Module 1 Basic mathematics In pricing of several risk management products, mathematics is extensively used. This course covers important mathematical topics related to derivative pricing. Many of the inputs of the course are used in subsequent courses.Set Theory Sets, Subsets, Set Operations, Disjoint Sets, Products of SetsLinear Algebra Vectors and vector spaces, atrices, Linear transforms, Systems of linear Equations. Eigen values and Eigen vectors. Real Symmetric matrices, Cholesky factorization. Function & Sequence Injections, Surjections, Bijections, Sequences, Countability, Functions on the Real Line Limits and Convergence of Sequences, Series-Ratio Test, Root Test, Power Series, Absolute Convergence Differential and Integral calculus basicsModule 2Statistics & probabilitySeveral concepts of statistics are extensively used in measuring financial risk. This first course on statistics is aimed to provide a strong foundation on statistics and statistical models. The course will primarily focus on statistics relevant for application in finance and financial risk management.Introduction to Statistics Basic concept Definition, Classification, Characteristics of statistics opulation and sample Descriptive Statistics Central tendency, Mean, Median,Mode Measures of location, Quartiles, Percentiles,Deciles Measures of variability or dispersion Range , Special range,Quartile deviation Mean deviation Variance and standard deviation Relative measures of dispersion Shape characteristics of a distribution, Skewness,Kurtosis Data Exploration with Graphical Means Bar diagram, Pie chart, Histogram, Scatter diagram Line diagram Probability Concept Random Phenomenon and Related Concepts Random Phenomenon and Related Concepts Interpretations and Laws of Probability Interpretations of probability Laws of probability Probability Theorems Total probability theorem Bayes' theorem Probability Distribution Functions Univariate and Bivariate distribution function Marginal, Conditional and Derived Distributions Marginal distribution Conditional distribution Derived distribution Properties of random variablesIntroduction to Estimation Theory Properties of Parameter Estimator Methods of Parameter Estimation Method of moments Method of maximum likelihood Probability distribution and their application Discrete Distributions Binomial, Poisson, Hypergeometric, Exponential ,Gamma distribution Multinomial distribution Continuos Distributions Normal distribution Uniform/Rectangular Exponentia, Erlangian, Weibull, Cauchy distribution Beta distribution Lognormal distribution Pareto distribution Synthesized Distributions, Mixed GaussianCorrelation and Regression Correlation and Partial Correlation Correlation Partial correlation Simple Linear Regression Partitioning the sum of squares in simple regression Coefficient of determination Testing a hypothesis and making an inference concerning Confidence interval for a mean value of Y given a value Prediction interval for a new individual value given a value Multiple Linear Regression Regression Diagnostics Issues of MulticollinearityModule 3Financial EconometricsThis course provides a comprehensive input to financial econometric models and their application to modeling and prediction of financial time series data. The course covers analysis and application of univariate financial time series, the return series of multiple assets and Bayesian inference in finance methods. Multivariate regression Use of dummy variables Logit and Probit ModelsConcept of Stochastic and Time series analysis MARKOV Process Brownian Motion Basics Concepts Martingales Properties of martingales Introduction to Time series modelling & steps in time series modelling Autoregressive Processes and ARMA Model Formulation, identification, estimation and diagnostic checking Forecasting Data generationGARCH Model Introduction ARCH(1) processes The AR(1) /ARCH(1) Model ARCH (q) Models GARCH (p,q) Models GARCH processes have heavy tails Comparison of ARMA and GARCH processes Module 4Corporate FinanceAn understanding of financial accounting and financial statements provides some basic idea about the way in which business organizations' function. Different sources of risk and their impact on business can be best explained in a non-technical manner through analysis of financial statements. The course aims to familiarize the students with the mechanics of preparation and presentation of financial statements and to acquire in-depth knowledge and skill in analyzing financial statements. Corporate Finance Understanding Financial Statements and Cash Flows Evaluating a Firm's Financial Performance Capital-Budgeting Techniques and Practice Cash Flows and Other Topics in Capital Budgeting Cost of Capital Determining the Financing Mix Dividend Policy and Internal Financing Short-term financial planning, Working-Capital management International Finance Mergers and AcquisitionsModule 5Investment ManagementA simple but most effective way of managing risk is holding diversified portfolio of assets. This course focuses on how risk and return of portfolio of assets differ from individual assets and different ways in which portfolio of assets are selected, measured and managed. Introduction to portfolio theoryPortfolio planning Markowitz MV model Capital Asset Pricing model (CAPM) Index tracking models Arbitrage pricing theory and factor model Cardinality restrictions Rebalancing model

Multiple Risk Measures in Portfolio PlanningPortfolio construction Portfolios of uncorrelated assets Portfolios of correlated assets Evaluation of portfolio Sharpe Index Sortino Index Value-at-risk Linear and Non-Linear portfolios Outline of the method: identifying worst cases Back testing, out of sample testing and stress testing Trading Strategies Pair trading, basket trading, volatility trading, program tradingModule 6Financial Intuitions and markets This course aims to provide an idea on the role and functioning of financial markets, financial products that are traded in such financial markets and institutions associated with financial markets. The focus of the course will be in the context of global financial markets and institutions. Various financial institutions and their activities Money market Bond market Equity market Market microstructure Efficiency hypothesis in capital market Stylized facts about the marketsModule 7Financial ModellingThis course aims to develop tools and techniques to implement and analyze the core models of modern finance, as applied in asset pricing, portfolio selection and risk management. Financial models will be implemented in Excel, supplemented where appropriate by Visual Basic for Applications (VBA). The course will enhance understanding of the theory and provide relevant tools for practitioners. Introduction to Financial Modelling Computing Tools used in Modelling Modelling Applications in Equity & Portfolio Modelling Applications in Derivatives Modelling Applications in Fixed Income Modelling Applications in ValuationsModule 8Option futures and other derivativesThis course extends the knowledge gained from the courses like Financial Markets, Institutions and Instruments and Mathematics of Finance.Options An overview of Options products Mechanics of Options markets Review of Option Pricing Models The Greek letter Volatility Similes Trading StrategiesInterest rate derivatives Interest Rate Derivatives Standard Market Models Modes of the Short Rate Advanced ModelsFutures and other derivatives Mechanics of Futures Markets Determination of Forward and Futures prices Swaps Insurance, weather and energy derivativesCommodity DerivativesModule 9Risk management in Banks and other financial institutions The phenomenal growth of the credit markets has led several new instruments for managing credit risk. This course covers tools and techniques in measuring and managing credit risk and loan pricing and structuring. Credit analysis Asset-based lending Credit Rating Agencies Credit risk models Testing and implementing credit risk models Default rates, losses, recoveries Credit Derivatives Asset Liability Management VAR and Cash Coherent Measures of RisksModule 10Accounting and taxation for financial instrumentsNew financial instruments including derivative and other structured products are often complex in structure and payoff. Accounting treatment and disclosure of the nature of risk associated with such financial instruments are given importance to ensure fairness of determining profitability of the organizations. Due to complexity of the instruments and payoff, tax authorities also prescribe treatment for tax purpose. This course covers important accounting and tax issues under various major regulations (US regulations, IAS and Indian regulations). Accounting and Disclosure regulations under FASB, IAS and AS Accounting for Equity derivatives Accounting for interest rate swaps and interest rate futures and options Accounting for currency derivatives Accounting for structured products Tax Treatment on Derivative InstrumentsModule 11Corporate governance, regulation & operational risk Overview and need for regulatory regime International perspectives National perspectives Relationship between national and international regulationsRegulation for finance sector Banking Insurance PensionRegulations for corporate governance and SOXIndian corporate regulation by SEBI Operational risk & mitigation Definition Operational Risks of Financial Institutions Operational Risks of non-Financial Institutions Risks from IT infrastructure Credit Risk and Operational risk

Module 12Fixed income market Term structure of interest rate Fixed income valuation Fixed income market risk analysis Repo market Fixed income derivatives Asset backed/mortgaged backed securitization Benchmark rates and indices