Financial Engineering and Risk Management Specialization

What you will learn
This course focuses on the applications of optimization methods in portfolio construction and risk management. The first module covers portfolio construction via mean-variance analysis and the capital asset pricing model (CAPM) in an arbitrage-free setting. Then, it demonstrates the application of the stock market line and the Sharpe optimal portfolio in exercises. The second module discusses the challenges of implementing mean-variance analysis techniques in a real-world setting and potential methods to address them. We will introduce Valueat- Risk (VaR) and Conditional Value-at-Risk (CVaR) as risk measures, as well as 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 performing real-world statistical estimations. The last module directly addresses the modeling of transaction costs in the real world. It includes basic market microstructures including order book, bid-ask spread, liquidity measurement and their effects on transaction costs. We then enrich mean-variance portfolio strategies by accounting for transaction costs.

What you will learn
This course covers topics related to derivatives pricing. The first module is designed to understand the Black-Scholes model and use it to derive Greeks, which measure the sensitivity of the option value to variables such as the underlying asset price, volatility, and time to maturity. Greeks are important in risk management and hedging and are often used to measure the change in the value of a portfolio. We will then analyze the risk management of derivatives portfolios from two perspectives: the Greeks approach and scenario analysis. The second module shows how the theoretical price of an option is related to the actual market price through implied volatility. We will discuss volatility surface pricing as well as explain the volatility smile and skew, which are common in real markets. The third module is on credit derivatives and structured products and focuses on Credit Debit Obligations (CDOs), which played an important role in the last financial crisis starting in 2007. We will cover the definition of CDOs, simple and synthetic versions of CDOs and CDO portfolios. The last module focuses on the application of option pricing methodologies and takes natural gas and electricity options as examples to introduce valuation methods such as dynamic programming in real options.

What you will learn
This course focuses on computational methods in the field of options and interest rates, product valuation and model calibration. The first module will introduce the different types of options in the market, followed by an in-depth discussion of numerical techniques useful for valuing them, for example the Fourier Transform (FT) and Fast Fourier Transform (FFT) methods. We will explain models such as Black-Merton-Scholes (BMS), Heston, Variance Gamma (VG), which are essential for understanding stock price evolution, through case studies and Python codes. The second module introduces concepts such as bid-ask prices, implied volatility and option surfaces, followed by a demonstration of model calibration to adjust market option prices using optimization routines such as brute force search, Nelder-Mead algorithm and BFGS algorithm. The third module introduces interest rates and financial products built around these instruments. We will introduce fundamental concepts such as forward rates, spot rates, swap rates, and the term structure of interest rates, extending them further to create, calibrate, and analyze LIBOR and swap curves. We will also demonstrate the pricing of bonds, swaps, and other interest rate products using Python codes. The last module focuses on model calibration techniques used by practitioners to estimate interest rate processes and derive prices for different financial products. We will illustrate several regression techniques used for calibrating interest rate models and conclude the module by covering the Vasicek and CIR model for valuing fixed income instruments.