Quantie Institute of Advance Studies

📚 Course Curriculum

Module 0: Mathematics Primer

Linear Algebra, Differential and Integral Calculus, Differential Equation, Probability and Statistics

A crash course will be provided in addition to self-guided revision.

Module 1: Data Science

1.1 Python Primer:

Introduction to Python, Python Variables, Python Data Types, Python Lists, Python Tuples, Python Sets, Python Dictionaries, Python If Else, Python Loops, Python Functions, Python Lambda, Introduction to NumPy, Advance Numpy, Introduction to Pandas, Matplotlib Tutorial, Matplotlib Practice, Data Visualization, 3D Interactive Plot, Stock Plot, File Handling, Directory Handling, Python Classes, Python Inheritance, Python Polymorphism, Python Iterators, Python RegEx

1.2 Time Series Analysis with Python

Simple and Multivariate Linear Regression Assumptions and Derivation, Hypothesis Testing, Modeling Dummy Variables, Heteroskedasticity, Multicollinearity, Autocorrelation, Weighted OLS, Normality Test, Autoregressive (AR), Moving Average (MA), and Autoregressive Integrated Moving Average (ARIMA) Processes, Cointegrated Processes, Vector Autoregression (VAR), Generalized Autoregressive Conditional Heteroskedasticity (GARCH), EWMA Volatility, Parkinson (1980), Garman and Klass (1980), Rogers and Satchell (1991), Yang and Zhang (2000).

1.3 Machine Learning for Finance

OLS, Lasso, Ridge, and Elastic-Net Regression, Logistic Regression, Decision Trees, Support Vector Machines (SVM), Ensemble Learning, Imbalanced Classification, Principal Component Analysis (PCA), Linear Discriminant Analysis (LDA), T-distributed Stochastic Neighbor Embedding (t-SNE), Self-Organizing Map, Clustering (K-Means, DBSCAN, Gaussian Mixtures), Feature Engineering, Hyperparameter Tuning and Model Optimization, Cross Validation, Pipeline Development

1.4 Deep Learning in Finance

Introduction to Deep Learning Concepts, Multilayer Perceptron (MLP), Convolutional Neural Networks (CNNs), Recurrent Neural Networks (RNNs), Long Short-Term Memory (LSTM) Networks, Gated Recurrent Unit (GRU) Networks, Hyperparameter Tuning, Activation Functions, Optimizers.

Module 2: Portfolio Optimization

2.1 Portfolio optimization

Introduction to Portfolio Theory, Markowitz Mean-Variance Optimization, Efficient Frontier Analysis, Capital Allocation Line (CAL), Sharpe Ratio Maximization, Modern Portfolio Theory (MPT), Black-Litterman Model, Factor Models and Smart Beta Strategies, Risk Budgeting Portfolio, Risk Parity Portfolios, Minimum Variance Portfolios, Mean-Semivariance Optimization Mean-Downside Risk Optimization, Mean-Variance-Skewness Optimization, Mean-Variance-Skewness-Kurtosis Optimization Mean-VaR Optimization, Mean-Conditional VaR Optimization, Mean-Marginal VaR Optimization, Mean-Max Drawdown Optimization, Mean-Avg Drawdown Optimization, Multi-Period Portfolio Optimization, Dynamic Asset Allocation Strategies, Performance Measurement and Attribution, Monte Carlo Simulation for Portfolio Optimization, and other Optimization Techniques. Portfolio Risk: Risk Budgeting, Component VaR, Incremental VaR, Marginal VaR.

Module 3: Derivatives and Stochastic Calculus

3.1 Derivatives

Introduction to Derivative Instruments, Put-Call Parity and Option Strategies, Black-Scholes Model, Binomial Option Pricing Model: European, American, and Asian Options, Convergence of Binomial Model to the Black-Scholes using both mathematics and Python, Trinomial Option Pricing Model: European and American Options, Greeks: Delta, Gamma, Theta, Vega and Rho, Implied Volatility and Volatility Smile

3.2 Stochastic Calculus

Introduction to Stochastic Processes, Kolmogorov Forward and Backward Equation, Brownian Motion and Wiener Processes, Ito's Lemma and its Applications, Stochastic Differential Equations (SDEs), Martingale Theory and Martingale Representation Theorem, Girsanov's Theorem and Change of Measure, Stochastic Integration, Feynman-Kac Formula, Black-Scholes Equation and its Derivation, Risk-Neutral Pricing and the Fundamental Theorem of Asset Pricing. Stochastic Integration

Module 4: Numerical Methods and Stochastic Modeling

4.1 Numerical Methods

Generating Random Numbers: Inverse Transform Approach, Acceptance Rejection Approach, Polar Method, Box-Muller Approach, Rational Approximation Method; Variance Reduction Method, Monte-Carlo Simulations for Option Pricing, Finite Difference Method: Explicit, Implicit, Crank-Nicolson for Option Pricing, Euler Discretization, Cholesky Decomposition, LU Decomposition, Simulation of Financial Processes, Implementation in Python.

4.2 Stochastic Modeling

Maximum Likelihood Estimation, Monte Carlo Simulation, Cox-Ingersoll-Ross Model (CIR), Vasicek Model, Ho-Lee Model, Hull-White Model, Heston Model, Merton Jump Diffusion Model, SABR Model, Simulation-Based Pricing and Valuation, Stochastic Differential Equations (SDEs), Calibration Techniques, Volatility Surface Modeling, Interest Rate Models, Application in Derivatives Pricing, Risk Management, and Hedging Strategies, Local Volatility Models, Stochastic Volatility Models.

Module 5: Financial Risk

5.1 Market Risk

Historical VaR, Parametric VaR, Monte Carlo VaR, VaR Mapping, Backtesting VaR, Expected Shortfall, Coherent Risk Measure, Stress Testing, Scenario Analysis, Sensitivity Analysis, Risk Aggregation, Liquidity Risk, Tail Risk, Regulatory Frameworks, Basel, FRTB, Stress Testing.

5.2 Credit Risk

Credit Analysis, Default Risk, Credit Scoring Models, Expected and Unexpected Loss, Probability of Default (PD), Loss Given Default (LGD), Exposure at Default (EAD), Counterparty Risk, Credit Valuation Adjustment (CVA), Debit Value Adjustment (DVA), Credit Risk Mitigation Techniques, Credit Derivatives, Stress Testing, Rating Agencies.

Module 6: Fixed-Income and Credit Derivatives

6.1 Fixed-Income Securities

Bond Valuation, Bond Price Sensitivities (Duration and Convexity with derivation), Bond Immunization (Cash Flow and Duration), Hedging, Asset-Liabilities Management, Callable and Putable Bonds, Yield Curve Strategies, Hedging and risk management of Bond Portfolio using Principal Components, Swaps, Forward Rate Agreements (FRAs), Securitization.

6.2 Credit Derivatives

Swaps, Forward Rate Agreements (FRAs), Interest Rate Futures, Interest Rate Options, Cross Currency Swaps, Cross Currency Basis Swaps, Swaptions, Swaption Collar, Interest Rate Caps and Floors, Interest Rate Exotics, Credit Default Swaps (CDS), Credit-Linked Note, Variance Swaps.