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