Certificate in Financial Engineering (CFE) in... · 2019-01-14 · Certificate in Financial...

Risk Latte

www.risklatte.xyz +1 514 910 1830 [email protected]

Certificate in

Financial Engineering

(CFE)

and

Financial and Engineering Mathematics (FEM)

❖ CFE Certificate Program ❖ CFE+FEM Dual Certificate Program

❖ Classroom Course in New York, London, Montreal, Singapore, Tokyo and

Mumbai

CFE School, Risk Latte Americas Inc.

Risk Latte Certificate in Financial Engineering (CFE)

www.risklatte.xyz/cfe Risk Latte Americas Inc.

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CFE Summary

Certificate in Financial Engineering (CFE) Program is a Certification Program in the field of Quantitative Finance (Financial Engineering) and is a unique online educational initiative by Classes For Everyone (CFE), a Social Learning venture by Risk Latte Americas Inc.

CFE Course, the bulk of which comprises course materials developed using Excel™/VBA

spreadsheets is delivered online. CFE course materials are designed to provide a broad and detailed road map to all those who want to gain advanced level knowledge and acquire skills in the area of financial engineering and quantitative finance.

CFE is a skill based educational course and it tests a candidate’s thinking, applications and

quantitative modeling skills. Major emphasis of the CFE is on implementing detailed and advanced level mathematical and quantitative models in Quantitative and Mathematical Finance on Excel™/VBA spreadsheet.

CFE is recognized by top tier global banks and financial institutions and the program is designed

to test candidates who can be fit and worthy to work in these institutions. A vast majority of CFE Graduates are from banks and financial institutions such as Goldman Sachs, Barclays, RBS, Bloomberg, Bank of America Merrill Lynch, BNP Paribas, Deutsche Bank, Citigroup, Standard Chartered Bank, ABN Amro, ING, UBS, HDFC Bank, ICICI Bank, Kotak Mahindra Bank, Shinsei Bank, HSBC, etc.

CFE Program is overseen by two apex bodies: CFE Executive Committee and CFE Academic

Committee and the members of both these committees are middle to senior level professionals from top tier global banks and financial institutions and all members have graduated from the CFE Program.

CFE Program is delivered via both Classroom and Online method; however, CFE Classroom

program – which comprises yearlong classroom and tutorial sessions in onsite locations, led by instructors – is only via invitation and for a select group of banking and finance professionals in New York, London, Montreal, Tokyo, Singapore and Mumbai.

Regardless of whether a student is enrolled in the Classroom or the Online program, he or she

will have to go through the Alternative Assessment Method (AAM) in order to qualify for the award of the CFE Certificate.

CFE is an advanced level program, designed and developed by industry professionals (traders,

quants, structurers, risk managers, asset managers and analysts) almost all of whom has already graduated from the CFE Classroom Program. Even though the curriculum starts off from the very basics in the field of Quantitative Finance, the emphasis is on intermediate to advanced level topics.



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Certificate in Financial Engineering (CFE) Program

Certificate in Financial Engineering (CFE) Course is a unique initiative by CFE School, a Social Learning Venture of Risk Latte Americas Inc., in the field of financial engineering and quantitative finance. The initial subscription period (Enrolment Term) of the CFE Course is 2-years. Thereafter, a student can renew his or her enrolment on an annual basis.

CFE Course is delivered online (via internet). However, for a select group of highly skilled professionals who are sponsored by their banks or institution the Course is offered in a classroom format in London, New York, Montreal, Tokyo, Singapore and Mumbai. The CFE Course, both the Online and the Classroom course, is designed to help students understand and navigate the CFE syllabus better.

The Academic Committee of the CFE School is responsible for preparation of course materials and its delivery plus the development and administration of the Alternative Assessment Method (AAM) that is mandatory for every student if he or she wants to get awarded the CFE (or, the FEM) Certificate. The CFE Executive Committee is the overall supervisory body for the CFE School and it oversees the delivery and administration of CFE Course and the CFE Exam. Both the CFE Academic Committee and the Executive Committee members are chosen from amongst the CFE Graduates who are all industry professionals (senior level bankers and finance professionals) and professionals from Risk Latte Company.

Assessment Process

CFE Assessment is a key part of the CFE Program and mandatory for those who are desirous of obtaining a CFE Certificate. It is designed to test a student’s analytical, thinking and application skills in the field of Quantitative Finance and Financial Engineering.

A student can opt to get tested via the Alternative Assessment Method (AAM) during the term of his Subscription (Enrolment). This is necessary if a student wants to get the Certificate.

The Alternative Assessment Method comprises exams, online assessment, projects and tutorials, Skype and video interviews and both peer group and Academic Committee assessments.



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CFE Course

CFE Course is primarily delivered in Online (via internet) format; Only for a select group of banking and finance professionals (and some other sponsored

professionals) CFE Course is offered onsite, in a classroom format at six global locations: New York, London, Singapore, Tokyo, Hong Kong and Mumbai. Over term of the program a student enrolled in the Classroom program, besides doing self-study via online course materials, gets to complete a total of 16 days of classes and tutorials.

CFE is an applications based course with major emphasis on hands-on quantitative modeling; the course focuses on the application of advanced theoretical and mathematical concepts used in Quantitative Finance to solve problems of valuation and risk analysis;

CFE Course makes extensive use of Excel™/VBA and all quantitative and mathematical models are implemented and developed in Excel™/VBA. Besides, Excel™/VBA spreadsheets the course materials also contain theory notes and lecture notes in PDF format.

CFE Course materials and curriculum are designed and developed by industry practitioners and banking / finance professionals from top tier global banks and financial institutions who have graduated from the CFE Program.

CFE Course is a self-help course (with very limited instructor help). A student has to access and download all course materials from the CFE Online site and do self-study. The course materials are all in the form of Excel™/VBA spreadsheets and PDF files. Besides providing proprietary course materials, sufficient reference materials are also provided to the student to help him with self-study.

CFE Course is an open curriculum course. All our courses are designed and developed on an open curriculum basis and both the curriculum and the course materials get continuously expanded, both vertically and horizontally, in quality (depth) as well as in scope (breadth) and hence each course is an expanding universe of knowledge in itself. Every month new course materials are added to the Course forum and the Course forum keeps expanding forever.



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Financial and Engineering Mathematics (FEM) is an applied and financial mathematics Certificate course that can be combined with the CFE Course to create a CFE+FEM Dual Certificate Course. As far as the formatting, design and delivery of the FEM course is concerned, it is identical to the CFE Course. It focuses on implementing advanced level engineering mathematics and financial

mathematics on Excel™/VBA spreadsheets to gain a perspective on how the math can facilitate solution of problems in the fields of quantitative finance, engineering and physics.

It is essentially a computational mathematics course and is highly interdisciplinary in nature borrowing from physics, engineering and financial mathematics;

Anyone can combine FEM with the CFE Course work and create a CFE+FEM Dual Certificate Program.

FEM Course materials are accessible online (via internet);



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CFE Program Fees

Here’s the fee schedule for the CFE Online Program. The Fees are for CFE+FEM Dual Certificate Online Program. Fees include the fee for Alternative Assessment Method (for Certification) plus all CFE course materials (delivered online via internet) and valid for the 2-year Subscription (Enrollment) Term.

Professionals working in banks, financial institutions, securities and financial services companies and all other companies: US$850

Full time University students: US$450 Extra Classroom Option: All those who enroll for the CFE Program also have the option to choose an extra onsite classroom option whereby they can attend 16 (Sixteen) onsite classroom sessions (one session is one whole 6-hour day) in a 2-year Subscription Term where an instructor is present for one whole day session going over various topics and subject areas, especially focusing on implementation of quant models on Excel™/VBA spreadsheets. Classroom sessions are held in New York, London, Montreal, Singapore, Tokyo and Mumbai. Fees for the Extra onsite (classroom) coaching: US$4,000



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Certificate in Financial Engineering (CFE)

DISCLAIMER: This is only a broad curriculum and is indicative of the breadth and the scope of the discipline. A student is required to be familiar with most of the topics and a large number of these topics and subject areas are covered in the CFE Course materials. Each and every topic mentioned below may not be covered in the actual course materials and Course materials from these broad set of topics will get uploaded on the course forums over the lifetime of the course. Financial Mathematics

Stochastic calculus, Weiner process, random Walk, Brownian motion, first exit times, stopping times, arc sine law, probability distributions (Gaussian, Poisson, Gamma, etc.), foundations of measure theory, differential and integral calculus, matrices and matrix theory, differential equations, Fourier and Laplace transforms, linear and non-linear optimization, solution of non-linear equations, root finding.

Applications of Matrices in Finance

Solution of system of linear equations: (applications to option portfolio, Vanna-Volga weight calculation, etc.), variance-covariance matrix calculation from market data, VaR estimation, estimation of bond returns with default and transition matrices, mean-variance optimization, optimization and asset allocation problems, risk minimization and other applications in algorithmic / quantitative trading, credit risk loss modeling, random matrices and application to portfolio analysis.

Stochastic Models in Finance (Modeling Equity, Interest Rate, FX, Commodities & Volatility)

Stochastic Process and a Markov Process, Random Walk, Geometric Brownian motion, Reimann Zeta Function and the Brownian motion, Brownian motion for the Inverse of the Asset Price, Brownian motion with default, Stochastic Process for the Relative Process of Two Assets, Arithmetic Brownian motion, Mean Reverting Brownian motion, Brownian Bridge Process, Cox-Ross Square Root Process, Ornstein-Uhlenbeck Process, Vasicek Process, Cox-Ingersoll-Ross Process, Black Derman Toy (BDT) Process, Black Karisinski Process, Poisson Jump Diffusion Process, Kou’s Double Exponential Process Heston Stochastic Volatility Model, Heston-Nandi GARCH model, Double Mean Reverting Process for Variance, Constant Elasticity of Variance (CEV) Process, Stochastic Alpha Beta Rho (SABR) Model, Longstaff’s Double Square Root Model, Stochastic Local Volatility (SLV) Process, SLV Bloomberg Model, GARCH Diffusion Process, Gibson & Schwarz Stochastic Convenience Yield Process, Stochastic Correlation Process, Mixture of Normals Process, Variance Gamma (VG) Process, Monte Carlo Simulation for VG Process, Displaced Diffusion Model, Libor Market Model (LMM), BGM Model, Heath Jarrow Morton (HJM) model, Homogenous Poisson Process, Monte Carlo Simulation for Valuation of Single Asset options, Multi-asset Stochastic Process, Cholesky Decomposition, Eigenvalue decomposition, Monte Carlo Simulation of Valuation of Multi-asset options, Cleaning Correlation Matrices, Quantum Random Walk.



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Numerical Methods in Finance

Monte Carlo simulation methodology, simulating a random walk and a Brownian motion, simulating other stochastic processes as given in Module III above, Cholesky and Eigenvalues decomposition, simulating multi-asset stochastic processes, variance reduction techniques, generating pseudo and quasi random numbers, Cox-Ross-Rubenstein (CRR) tree and other kinds of binomial trees, CFEE trinomial trees and other kinds of trinomial trees, numerical integration routines, trapezoidal and other rules for numerical integration Gaussian Quadrature Methods, solution of Black-Scholes equation using Green’s function, finite difference methods, forward difference and Crank-Nicholson method, implementation of Fourier transforms and fast Fourier transforms (FFT), copula methods in finance and implementation of copula models.

Financial Products and Product Engineering (Structuring and valuation of Equity, FX, Interest Rate, Commodity and Credit Derivatives)

Vanilla Options, Straddles and zero beta straddles, Binary Options, Outperformance Digital options, Money back options, Fixed and Floating Strike Lookback Options, Arithmetic Average Options, Chooser Options, Symmetric and Asymmetric Power Options, Forward Starting and Cliquet Options, Reverse Cliquet Options, Napoleon Options, Exchange Options, Amortizing Options, Pyramid and Madonna Options, Basket Options, Best of and Worst of Options, Himalaya, Altipano and Everest Options, Capped Bull Note, Principal Protected Bull Note, Principal Protected Bear Note, Principal Protected Mixed Note, Equity Linked Basket Note, Note with a Short Put option embedded, Perpetual Capped Call Note (American style) with no maturity, Accumulators, Target Redemption notes (TARN), Equity Linked Savings, Equity linked barrier, digital and lookback notes, chooser notes and notes with Asian tail, fixed income floating rate notes (FRN), inverse FRNs, CMS linked notes, inflation linked notes, Decomposition of Structured Product through Payoff Diagram, Convertible Bonds and Reverse Convertible Bonds, Caplet and Snowball options, Sycurve Options, Compound options, Installment options, Israeli options, Timer options. Credit linked notes, Credit default swaps (CDS), Collateralized Bond Obligations (CDOs), synthetic CDOs;

Implied Volatility Numerical Estimation of Implied Volatility, Leland’s Formula, Brenner-Subrahmanyam Approximations, Corrado Miller Approximation, Steven Li’s Approximation, SABR Volatility, CEV Volatility, Volatility Skew, Implied Volatility Surface and Interpolating Implied Volatility, Vanna Volga Methodology, Local Volatility, Local Volatility in presence of default and jumps; Historical Volatility Historical Volatility using close to close price, Parkinson’s Number, Garman-Klass Estimator, EWMA Volatility, GARCH Process, estimation of variance-covariance matrix from market data, correlation matrix and positive semi-definiteness.



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Stochastic Volatility

Heston’s stochastic volatility model: closed form implementation using complex integrals, Heston-Nandi GARCH model implementation, evaluation of Greeks in Heston and Heston-Nandi model, Full valuation of Heston and Heston-Nandi models using Monte Carlo simulation, calibration of stochastic volatility models, stochastic local volatility models (SLV).

Model Free Volatility and Variance Swaps Log Contract, Britten-Jones & Neuberger Model, Variance Swap, VIX Index, Volatility Swap, Correlation and Implied Correlation, Correlation Skew, Dispersion, Model free higher moments.

Options and Financial Derivatives Valuation (Closed Form solutions and Analysis)

Vanilla Options using Black-Scholes Model, Put-Call Parity and Put-Call Symmetry, Straddle Options, Option pricing using Displaced Diffusion model, Power Option, Exchange Option, Binary Option, Barrier Option, One Touch Option, Double Barrier (Binary) Option, Fixed and Floating Strike Lookback options, Arithmetic Average option, Forward Starting option, Caps and Floors, Swaption Valuation using Black’s formula, SYCURVE Options, Bond Option pricing using Black’s formula, Options on Zero Coupon Bond using Vasicek’s Model, Options on Variance.

Greeks

Call and Put Delta, Call and Put Gamma, Vega of Options, Hedging Error due to Volatility Smile, Theta and Rho of Vanilla options, Binary Call and Put Delta, Dirac Delta Function and the Binary, Binary Gamma and Vega, Variance Swap Greeks, Greeks for barrier options and other exotic options, estimation of Greeks using numerical methods, using Greeks for hedging option books,

Options Trading

Market making and proprietary trading, liquidity and liquidity holes, trader’s edge and Dubins Savage theorem, delta hedging, lock delta, partial and total delta, managing gamma and shadow gamma, moments of option position, bucketing and topography, modified vega analysis, understanding fat tails, orders of volatility trade (first order, second order and higher order volatility trades), managing a book of binary and barrier options, using straddles, strangles and risk reversals, vanna-volga overhedge, price-volatility matrix and analyzing vega convexity.

Portfolio Analysis & Asset Allocation (Including Algorithmic Trading)

Sharpe Ratio, Treynor Ration and Jensen’s Alpha, Portfolio Volatility, Expected Return for Stocks and Bonds, Volatility of Spreads, Probability of Stocks Outperforming Bonds, Mean-Variance Optimization for a Total Return Objective, Mean-Variance Optimization by maximizing Sharpe Ratio, Sharpe’s



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Algorithm for Efficient Frontier, Portfolio Insurance, Constant Proportion Portfolio Insurance (CPPI), Capital Asset Pricing Model (CAPM), Minimization of Risk and MCR Algorithm, Statistical Arbitrage, Triangular Arbitrage, pre-trade and post-trade analysis, market impact and timing risk, Principal bid transactions, efficient trading frontier and advanced program trading models, VWAP strategy.

Risk Management (Market, Credit and Counterparty Risk Modeling)

Spot and forward risk, parametric VaR estimation, VaR using Monte Carlo simulation, Cornish-Fisher transformation, Portfolio VaR, marginal VaR, Principal Components Analysis (PCA), VaR for equity, bond and FX portfolios, cash flow mapping techniques and application to FX forwards and fixed income products, VaR for options book: delta normal VaR and delta-gamma VaR, Vega VaR, structural approach to predicting default and valuation models, transition matrices and prediction of default and transition rates, Loss given default (LGD), asset value approach and estimation of credit portfolio risk, credit portfolio models and their validations, Basel II and Internal Ratings methodology, Basel III implementation.

Excel™/VBA Spreadsheet Coding & Modeling

Financial functions: NPV, IRR, PMT, XIRR, XNP, Date functions: Now, Today, Date, Weekday, Month, Datedif, Statistical functions: Average, Var, Varp, Stdev, Stdevp, Correl, Covar, Regression functions: Slope, Intercept, Rsq, Linest, Conditional functions: If, VLookup, HLookup, Boolean functions: And, Or, Count, CountIf, Offset, Statistical functions: Rand, Normsdist, Normsinv, Skew, Other functions: Large, Small, Rank, Percentile, Count, Countif, Math Functions: Trigonometric functions, Engineering functions, Multiple Regression functions in Excel and making scatter plots, generation of regression equations, Handling arrays and array functions and matrix functions: Transpose, matrix multiplication, inverse of a matrix and determinant, power of a matrix, subtracting a constant from a matrix, using GoalSeek and Solver in Excel: Application & mini tutorial, introduction to VBA Editor and using VBA sub-routines (macros) and user defined functions in Excel spreadsheet (only the use of readymade VBA programs will be demonstrated, no VBA programming will be done), formula Auditing, use of subscripts and superscripts, naming and hiding cells, addition of Greek symbols in an Excel spreadsheet and use of Equation Editor for embedding / writing mathematical formulas (images) in the sheet. Investment Banking

Company valuation models: comparable companies analysis and transaction analysis, discounted cash flow (DCF) analysis, Leveraged buyouts (LBOs), LBO analysis, buy side mergers and acquisitions (M&A), sell side M&A, valuation models for banks and financial institutions, macro-economic analysis and econometric models (to understand the environment in which banks and financial institutions operate).



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Basic Level Excel™ for Financial and Engineering Mathematics (Mandatory Module)

Cells, worksheets and workbooks, cell references and naming a cell; Insert, Format and Tools menu (2003 & 2010); Quick Start Math and Excel™ formulas – Time, Financial and Math & Statistical formulas; Using Excel™ Object, Equation Editor 3.0, Insert Equation, how to handle arrays (single arrays and matrices); Data Analysis – Histogram, Random number generation, goal seek, charting in Excel™ and trend lines, 2-D and 3-D charts; Other essential features and coding characteristics in Excel™ helpful in financial modeling; Matrix and array functions in Excel™.

Advanced Excel™/VBA for Engineers and Quants (Optional Module)

Boolean and Engineering functions and their types; Using Complex Number libraries and writing complex functions, Trigonometric functions – solution of an inclined plane problem; Implementing Fourier series, hyperbolic functions and Bessel functions – applications; Real and imaginary parts of a complex number and complex number operations, evaluating complex integral (integrals with imaginary parts) – applications in Finance; Boolean functions and applications in Electrical Engineering – railroad crossing signals and digital locks; Using the Developer tool and handling Modules, link to VBA; Advanced array handling in Excel™, Lookup functions; Analysis Tool Pack - descriptive statistics, histogram, random number generator, Fourier analysis; Applications of Goal Seek; Excel™ Solver for optimization problems, application of Excel™ Solver for non-linear problems and optimizations;

Visual Basic for Applications (VBA) for Financial Mathematics (Optional Module)

Organization of the VBA Editor VBA Procedures: VBA macros and VBA User defined functions; Elementary VBA code and writing custom functions VBA statements, Objects, Properties and Methods Using worksheet functions with VBA Program control, Logical operators and Data types; conditional execution Types and Loops, Boolean operators, Arrays in VBA, dynamic arrays, arrays in function procedures VBA Command macros, arguments of methods, handling cell references, interacting with the user; Multidimensional arrays, array assignment, variants containing an array, arrays as parameters in functions; Objects and Add-ins, worksheet objects, active cell range as object variables, range object, Collections, Names, naming a range using a Macro, references to external functions in VBA, using a Function in a reference Writing a custom (user defined) functions for mathematical applications Testing and debugging the code;



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DISCLAIMER: This is only a broad curriculum and is indicative of the breadth and the scope of the discipline. A student is required to be familiar with most of the topics and a large number of these topics and subject areas are covered in the FEM Course materials. Each and every topic mentioned below may not be covered in the actual course materials and Course materials from these broad set of topics will get uploaded on the course forums over the lifetime of the course. Matrix Algebra and Applications Matrix multiplication and finding the inverse of a matrix; Determinant of a matrix and its application; Square and non-square matrices and their applications (unique application of non-square matrices in cryptography and unique application of non-singular, square matrices for solutions of linear equations, etc.), Cholesky matrix and its use in Finance; Eigenvalues and eigenvectors of matrices, Power method and Jacobi method for computation of eigenvectors and eigenvalues; Application of eigenvalues and eigenvectors in Finance; Diagonalization of a matrix, positive semi-definite matrices and finding the square root of a matrix; Principal Components Analysis (PCA) of data; Solution of a system of a linear equations using matrices, Cramer’s rule, Gauss-Jordan method; Solving linear systems by iteration, Gauss-Seidel method; solving systems of complex equations using matrices; solving non-linear equations using matrices; correlation matrix and variance-covariance matrix; transition matrices in finance and Markov models. Differential and Integral Calculus What is a function and types of functions; What is meant by mathematical derivative of a function, interpretation; Estimating Limits of functions and Using first principles to calculate first mathematical derivative of a function; Second mathematical derivative of functions, Maxima and minima of functions; Mathematical derivatives of Data in a Table; Estimation of first and second derivatives; Definite and indefinite integrals – concept of area of a curve; Estimation of area under a curve defined by table of Data points – single integral; Integrating a function – Simpson’s Rule, Trapezoidal Rule; Integrating with an upper or lower limit of infinity; Distance traveled along a curved path; Statistics, Probability Distributions and Random Number Mathematics Estimation of mean and variance of a time series and correlation between two time series, rank correlation, bi-serial correlation; Exponential weighted moving average of variance; Moving average and exponential smoothing techniques Estimation of the third and fourth moment of distribution; Estimating auto-correlation amongst data, heteroscedasticity of data; Generalized autoregressive conditional heteroscedasticity (GARCH) techniques; Linear regression and line of best fit, coefficient of determination; Gaussian, Binomial, Poisson distributions – probability density functions, cumulative probability function; Introduction to Complex Number math and Characteristic function of a distribution; Other Distributions: Cauchy, Gamma, Double Exponential and Levy; Generation of uniform random numbers using Excel library functions and writing customized routines to generate uniform



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random numbers using math algorithms; Adding Noise to a signal generated by a formula; Difference between pseudo random and quasi random numbers, efficiency and accuracy; generation of low discrepancy sequences, Halton numbers, Sobol sequences; generation of random normal numbers, Box-Muller algorithms; Random sampling to approximate solutions of quantitative problems – introduction to Monte Carlo simulation; Estimation of the constants, such as pi() using Monte Carlo simulation; Monte Carlo simulation of a stock price; Estimation of an area under irregular polygon; Using Monte Carlo integration to estimate values of functions; Monte Carlo integration of single integrals and multiple integrals; Interest Rate Mathematics Time value of money, compound interest discount factors, discounting functions and mathematics of annuities; Present value and future value of cash flows; Net Present Value (NPV) and Internal Rate of Return (IRR) of investments; Zero rates, par rates and forward rates, Linear and cubic interpolation of rates; Duration, convexity of cash flows, pricing interest rate swaps (IRS). Linear and non-Linear Optimization Methods Linear programming and its applications in Finance, dynamic programming; Mean-variance optimization methodologies using first derivatives, constrained optimization methods, Lagrangian multiplier methodology; optimization of complex and non-linear problems using Solver in Excel™; Solving a system of non-linear equations by iteration, Newton’s method; Non-linear regression analysis and least squares curve fitting using Excel™ Solver Statistics of non-linear regressions Numerical Integration Newton-Cotes methodology for integration and incline functions Numerical integration using Simpson’s rule, trapezoidal rule; Gaussian quadrature methodologies Gauss-Legendre, Gauss-Laguerre quadrature methodology, Gauss- Hermite methodology. Ordinary Differential Equations (ODEs) – Numerical Solutions What are Ordinary Differential Equations (ODEs) and their examples in Finance; Solution of ODEs for Physics and Engineering problems; Solution of first order differential equation using separation of variables and Euler’s numerical method; Fourth order Runge-Kutta Method, application to differential equations using both x and y variables; Systems of first order differential equations and fourth order Runge Kutta functions for systems of differential equations; Predictor Corrector methods and higher order differential equations, Finite Difference methods and solving second order differential equations.



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Partial Differential Equations (PDEs) What are partial differential equations (PDEs) and their examples in physics, engineering and finance; Types of PDEs: Elliptic, Parabolic and Hyperbolic and where do we encounter them in Finance; Relationship between Heat Equation and the Black-Scholes PDE for Option Pricing; Green’s theorem approach to solution of Black-Scholes PDE for exotic options pricing; Numerical methods: forward and backward difference methods, explicit methods for solving PDEs Using Laplace’s finite element method and solution of Laplace’s PDE Using separation of variables method for solving PDE and solution of Schrodinger’s Wave equation; The Crank-Nicholson (Implicit) method for solving PDEs; Stochastic Processes

Continuous time Diffusion process: Weiner process and random walk, Ito process; Simple rules of stochastic differentiation and integration, Gaussian stochastic integrals; Simulation of a Weiner process, finite difference method, integral equation method; Feynman-Kac theorem and the expectations approach to solution of diffusion equation; Arbitrage free valuation, risk neutral measure, Radon-Nikodym derivative Change of probability measure under continuous probability density, Girsanov’s theorem, forward measure; Maxima and minima of Brownian motion and the first exit time problem; Dynamics of the Jump diffusion process and simulation of jump processes; Mean reverting Ornstein-Uhlenbeck (OU processes, Square root processes and Bessel processes GARCH diffusion processes Introduction to Stochastic Control Theory: Dynamic programming and Hamilton Jacobi Bellman equation; Integral Transforms

Infinite series, Fourier series and Fourier analysis of waves, Fourier Transforms and its applications in Signal processing; Relationship between characteristic functions of probability distribution and Fourier transform, using Fourier transform to solve option pricing problems; Introduction to Laplace transforms and application of Laplace transforms; Advanced applications of Fourier and Laplace transforms in physics and engineering problems; Applications of Fourier and Laplace transforms in quantitative finance.



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Placement and Career Counseling Services

CFE School has recently started a Placement and Career Counseling Cell for full time University students and young working professionals who are enrolled in the CFE and the CFE+FEM Dual Certificate Program.

❖ CFE School will actively assist all CFE and CFE+FEM Graduates to find the right kind of job within the banking and finance industry, as well as in other industries requiring quantitative, analytical and computing skills; such assistance shall be in the form of advice on the right kind of job, arranging job interviews and internship interviews with banks, financial institutions and other firms, wherever possible, help with the preparation of job interviews and long term assistance in finding the right job;

❖ CFE School will guide and advise all CFE and CFE+FEM students in matters of career choice within the banking and finance industry, as well as in other industries where quantitative and computing skills are greatly required; advise will also be given on the new landscape that is evolving for quants, bankers and finance professionals and how to succeed in these times, what kind of companies and firms to target for job applications given the candidates’ skills, prior education and interests, etc.

Certificate in Financial Engineering (CFE) in... · 2019-01-14 · Certificate in Financial...

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