Risk Latte - Certificate in Financial Engineering (CFE), London

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 (2009) 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, 9^th Floor, Somptueux Central, 52 – 54 Wellington Street, Central, Hong Kong or you can call us on +852 3752 0662

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