Financial Engineering and Risk Management Specialization

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).

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.

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.

This course focuses on computational methods in option and interest rate, product’s pricing and model calibration. The first module will introduce different types of options in the market, followed by an in-depth discussion into numerical techniques helpful in pricing them, e.g. Fourier Transform (FT) and Fast Fourier Transform (FFT) methods. We will explain models like Black-Merton-Scholes (BMS), Heston, Variance Gamma (VG), which are central to understanding stock price evolution, through case studies and Python codes. The second module introduces concepts like bid-ask prices, implied volatility, and option surfaces, followed by a demonstration of model calibration for fitting market option prices using optimization routines like brute-force search, Nelder-Mead algorithm, and BFGS algorithm. The third module introduces interest rates and the financial products built around these instruments. We will bring in fundamental concepts like forward rates, spot rates, swap rates, and the term structure of interest rates, extending it further for creating, calibrating, and analyzing LIBOR and swap curves. We will also demonstrate the pricing of bonds, swaps, and other interest rate products through Python codes. The final module focuses on real-world model calibration techniques used by practitioners to estimate interest rate processes and derive prices of different financial products. We will illustrate several regression techniques used for interest rate model calibration and end the module by covering the Vasicek and CIR model for pricing fixed income instruments.