Computational Methods in Pricing and Model Calibration from Coursera

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Syllabus

Course Overview

Option Pricing and Numerical Approach

In this week, we will study option pricing via a numerical approach. In many cases, analytical (explicit) solution of option prices is not obtainable, which requires numerical solutions. For example, if we switch the stock dynamics from geometric Brownian motion to another model, or switch the option from vanilla style to exotic style, explicit pricing formula will become unrealistic. Firstly, we start from introduction to options, where you can learn different types of options and different perspectives of option market participants. Then we will talk about option pricing via numerical integration both in general and in details. In particular, we will focus on Fourier transform and fast Fourier transform (FFT). We also provide Python codes for you to learn how to apply these techniques in practice. In the end of this week, you will be exposed to several cases studies, from time cost comparison to different models. There are lots of models which estimates the stock price evolution. Among these models, we will mainly focus on Black-Merton-Scholes (BMS), Heston, and Variance Gamma (VG) model, where you will learn the motivation and characteristic of each model. Afterwards, you will have an assignment about option pricing, where you can utilize all the theoretical knowledge and Python codes to price different options under different stock dynamics.

Model Calibration

In this week, we will study model calibration, which follows the topics in last week. You have been exposed to many models, but you have no information about how to choose the model and parameters. Fortunately, you will learn how to solve this problem in this week from different approaches. Firstly, we start from an introduction to bid and ask prices and option surface. Then we will talk about the model calibration in regards with fitting the market option price, also with pictorial demonstration about implied volatility. Next, you will learn the calibration recipe, involving objective functions and initial parameter set. You will also learn how to do calibration in practice, which is an optimization problem. We will introduce three routines: brute-force search, Nelder-Mead algorithm, and BFGS algorithm. Except from learning these routines theoretically, you will also learn how to apply them in the optimization problem from Python codes. Followingly, you can apply what you learn about calibration in the assignment.

Interest Rates and Interest Rate Instruments Part I

We will start learning interest rates and interest rate instruments from this week. Interest rates play a very important role in measuring the future and present value of financial products. People also use market interest rates to analyze the economic situation. At the very beginning, we will introduce fundamental interest rate concepts, including forward rates, spot rates, swap rates and term structures of interest rates. Then we will apply data-driven analysis to calibrate LIBOR and swap curves and cross-correlations between these rates. Using the term structure of these interest rates, we should be able to price market value of bonds, swaps and other interest rate products. We also provide you with Python codes in order to show how to obtain the LIBOR curve and how to use it to price bonds. After learning this module, you will have a brief overview of interest rates and their applications in bond and swap pricing. We will talk about complex stochastic models and calibrate interest curves with these models next week.

Interest Rates and Interest Rate Instruments Part II

This week we will use different models to estimate interest rate processes and implement regression analysis to calibrate the processes. The models in this week are very important in practice. For instance, market makers need good models to help them interpolate or extrapolate market prices of illiquid interest-rate products, while speculators need models to help them understand the prices of fixed income securities so that they can bet on interest rates, etc. So in this module, we will first provide different regression techniques used to fit data in the market. Then we will introduce Vasicek model and CIR model for bond pricing. We also show how to use regression to fit data with our models. We provide all codes needed and also go through the codes to help you know how to apply them. At the end of the lecture, you will be asked to practice interest rate models by fitting LIBOR rates in the assignment.

Good to know

Know what's good

, what to watch for

, and possible dealbreakers

Emphasizes computational methods used in finance, including Fourier Transform (FT) and Fast Fourier Transform (FFT) methods

Employs up-to-date Python coding to illustrate concepts, providing practical examples for better understanding

Introduces different stock dynamics models, such as Black-Merton-Scholes (BMS), Heston, and Variance Gamma (VG), for understanding stock price evolution

Provides hands-on practice through coding assignments to reinforce learning

Taught by instructors with industry experience, ensuring practical relevance of the course material

Covers a comprehensive range of topics related to option and interest rate products, providing a broad understanding of the financial markets

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 Computational Methods in Pricing and Model Calibration with these activities:

Review the basics of programming using Python

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Reviewing the basics of programming using Python will help you brush up on the programming skills that are essential for completing the assignments and projects in this course.

Browse courses on Python

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Go over your notes from a previous programming course.
Work through some practice problems.

Review the fundamentals of calculus

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Reviewing the fundamentals of calculus will help you brush up on the mathematical concepts that are essential for understanding the financial models and techniques covered in this course.

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Go over your notes from a previous calculus course.
Work through some practice problems.

Compile a list of resources for learning about financial modeling

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Compiling a list of resources for learning about financial modeling will help you identify additional materials that you can use to supplement your understanding of the course material.

Browse courses on Financial Modeling

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Search the internet for resources on financial modeling.
Review the resources and select the ones that you find most helpful.
Organize the resources into a list.

Six other activities

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Join a study group with other students in this course

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Joining a study group with other students in this course will provide you with the opportunity to discuss the course material with your peers and get help with any concepts that you are struggling with.

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Find other students in your course who are interested in forming a study group.
Decide on a meeting time and location.
Discuss the course material and help each other with any challenging concepts.

Price options using Excel

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Practicing option pricing using Excel will help you develop the skills necessary to apply the financial models and techniques covered in this course to real-world scenarios.

Browse courses on Option Pricing

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Download a free Excel template for option pricing.
Input the relevant data, such as the stock price, strike price, time to expiration, and risk-free rate.
Use the Excel formulas to calculate the option price.

Mentor a new student in this course

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Mentoring a new student in this course will help you to solidify your understanding of the course material by explaining it to someone else.

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Identify a new student in this course who could benefit from your help.
Offer your help to the student.
Meet with the student regularly to discuss the course material.

Volunteer at a financial institution

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Volunteering at a financial institution will provide you with practical experience in the field of finance and help you apply the financial models and techniques covered in this course to real-world scenarios.

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Research financial institutions in your area.
Contact the institutions and inquire about volunteer opportunities.
Attend training and orientation sessions.
Perform your volunteer duties under the supervision of a mentor.

Develop a Python script to calibrate an interest rate model

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Developing a Python script to calibrate an interest rate model will help you gain hands-on experience with the financial models and techniques covered in this course and enhance your programming skills.

Browse courses on Interest Rate Modeling

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Choose an interest rate model to calibrate.
Gather the necessary data.
Write the Python script to calibrate the model.
Test the script to ensure that it is working correctly.

Develop a trading strategy using the models covered in this course

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Developing a trading strategy using the models covered in this course will help you apply the financial models and techniques covered in this course to real-world scenarios and gain valuable experience in the field of finance.

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Choose a financial market to trade in.
Select the financial models that you will use to develop your strategy.
Backtest your strategy using historical data.
Refine your strategy based on the backtesting results.
Implement your strategy in a live trading environment.

Career center

Learners who complete Computational Methods in Pricing and Model Calibration will develop knowledge and skills that may be useful to these careers:

Quantitative Analyst

Quantitative Analysts, also known as Quants, use mathematical and statistical models to analyze financial data and make investment decisions. This course may be useful for those interested in a career as a Quant, as it provides a strong foundation in the computational methods used to price and calibrate financial models. The course's focus on interest rate models and their application in bond and swap pricing is particularly relevant for Quants who work in fixed income markets.

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Financial Modeler

Financial Modelers develop and use financial models to analyze and forecast financial performance. This course may be useful for those interested in a career as a Financial Modeler, as it provides a strong foundation in the techniques used to build and calibrate financial models. The course's focus on option pricing and interest rate models is particularly relevant for Financial Modelers who work in the investment banking and corporate finance industries.

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Risk Manager

Risk Managers are responsible for identifying, assessing, and managing financial risks within an organization. This course may be useful for those interested in a career in risk management, as it provides a strong foundation in the techniques used to price and calibrate financial models. The course's focus on model calibration and the use of optimization routines is particularly relevant for Risk Managers who need to develop and implement risk management models.

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Private Equity Analyst

Private Equity Analysts evaluate and invest in private companies. This course may be useful for those interested in a career as a Private Equity Analyst, as it provides a strong foundation in the techniques used to price and calibrate financial models. The course's focus on option pricing and interest rate models is particularly relevant for Private Equity Analysts who work in the leveraged buyout and venture capital industries.

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Investment Banker

Investment Bankers provide financial advice and services to corporations and governments. This course may be useful for those interested in a career as an Investment Banker, as it provides a strong foundation in the techniques used to price and calibrate financial models. The course's focus on option pricing and interest rate models is particularly relevant for Investment Bankers who work in the mergers and acquisitions and capital markets divisions.

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Corporate Finance Analyst

Corporate Finance Analysts provide financial advice and services to corporations. This course may be useful for those interested in a career as a Corporate Finance Analyst, as it provides a strong foundation in the techniques used to price and calibrate financial models. The course's focus on option pricing and interest rate models is particularly relevant for Corporate Finance Analysts who work in the mergers and acquisitions and capital markets divisions.

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Hedge Fund Analyst

Hedge Fund Analysts evaluate and invest in a wide range of financial instruments. This course may be useful for those interested in a career as a Hedge Fund Analyst, as it provides a strong foundation in the techniques used to price and calibrate financial models. The course's focus on option pricing and interest rate models is particularly relevant for Hedge Fund Analysts who work in the equity, fixed income, and currency markets.

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Portfolio Manager

Portfolio Managers are responsible for managing investment portfolios on behalf of clients. This course may be useful for those interested in a career as a Portfolio Manager, as it provides a strong foundation in the techniques used to price and calibrate financial models. The course's focus on option pricing and interest rate models is particularly relevant for Portfolio Managers who manage fixed income and equity portfolios.

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Academic Researcher

Academic Researchers conduct research and publish papers in academic journals. This course may be useful for those interested in a career as an Academic Researcher, as it provides a strong foundation in the techniques used to develop and test financial models. The course's focus on computational methods, including Fourier Transform (FT) and Fast Fourier Transform (FFT), is particularly relevant for Academic Researchers who work in the field of financial modeling.

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Trader

Traders buy and sell financial instruments for their own account or on behalf of clients. This course may be useful for those interested in a career as a Trader, as it provides a strong foundation in the techniques used to price and calibrate financial models. The course's focus on option pricing and interest rate models is particularly relevant for Traders who work in fixed income and equity markets.

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Financial Analyst

Financial Analysts typically work for banks, investment firms, or asset management companies, where they examine the performance and financial position of businesses and recommend investment strategies to clients. This course may be useful for those interested in a career in financial analysis, as it provides a strong foundation in the techniques used to price and calibrate financial models. The course's focus on computational methods, including Fourier Transform (FT) and Fast Fourier Transform (FFT), is particularly relevant for financial analysts who use these techniques to value complex financial instruments.

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Actuary

Actuaries use mathematical and statistical techniques to assess and manage financial risks. This course may be useful for those interested in a career as an Actuary, as it provides a strong foundation in the techniques used to price and calibrate financial models. The course's focus on interest rate models and their application in bond and swap pricing is particularly relevant for Actuaries who work in the insurance industry.

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Data Scientist

Data Scientists use mathematical and statistical techniques to analyze data and extract insights. This course may be useful for those interested in a career as a Data Scientist, as it provides a strong foundation in the computational methods used to analyze financial data. The course's focus on Fourier Transform (FT) and Fast Fourier Transform (FFT) is particularly relevant for Data Scientists who work in the financial industry.

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Consultant

Consultants provide advice and services to businesses and organizations. This course may be useful for those interested in a career as a Consultant, as it provides a strong foundation in the techniques used to analyze and solve business problems.

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Software Engineer

Software Engineers design, develop, and maintain software applications. This course may be useful for those interested in a career as a Software Engineer, as it provides a strong foundation in the computational methods used to develop financial software. The course's focus on Python coding is particularly relevant for Software Engineers who work in the financial industry.

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