- Quantitative Analysis
- Asset Allocation
- Algorithmic Trading
- Portfolio Optimization
- Mathematical Finance
- Derivatives
- Swaps and options
- Fixed Income
- Binomial Distribution
- black scholes model
- model calibration
- modeling and pricing Credit Default Swaps
Financial Engineering and Risk Management Specialization
Advance Your Knowledge in Financial Engineering . Build the fundamentals and technical skills in financial engineering
Offered By


What you will learn
1. Valuing options, swaps, forwards, futures, and other complex financial derivatives using stochastic models
2. Develop a systematic, data-driven approach to formulating modeled returns and risks for significant asset classes and optimal portfolios
3. Back test and implement trading models and signals in an active, live trading environment
Skills you will gain
About this Specialization
Applied Learning Project
Learners will apply the knowledge and skills to various problems in the financial engineering area, including pricing derivatives of futures, equities, interest rates, and credit, conducting delta hedging, mean-variance portfolio construction, model fitting and optimization.
Intermediate knowledge of probability, statistics, linear algebra, and calculus. Proficient with Excel and working knowledge in Python.
Intermediate knowledge of probability, statistics, linear algebra, and calculus. Proficient with Excel and working knowledge in Python.
How the Specialization Works
Take Courses
A Coursera Specialization is a series of courses that helps you master a skill. To begin, enroll in the Specialization directly, or review its courses and choose the one you'd like to start with. When you subscribe to a course that is part of a Specialization, you’re automatically subscribed to the full Specialization. It’s okay to complete just one course — you can pause your learning or end your subscription at any time. Visit your learner dashboard to track your course enrollments and your progress.
Hands-on Project
Every Specialization includes a hands-on project. You'll need to successfully finish the project(s) to complete the Specialization and earn your certificate. If the Specialization includes a separate course for the hands-on project, you'll need to finish each of the other courses before you can start it.
Earn a Certificate
When you finish every course and complete the hands-on project, you'll earn a Certificate that you can share with prospective employers and your professional network.

There are 5 Courses in this Specialization
Introduction to Financial Engineering and Risk Management
Introduction to Financial Engineering and Risk Management course belongs to the Financial Engineering and Risk Management Specialization and it provides a fundamental introduction to fixed income securities, derivatives and the respective pricing models. The first module gives an overview of the prerequisite concepts and rules in probability and optimization. This will prepare learners with the mathematical fundamentals for the course. The second module includes concepts around fixed income securities and their derivative instruments. We will introduce present value (PV) computation on fixed income securities in an arbitrage free setting, followed by a brief discussion on term structure of interest rates. In the third module, learners will engage with swaps and options, and price them using the 1-period Binomial Model. The final module focuses on option pricing in a multi-period setting, using the Binomial and the Black-Scholes Models. Subsequently, the multi-period Binomial Model will be illustrated using American Options, Futures, Forwards and assets with dividends.
Term-Structure and Credit Derivatives
This course will focus on capturing the evolution of interest rates and providing deep insight into credit derivatives. In the first module we discuss the term structure lattice models and cash account, and then analyze fixed income derivatives, such as Options, Futures, Caplets and Floorlets, Swaps and Swaptions. In the second module, we will examine model calibration in the context of fixed income securities and extend it to other asset classes and instruments. Learners will operate model calibration using Excel and apply it to price a payer swaption in a Black-Derman-Toy (BDT) model. The third module introduces credit derivatives and subsequently focuses on modeling and pricing the Credit Default Swaps. In the fourth module, learners would be introduced to the concept of securitization, specifically asset backed securities(ABS). The discussion progresses to Mortgage Backed Securities(MBS) and the associated mortgage mathematics. The final module delves into introducing and pricing Collateralized Mortgage Obligations(CMOs).
Optimization Methods in Asset Management
This course focuses on applications of optimization methods in portfolio construction and risk management. The first module discusses portfolio construction via Mean-Variance Analysis and Capital Asset Pricing Model (CAPM) in an arbitrage-free setting. Next, it demonstrates the application of the security market line and sharpe optimal portfolio in the exercises. The second module involves the difficulties in implementing Mean-Variance techniques in a real-world setting and the potential methods to deal with it. We will introduce Value at Risk (VaR) and Conditional Value at Risk (CVaR) as risk measurements, and Exchange Traded Funds (ETFs), which play an important role in trading and asset management. Typical statistical biases, pitfalls, and their underlying reasons are also discussed, in order to achieve better results when completing real statistical estimation. The final module looks directly at real-world transaction costs modeling. It includes the basic market micro-structures including order book, bid-ask spread, measurement of liquidity, and their effects on transaction costs. Then we enrich Mean-Variance portfolio strategies by considering transaction costs.
Advanced Topics in Derivative Pricing
This course discusses topics in derivative pricing. The first module is designed to understand the Black-Scholes model and utilize it to derive Greeks, which measures the sensitivity of option value to variables such as underlying asset price, volatility, and time to maturity. Greeks are important in risk management and hedging and often used to measure portfolio value change. Then we will analyze risk management of derivatives portfolios from two perspectives—Greeks approach and scenario analysis. The second module reveals how option’s theoretical price links to real market price—by implied volatility. We will discuss pricing by volatility surface as well as explanations of volatility smile and skew, which are common in real markets. The third module involves topics in credit derivatives and structured products and focuses on Credit Debit Obligation (CDO), which played an important part in the past financial crisis starting from 2007. We will cover CDO’s definition, simple and synthetic versions of CDO, and CDO portfolios. The final module is the application of option pricing methodologies and takes natural gas and electricity related options as an example to introduce valuation methods such as dynamic programming in real options.
Offered by

Columbia University
For more than 250 years, Columbia has been a leader in higher education in the nation and around the world. At the core of our wide range of academic inquiry is the commitment to attract and engage the best minds in pursuit of greater human understanding, pioneering new discoveries and service to society.
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