Suggestions for Rutgers 

Bruno Dupire 

Computational finance 

Partial Differential Equations 

• Theory, reduction to canonical form 

• Finite difference: explicit, implicit schemes, Cranck-Nicholson 

• Boundary conditions 

• nD case: ADI, degenerate cases (Asian options, Lookbacks) 

• Finite elements 

Monte Carlo simulations 

• Theory, CLT, time and space discretisation 

• Euler and Milstein schemes, spectral decomposition 

• Variance reduction: antithetic, control variates, importance sampling, stratification… 

• Low discrepancy sequences 

Fourier transform 

• FFT, fractional FFT 

• Convolution methods 

• Application to PIDE 

Statistics 

• Parameter estimation 

• GARCH methods 

• Principal Component Analysis 

• Independent Component Analysis 

Optimisation 

• Gradient and Hessian methods, Levenberg-Marquardt algorithm 

• Application to calibration 

• Linear Programming for arbitrage bounds 

Interpolation 

• Splines: cubic, B-splines 

• Monotonic Hermite interpolation 

• Model based interpolation 

• Quadrature methods 

Recent topics 

Equity Derivatives 

• Pricing of Cliquets 

• Computation of fair skew 

• Computation of Variance Swaps 

• Optimal hedge with move based strategies 

Credit Derivatives 

• Link equity options/equity default swaps/credit default swaps 

• Credit models with realistic dynamics 

General 

• Cross volatilities for FX 

• Incomplete markets: optimal hedge, applicability of indifference pricing 

• Electronic trading of blocks