present it in a clear and concise way.

Browse courses on Heston Model

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Research the Heston Model and its applications.
Create a presentation outline.
Develop the presentation slides.
Practice your presentation.

Develop a trading strategy using options

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This project will allow you to apply the concepts learned in the course to a real-world scenario, giving you a deeper understanding of option pricing and trading.

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Identify a trading opportunity.
Develop a trading strategy.
Backtest your strategy using historical data.
Implement your strategy in a live trading environment.

Career center

Learners who complete Greeks, American Options and Volatility will develop knowledge and skills that may be useful to these careers:

Quantitative Analyst

Quantitative Analysts, or "quants," use advanced mathematical and statistical techniques to build and implement financial models. They use these models to identify and manage risk, measure investment performance, and optimize portfolios. This course helps build a foundation in the stochastic calculus and numerical methods used by quants.

See salaries and explore the career path for Quantitative Analyst

Portfolio Manager

Portfolio Managers make investment decisions for individuals and institutions. They use a variety of investment strategies to achieve their clients' financial goals. This course helps Portfolio Managers understand the factors that affect option prices and manage risk in their portfolios.

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Financial Analyst

Financial Analysts apply their knowledge of investment instruments, analyze financial data and make projections on future economic trends. They use the Black-Scholes formula to price options, identify market risks, and provide investment advice to clients.

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Hedge Fund Manager

Hedge Fund Managers manage investment funds for high-net-worth individuals and institutions. They use a variety of investment strategies, including options and derivatives, to generate returns for their investors. This course may be useful for Hedge Fund Managers who want to better understand the pricing and risk management of options.

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Actuary

Actuaries use mathematical and statistical techniques to assess risk and determine insurance premiums. They use the Black-Scholes formula to price options and other insurance products. This course may be useful for Actuaries who want to better understand the pricing of options and derivatives.

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Insurance Actuary

Insurance Actuaries use mathematical and statistical techniques to assess risk and determine insurance premiums. They use the Black-Scholes formula to price options and other insurance products. This course may be useful for Insurance Actuaries who want to better understand the pricing of options and derivatives.

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Data Scientist

Data Scientists use statistical and machine learning techniques to extract insights from data. They use these insights to improve business decisions and develop new products and services. This course may be useful for Data Scientists who want to learn more about the pricing of options and derivatives.

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Business Analyst

Business Analysts use data and analysis to improve business processes and make better decisions. They use a variety of tools and techniques to identify and solve business problems. This course may be useful for Business Analysts who want to learn more about the pricing of options and derivatives.

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Risk Manager

Risk Managers identify and assess financial risks for businesses and organizations. They develop and implement risk management strategies to protect against potential losses. This course may help Risk Managers better understand and manage volatility in financial markets.

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Financial Planner

Financial Planners help individuals and families plan for their financial future. They provide advice on investment, retirement, insurance, and estate planning. This course may be useful for Financial Planners who want to better understand the role of options and derivatives in financial planning.

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Consultant

Consultants provide expert advice to businesses and organizations on a variety of topics. They use their knowledge and experience to help clients improve their operations, make better decisions, and achieve their goals. This course may be useful for Consultants who want to learn more about the pricing of options and derivatives.

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Investment Banker

Investment Bankers provide financial advice to companies and governments. They help companies raise capital, merge with other companies, and make other strategic decisions. This course may be useful for Investment Bankers who want to better understand the pricing of options and derivatives.

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Software Engineer

Software Engineers design, develop, and maintain software applications. They use a variety of programming languages and technologies to create software that meets the needs of businesses and consumers. This course may be useful for Software Engineers who want to learn more about the pricing of options and derivatives.

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Accountant

Accountants prepare and maintain financial records for businesses and organizations. They use accounting principles and regulations to ensure that financial statements are accurate and reliable. This course may be useful for Accountants who want to learn more about the pricing of options and derivatives.

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Teacher

Teachers educate students at all levels, from preschool to college. They develop lesson plans, teach課程, and assess student learning. This course may be useful for Teachers who want to learn more about the pricing of options and derivatives.

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