Curriculum

Linear Algebra, Calculus, Adjoint Algorithmic Differentiation, Kalman Filter, Probability, Statistics, Numerical Method

Regression, Classification, Clustering, Time Series Analysis, Deep learning, Reinforcement learning, PCA, Kalman filter and use of all of these in Quantitative Finance

Market microstructure, Trading instruments, Backtesting frameworks (Statistical arbitrage, Pairs trading using cointegration, Kalman Filter for dynamic hedge ratios, Z-score based spread trading, Dispersion trading with volatility arbitrage, Realized vs implied vol, Vega-neutral trade construction, Feature engineering for signals, Clustering for asset selection, Machine learning for trade signals, Slippage and Transaction Cost, Option strategies

​Linear systems, LU decompositions, positive definite systems, Cholesky decomposition - sensitivity analysis; Gram-Schmidt orthonormal process, singular value decomposition(SVD), polar decomposition, Moore-Penrose inverse; Rank deficient least-squares problems; Sensitivity analysis of least-squares problems; Review of canonical forms of matrices; Sensitivity of eigenvalues and eigenvectors. Reduction to Hessenberg and tridiagonal forms; Power, inverse power and Rayleigh quotient iterations; Explicit and implicit QR algorithms for symmetric and nonsymmetric matrices; Reduction to bidiagonal form; Golub- Kahan algorithm for computing SVD.

Random Walk, Weiner Process, Markov Chain, Martingale, Stochastic Differential Equation, Ito’s formula, Probability Measures, Change of measures, Radon-Nikodym Derivatives, Girsanov theorem, Ito’s Integral, Fractional Brownian Motion, Gyongy’s theorem, multi-variable stochastic calculus, Feynman-Kac theorem and its applications

Monte Carlo, Variance reduction techniques like using antithetic variables, control variates etc.

Options Basics, Arbitrage and Hedging, Option Payoff Structures, Time Value and Intrinsic Value, Put-Call Parity, Introduction to Greeks, Black-Scholes Model Assumptions, Derivation of Black-Scholes PDE, Risk-Neutral Valuation, Numerical Solutions to Black-Scholes (Finite Difference, Binomial Trees, Monte Carlo Simulations), Delta, Gamma, Vega, Theta, and Rho (First Order Greeks), Second-Order Greeks (Vanna, Charm, Vomma), Volatility Smile and Skewness, Kurtosis in Options, Implied Volatility and Volatility Surface

Exotic Options (Barrier, Lookback, Asian, Digital), Pricing Exotic Options (Monte Carlo and PDE methods), American Option Pricing (Finite Difference and Binomial Methods), Model Calibration Techniques, American Monte Carlo Method [Longstaff and Schwartz Simulation], Carr-Madan Formula, Implicit, Explicit and CN method of solving PDE for Vanilla options, American options, Barrier options and their stability criteria

Introduction to Volatility Models, Implied Volatility Basics, Volatility Smile and Skew, Local Volatility Models, Deriving Dupire's Formula, Numerical Implementation of Dupire's Formula, Relationship between Local Volatility and Implied Volatility, Understanding Volatility Surfaces, Calibration of Local Volatility Models, Stochastic Volatility Models, Heston Model Introduction and Derivation, Heston Model Parameter Estimation (Maximum Likelihood, Method of Moments), Solving Heston Model (PDE and Monte Carlo Methods), Volatility of Volatility, SABR Model Basics, Calibration of SABR Model, Comparison between Local and Stochastic Volatility Models, Local Stochastic Volatility Models, Bridging Local and Stochastic Volatility (LSV), Calibration of Local Stochastic Volatility Models, SVI Parametrization, Bergomi-Guyon Model, Pricing under Local Stochastic Volatility, Managing Volatility Risk, Applications of Volatility Models in Option Pricing, SVI, SSVI

Introduction to Bonds and Fixed Income Securities, Bond Pricing Basics, Zero-Coupon Bonds (ZCB) and Yield Calculation, Coupon Bonds and Pricing Formulas, Yield to Maturity (YTM) and Yield Curves, Spot Rates and Forward Rates, Bootstrapping Yield Curves, Constructing Discount Curves, Par Yield and Par Yield Curve, Duration and Convexity, Modified Duration and Interest Rate Sensitivity, Introduction to Interest Rate Models, Short Rate Models (Vasicek, CIR, Hull-White), Calibration of Short Rate Models, Pricing Bonds using Short Rate Models, Two factor Interest Rate Models, Heath-Jarrow-Morton (HJM) Framework, Forward Rate Models, Libor Market Model (LMM), Interest Rate Derivatives Basics, Forward Rate Agreements (FRAs), Swaps (Interest Rate Swaps, Currency Swaps), Pricing Interest Rate Swaps, Swap Curve Construction, FX Swaps and Cross Currency Swaps, Options on Bonds, Jamshidian Decomposition, Swaptions and their Pricing, Black Model for Swaptions, Caps and Floors (Basics and Pricing), Caplets and Floorlets, Implied Volatility in Interest Rate Derivatives, Convexity and Timing Adjustments in Swaps, Structured Interest Rate Products, Managing Interest Rate Risk, Applications of Interest Rate Models in Risk Management and Hedging, Recent Developments in Fixed Income and Interest Rate Derivatives

Introduction to Portfolio Theory, Expected Return and Risk, Variance-Covariance Matrix Construction, Mean-Variance Optimization (MVO), Efficient Frontier and Capital Market Line (CML), Risk-Return Trade-Off, Constraints in Portfolio Optimization, Introduction to Factor Models (Single-Factor and Multi-Factor Models), Fama-French Factor Model, Principal Component Analysis (PCA) in Portfolio Construction, Black-Litterman Model Basics, Bayesian Approach to Portfolio Optimization, Incorporating Views in Black-Litterman Model, Covariance Matrix Adjustment in Black-Litterman, Entropy Pooling for Portfolio Optimization, Combining Views with Entropy Pooling, Sequential Entropy Pooling, Practical Implementations of Entropy Pooling, Robust Portfolio Optimization, Shrinkage Methods for Covariance Estimation, Risk Parity and Equal Risk Contribution Portfolios Techniques

Introduction to Market and Credit Risk, Market Risk Metrics (Volatility, Beta, Drawdown), Value at Risk (VaR) - Historical, Parametric, and Monte Carlo Methods, Expected Shortfall (CVaR), Backtesting and Stress Testing for VaR, Credit Risk Fundamentals, Probability of Default (PD), Loss Given Default (LGD), Exposure at Default (EAD), Credit Exposure Measurement, Credit Migration and Rating Transitions, Counterparty Credit Risk (CCR), Credit Valuation Adjustment (CVA) and Wrong-Way Risk, Debt Valuation and Spread Analysis, Credit Default Swaps (CDS) - Basics and Pricing, Credit Spread and Default Probability, Credit Risk Models (Structural and Reduced-Form Models), Merton and KMV Models, Basel Accords - Regulatory Requirements for Market and Credit Risk, Capital Adequacy and RWA Calculation, Applications of Machine Learning in Risk Management, Recent Trends in Market and Credit Risk Management