• Calculation of covariance and correlation matrices

Matrix Algebra

• Product
• Transpose
• Inverse
• Determinant
• Kronecker Product
• Trace of a Matrix

Matrix Transformation Methods

• Row Echelon Form
• Reduced Row Echelon Form
• Rank of a Matrix

Eigen Systems

• Eigen Values
• Eigen Vectors

Matrix Decomposition Methods

• Norm of a Matrix
• LU Decomposition
• Cholesky Decomposition
• QR decomposition
• Singular Value Decomposition
• Jordan Decomposition
• Schur Decomposition
• Generalized Schur Decomposition
• Hessenberg Decomposition

Simulation

Univariate

• Continuous Symmetric  -Cauchy, Cosine, Double Gamma, Double Weibull, Hypoebolic Secant, Laplace, Logistic, Normal, Semi Circular, Student’s T, Uniform
• Continuous Skewed - Beta, Bradford, Burr, Chi, Chi-Square, Erlang, Exponential, ExtremeLB, Fisk, Folded Normal, Gamma, Generalized Logistic, Gumbel, Half Normal, Inverse Gamma, Inverse Normal, Log Normal, Maxwell, Pareto, Power, Reciprocal, Rayleigh, Transformed Beta, Triangular, Weibull
• Discrete - Binomial, Geometric, Logarithmic, Negative Binomial, Poisson

Multivariate

• Normal Copula,  Student’s T Copula, Wishart Distribution, Weibull Copula , Marshall Olkin Copula,  Clayton Copula, Gumbel Copula, Frank Copula

Gibbs Sampling

• Linear Regression, Logistic Regression, Seemingly Unrelated Regression (SUR), Survival Model

Data Mining Techniques

Mixed Model and Generalized Linear Model (GLM)

• Mixed model with fixed and random effects
• Restricted Maximum Likelihood Estimation (REML)
• Best Linear Unbiased Predictor (BLUP) and Best Linear Unbiased Estimator (BLUE)
• Least Square Means (LS Means)

• Calculation of regression coefficients (s), standard error of coefficient , t Statistic, p Value, confidence interval
• Goodness of fit measures -F statistic, R-squared, adjusted R-squared, residuals and tests for heteroschedasticity
• Variable subset selection using variance inflation factor (VIF), single variable analysis, stepwise regression, backward regression, fast backward regression
• Boot strap sampling for ensuring stability of models
• Support for sparse data
• Scoring production samples using developed models

Logistic Regression & Probit Model

• Calculation of regression coefficients (’s), standard error of coefficient estimate, chi-square, p Value
• Goodness of fit measures – concordance/discordance, Gini coefficient, c-Statistic, false positives, false negatives
• Variable subset selection using variance inflation factor (VIF), single variable analysis, stepwise regression, backward regression, fast backward regression
• Support for weighted logistic regression
• Boot strap sampling for ensuring stability of models
• Support for sparse data
• Scoring production samples using developed models

Decision Tree

• Implementation of CART & CHAID
• Multi-level top-down splitting into nodes and leaves based on the best splitting variable at each level
• Split based on Gini and Entropy
• Level of tree determined by optimal gain at each splitting node
• Support for continuous as well as categorical variables
• Support for sparse data
• Scoring based on attributes of a decision tree

Naïve Bayes

• Determination of probability based on categorical data
• Option for Laplacian correction

Hazard Model

• Kaplan Meier Estimate
• Kaplan Meier Hypothesis Test – Log Rank Test, Wilcoxon Test, Tarone-Ware Test
• Cox Proportional Hazard Model
• Best subset selection using backward and fast backward methods in Cox Proportional Hazard model

Clustering Methods

• K Means, K Medoids, Fuzzy K Means
• Hierarchical Clustering – Hierarchical K Means, Hierarchical O – Cluster

Nearest Neighbors

• Nearest Neighbors based on distance measures – Euclidean, Manhattan, Mahalanobis
• Distance measure using multiple dimensions

• Equity derivatives, Interest Rate derivatives, Currency derivatives
• Risk-neutral valuation of calls and puts using Black Scholes with and without dividends
• Binomial trees with and without dividends
• Greeks – Delta, Theta, Gamma, Vega, Rho with and without dividends

Time Series Analysis Autoregressive Moving Average

• ARMA Model –p, q model
• ARIMA Model – p, q, d model, support for exogenous variables

Conditional Heteroskedasticity

• ARCH/GARCH Model

Stationarity

• Unit Root and Co-integration – identification of stationarity, Augmented Dickey Fuller (ADF) test

Other Time Series Analysis

• Regime Switch Model

• Models for short rate i.e., Vasicek, Cox, Ingresoll and Ross, Ho & Lee, Hull & White, etc.

Valuation of Fixed Income Securities (Cash flow estimation, Rate determination, Zero-Coupon Bond)

• Price
• Coupon dates – first coupon date, all coupon dates
• Computation of yield measures for fixed-rate bonds (Current yield, Yield to maturity, Yield to first call, Yield to first par call date, Yield to put, Yield to worst, Cash flow yield, Bond equivalent yield)
• Discount Margin
• Duration, Modified Duration, McCaulay Duration
• DV01, Convexity
• Valuation of floating rate notes – binomial model, Monte Carlo simulation
• Computation of Forward Rates and bond valuation using forward rates
• Valuation of Callable, Putable and Convertible bonds, bonds with embedded options
• Spreads (Zero-Volatility Spread, Option-adjusted Spread (OAS), Option Cost, Nominal Spread)
• Spot rate using bootstrapping
• Historical and Implied Yield volatility
• Credit Default Swaps – risk-neutral probability, valuation of CDS, PV01