Online Certificate in Quantitative Finance

MODULE 1 - Building Blocks of Quantitative Finance

• Random behavior of assets
• Important mathematical tools and results
• Taylor series
• Partial differential equations
• Stochastic Calculus and Itô’s Lemma
• Transition density functions
• Fokker-Planck and Kolmogorov
• Martingales
• Manipulating stochastic differential equations
• The binomial model for asset prices

MODULE 2 - Quantitative Risk and Return

• Modern portfolio theory
• Portfolio optimization for portfolio selection
• Capital asset pricing model
• Risk regulation and Basel III
• Collateral and margins
• Value at risk and expected shortfall
• Asset returns: key, empirical stylized facts
• Liquidity asset liability management
• Volatility filtering (GARCH Family)
• Volatility models: The ARCH Framework

MODULE 3 - Equities and Currencies

• The Black-Scholes Model
• Options strategies
• Hedging and the Greeks
• Exotic options
• Early exercise and American options
• Monte Carlo simulations
• Finite-difference and methods
• Girsanov’s theorem
• Volatility arbitrage strategies
• Martingale's theory for pricing
• Advanced volatility modeling in complete markets
• Advanced Greeks
• Derivatives market practice
• FX Options
• Non-probabilistic volatility models

MODULE 4 - Data Science and Machine Learning I

• What is mathematical modeling?
• Principal component analysis
• Math toolbox for machine learning
• Penalized regressions: lasso, ridge, and elastic net
• Supervised learning techniques
• Linear regression
• K-nearest neighbors
• Logistic, SoftMax regression
• Decision tress
• Naïve Bayes classifier
• Support vector machines
• Ensemble models – bagging and boosting
• Python – scikit learn

MODULE 5 - Data Science and Machine Learning II

• Unsupervised learning techniques
• K-means clustering
• T-distributed Stochastic Neighbor Embedding
• Self-organizing maps
• Uniform manifold approximation and projection
• Autoencoders
• Neural network architectures
• Natural language processing
• Artificial neural networks
• Deep learning and NLP tools
• Reinforcement learning
• AI-based algo trading strategies
• Practical machine learning case studies for finance
• Quantum computing in finance
• Python – TensorFlow

MODULE 6 - Fixed Income and Credit

• Fixed-income products and market practices
• Yield, duration, and convexity
• Probabilistic methods for interest rates
• Stochastic interest rate models
• Calibration and data analysis
• Libor market model
• Structural models
• Heath, Jarrow, and Morton
• Reduced-form model and the hazard rate
• X-valuation adjustment (CVA, DVA, FVA, MVA)
• Risk of default, structural, and reduced form
• Credit risk and credit derivatives
• CDS pricing, market approach
• Implementation of copula models

Advanced Electives*