CERTIFICATE IN FINANCIAL ENGINEERING (CFE)
New York
January, 2010

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• Course Duration:
  • 6 months, only Weekends, approximately 80 hours of instructions
• Start Date:
• January, 2010.
• Venue:
• A 5 star / 3 star hotel or other suitable venue in New York City
• Batch Size:
• Around 25 (Twenty Five) persons
• Instructors:
• Risk Latte instructors
• Course Fee:
• US$4,000 (USD Four Thousand) per person
• Eligibility:
• All participants selected through FEAT* (Financial Engineering Aptitude Test) and/or internal selection process of Risk Latte.

*FEAT can be downloaded from www.risklatte.com or the test can be taken at Risk Latte's offices in Hong Kong or other locations in Asia at specified times. Sample FEAT problem sets are available on Risk Latte’s web site.

Broad Curriculum Outline

Module 1
Quantitative Modelling using Excel/VBA

Math Course Work
(Excel spreadsheet Implementation of all Math concepts)

• Differential Calculus - concept of slope and the differential, rate of change, first and second derivative estimation, first principles, limit of a function, L'Hospital's rule, local maxima and minima, rules of differentiation;
• Integral Calculus - area under the curve, rules of integration;
• Stochastic Calculus - Ito's Lemma, Weiner process, Stochastic integrals, stochastic differential equations;
• Complex Analysis and extended transform functions - Fourier and Laplace transforms;
• Solution to Partial Differential Equations (PDE) - elliptic, parabolic and hyperbolic partial differential equations.

Excel/VBA Spreadsheet Course Work

• Advanced Excel spreadsheet modelling - use mathematical, statistical and engineering functions, data manipulation, array handling;
• Fundamentals of programming with VBA - writing sub-routines (macros) and custom (user) defined functions;
• Mathematical Operations using Excel spreadsheet and VBA - Matrices and Linear Transformations, solution of system of linear equations, roots of a non-linear equation (the Regula Falsi method, Newton-Raphson method, etc.) and solution of system of non-linear equations;
• Using VBA user defined functions and sub-routines to solve problems in Differential Calculus;
• Using VBA user defined functions and sub-routines to solve problems in Integral Calculus - Simpson's and trapezoidal rule to evaluate integrals, Gaussian Quadrature;
• Solving stochastic integrals using Monte Carlo integration techniques;
• Solution of ordinary Differential equations - Euler's method for first order differential equation, Runge-Kutta Method, Predictor-Corrector methods, Boundary conditions, solving systems of differential equations
• Solution of Partial Differential Equations - solving elliptic partical differential equations with finite difference methods (FDM), solving parabolic partial differential equations with the Explicit Method, Crank-Nicholson method.
• Generating eigensystem of a matrix and estimating eigenvalues and eigenvectors of a matrix

Module II
Financial Derivatives - I

Math Modelling in Excel/VBA Course Work

• Convex functions and Jensen's inequality - concept of convexity and randomness;
• Financial options and Binomial model of option pricing;
• Black-Scholes model of option pricing and the Black-Scholes Partial Differential Equation;
• Feynman-Kac equation and the risk neutral expectation approach;
• Lattice method of estimating PDEs for derivatives;
• Numerical Integrals (single and double integrals) to estimate derivative payoff functions;
• Monte Carlo methods - math behind Monte Carlo methods, stochastic dynamics, generating low discrepancy numbers, variance reduction techniques;
• Correlation matrix analysis - semi-definiteness, cholesky decomposition, spectral decomposition, eigenvalues and eigenvectors of a correlation matrix, generating correlated random numbers;
• Copula methods in finance and Gaussian copula estimation techniques;

Volatility Modelling Course Work
(Excel/VBA spreadsheet Development)

• Estimation of historical volatility - un-weighted return approach, exponentially weighted moving average (EWMA), Parkinson Number, GK estimator;
• GARCH modelling;
• Implied volatility from Black-Scholes model, forward-forward volatility, volatility smile;
• Volatility surface modelling, Derman-Dupire-Kani surface, Dupire's equation, local volatility estimation;
• Volatility surface with jumps, local volatility in the presence of default risk;
• Stochastic volatility models - Heston (1993) model and Heston-Nandi (2000) model;
• Closed form solution of Heston model and full valuation approach (Monte Carlo simulation);
• Asymptotic Volatility Analysis, volatility information from the options market – straddle, risk reversal and butterflies;
• SABR stochastic volatility model for FX derivatives; implementation of full valuation approach and closed form solution of SABR;

Module III
Financial Derivatives - II

Valuation of Equity & FX Derivatives Course Work
(Excel/VBA spreadsheet development)

• Valuation of first generation Exotic options - digital, barrier (knock in, knock out, KIKO, reverse knock outs), lookback, Asian options using Monte Carlo simulation methodology;
• Closed form analysis - factoring skew in pricing of binaries, put-call symmetry and static hedging of barriers, lookback hedging argument, adjusting for discrete monitoring of the barriers;
• Closed form analysis - reverse engineering of structured (derivatives) payoffs, convergence of closed form and Monte Carlo price;
• Valuation of first generation structured payoffs - accumulators, bull-bear notes, (equity and FX) range accruals, other equity linked payoffs;
• Valuation of second generation exotic equity options - cliquet, Napoloen, reverse cliquets, etc. using Stochastic volatility models of Heston and Heston Nandi, accounting for the forward skew;
• Valuation of second generation exotics - Parisian option, Passport option, Chooser Passport option using finite difference methods;
• Using binomial trees to value Bermudan payoffs;
• Valuation of multi-asset options and payoffs - basket, best of, worst of, rainbow options - using Monte Carlo simulation (PCA and Cholesky);
• Valuation of multi-asset path dependent payoffs - Himalyan, Altiplano, Everest, etc. - using Gaussian copula approach;
• Valuation of CDO (collateralized debt obligations) using Gaussian copula approach;

Estimation of Greeks & Risk Analysis Course Work

• Estimation of first order greeks - delta, gamma, vega, theta and rho – in closed form and Monte Carlo framework; estimation issues, speed, stability.
• Estimation of second order greeks - Volga, vomma, etc. - and adjustment to the valuation.
• Stress testing options portfolio, price-volatility matrix, vega convexity;
• Analysis of raw vegas and modified vegas; Vega Value at Risk (VaR), delta-gamma VaR;
• Analysis of correlation risks, Correlation vega, partial and total delta of baskets;

Module IV
Financial Derivatives - III

Valuation of Interest Rate Derivatives Course Work
(Excel/VBA spreadsheet development)

• Analysis of Ornstein-Uhlenbeck processes, mean reverting random walks; normal models;
• Vasicek and Cox-Ingersoll-Ross (CIR) process for short rates; the extended Vasicek model, valuation of options on coupon bonds;
• Tree framework for Vasicek model, binomial and trinomial trees;
• CIR Process with jumps, extended CIR process with jumps;
• Two factor affine models and valuation under two factor models, Heath-Jarrow-Morton (HJM) Forward rate model;
• Lognormal model of rates, Black-Derman-Toy tree and valuation of caps and floors using BDT tree;
• Libor Market Model (LMM), lognormal forward libor model (LFM), analysis of volatilities and correlations, forward rate volatilities;
• BGM model implementation, valuation of FRNs, structured interest rate payoffs under BGM model;
• Stochastic Volatility models for pricing interest rate derivatives;
• Pricing vanilla IRS & FX swaps, complex swaps (overnight indexed swaps, Libor in arrears swap, CMT swaps, quanto swaps, etc.);
• Convexity adjustment in complex swaps,
• Calibration - Black Volatilities and Swaption Volatilities.

Module V
Optimization Procedures and Portfolio Modelling

• Solution of a system of linear equations using Matrix algebra;
• Generating efficient frontier for portfolios using constrained optimization and Lagrangian multiplier;
• Sharpe's algorithm to estimate the efficient frontier and mean-variance analysis;
• Portfolio allocation models using Solver and user defined optimization function;
• Algorithmic Trading models and optimization of marginal contribution of risk;
• Optimization of VaR and risk capital allocation for trading and investment.
• Quadratic Optimization and applications in portfolio risk problems;

To apply for the above course please write to info@risklatte.com with the subject header "CFE (2010) / New York" or send your request by fax to Ms Anna Cho at +852 3752 0662. You can also write to us at Risk Latte Company Limited, 9th Floor, Somptueux Central, 52 – 54 Wellington Street, Central, Hong Kong or you can call us on +852 3752 0662