Setting up Python Infrastructure

1. Anaconda installation
2. Exploring Jupyter

Arithmetic operations

1. Basic operators
2. Using the ‘math’ library

Data Structure

1. Int, float, bool, string
2. Tuple, list, set, dictionary

Object Oriented Programming

1. Functions

2. Class

PythonLab – Create a Custom Class for Black Scholes Option Price and Greeks

Numerical computing with NumPy

1. Lists vs NumPy arrays
2. Indexing
3. Vectorization
4. Linear algebra

Data Analysis with Pandas

1. The DataFrame Class
2. Data pre-processing
3. Basic Analytics
4. Basic Visualization
5. Concatenation, Joining & Merging
6. Pivot Table

Data Visualization with Matplotlib, Seaborn & Cufflinks

1. 2D plots (Scatter, line chart, column chart, bar chart, histograms)
2. 3D plots (3D scatter, Surface plots, Contour plots)
3. Financial Plots (Candle stick, Bollinger bands)

Calculus

1. Limits & Derivatives
2. Integration
3. ODEs / PDEs using SciPy.

Python Lab – Solving the heat equation

Numerical Integration

1. Riemann Integral
2. Trapezoidal method
3. Simpson’s method
4. Gaussian Quadrature

Python Lab – Custom class to find CDF of normal distribution using numerical integration

Probability & Statistics with SciPy

1. Discrete distributions (Bernoulli, Binomial, Poisson, Uniform)
2. Continuous distributions (Normal, T, lognormal, Chi-squared, F)

Python Lab – Custom Class for numerical computation of Expectation and Variance

Univariate Financial Time Series Analysis with Statsmodels

1. Prices and Returns
2. Moments (Mean, Variance, Skewness, Kurtosis)
3. Correlation & Covariance
4. ACF, PACF
5. AR, MA, ARMA, ARIMA models
6. Stationarity & Unit root tests
7. Regression with ARMA errors
8. Cointegration
1. Seasonality

Excel & Python Lab – Custom class to perform Box-Jenkins methodology to fit the best model.

Multivariate Financial Time Series Analysis with Statsmodels

1. VAR
2. VECM

Excel & Python Lab – Joint forecasting of macro-economic time series

Conditional Volatility Models

1. EWMA
2. GARCH

Excel & Python Lab – Custom Class for Value-at-Risk under different volatility models

Monte Carlo Methods

1. Generating Random numbers
2. Value of PI using Monte Carlo
3. Solving an integral with Monte Carlo
4. Acceptance Rejection Method
5. Conditional Monte Carlo
6. Variance Reduction techniques (Antithetic Sampling, Control Variate)
7. Low discrepancy sequence (Halton, Sobol)

Copula Models

1. Copula definition and properties
2. Gaussian and T copula
3. Archimedean Copula

Excel & Python Lab – Simulating default times for a nth to default basket CDS.

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Stochastic process

1. Random Walk process
2. Wiener process
3. Named stochastic process (ABM, GBM, OU)
4. Conditional Expectation
5. Martingales & Markov properties
6. Ito’s Lemma
7. Ito Isometry
8. Ito Integral
1. Estimation & Calibration

Change of Measure

1. Probability, Sigma Algebra, Filtration
2. Tower property
3. Radon Nikodym derivative
4. Girsanov theorem

Excel & Python Lab – ABM, GBM, OU

Binomial Asset Pricing Model

1. Stock price model
2. Valuing a European Option
   1. Replicating strategy
   2. Delta-hedging strategy
   3. Risk neutral expectation
3. Value an American Option
4. Option with dividends

Black Scholes

1. Derivation of BSM PDE
2. Formula for European Option Price and Greeks

Jump Process

1. Jumps in Asset Dynamics
2. Exponential Levy process
3. Variance Gamma process
4. Characteristic Function
5. Fast Fourier transform for Option pricing

Finite Difference Methods for Option pricing

1. Explicit Scheme
2. Implicit Scheme
3. Crank Nicolson
4. Stability Analysis

Excel & Python Lab – Price first generation exotics using Finite Difference

Monte Carlo methods for Option pricing

1. Fundamental theorem of Asset pricing
2. Feynman-Kac theorem
3. Simulating GBM (Euler Scheme, Milstein Scheme, Explicit Scheme)
4. Pricing First generation exotics using MCS.
5. Least Square Monte Carlo for Bermudan Options
6. Fast Monte Carlo Greeks (pathwise & likelihood ratio methods)

Excel & Python Lab – Custom class for Exotic pricing and Greeks

Volatility Surface

1. Historical volatility, Local volatility, Implied Volatility
2. Term Structure, Smile, Surface
3. Dupire Local volatility model
4. Stochastic volatility models (SABR, Heston)

Excel & Python Lab – Custom class for pricing under Heston and SABR models

Rates and Rate Instruments

1. Spot vs forward
2. Short rates vs instantaneous forward rates
3. Term structure concepts
4. Fundamental theorem of asset pricing
5. Bank account & zero-coupon bond
6. Coupon bond (fixed, floating)
7. FRAs, Swaps, CMS

Excel & Python Lab – valuation of Bonds, FRAs and Swaps

Term Structure Models

1. Short rate models (Vasicek, CIR)
2. No Arbitrage Models (Ho Lee, Hull-White I, Hull-White II)
3. The HJM framework
4. Market Models (BGM)

Options on rates

1. The Black-76 model.
2. Caps & Floors
3. Swaptions

Excel & Python Lab – Calibration of swaption volatility surface

FX Instruments

1. FX forward
2. FX option
3. FX swap
4. Cross Currency Interest rate swap

Excel & Python Lab – Pricing of FX derivatives with volatility smile

Excel & Python Lab – CVA calculation for a portfolio of derivatives

Portfolio Theory & Optimization

1. Modern Portfolio Theory
2. CAPM
3. Mean Variance Optimization
4. Black Litterman

Excel & PythonLab – A real life portfolio optimization problem

Excel & Python Lab – Implementation of Pairs-trading (A statistical arbitrage trading strategy)

Traditional Supervised algorithms using Scikit Learn

1. Logistic Regression for predicting default.
2. Support Vector Machines for anomaly detection 
3. Naïve Bayes for Sentiment Classification
4. Ensemble methods (Bagging, Boosting) for LGD

Traditional Unsupervised algorithms using Scikit Learn

1. PCA based value at risk for an interest rate portfolio.
2. K means clustering for volatility regime

Deep Learning with Tensorflow

1. Artificial Neural Network for Option Price
2. LSTM for stock price prediction
3. Building a Trading strategy with Reinforcement learning (OpenAI Gym)