Done
Implement Monte Carlo Numerical method to solve Stochastic Differential Equations/Simulation problems
CVA IRS portfolio calculation using LMM model
CVA IRS portfolio calculation using Gaussian HJM model
Monte Carlo Numerical method acceleration with NVIDIA CUDA (STREAMS)
Monte Carlo Numerical method acceleration with NVIDIA CUDA (Multiple-GPU)
Review NVIDIA Paper on Asian Option Pricing / Monte Carlo / GPU / CURAND
NEXT
CVA IRS portfolio Sensitivities Calculation using AD with dco/c++
Monte Carlo Predictor Corrector
Monte Carlo Variance Reduction Importance Sampling
Monte Carlo Variance Reduction Control Variate
Monte Carlo test different Random Numbers
Finish Nth to Default Credit Default Swap Basket C++20 Implementation
TODO
Compute Greek computations using AD dco/c++ (Uwe Neumann)
Acceleration of AD calculation using CUDA/SYCL and LLVM
Calculus, Linear Algebra, Statistics, Probability, Statistics (Spivak, Gilbert Strang, Grimmet)
Chebyshev Polynomials and General Numerical analisys , Numerical Linear Algebra (Burden & Feires, Volkov, Threfethen, Demmel)
Study Direct Delta Functions, Green Functions (Riley, Hobson, Bence)
Study Stochastic PDE, DE, Direct Delta Functions, Boundary Conditions BVP (Willmot, Threfethen, Duffy)
Study Measure Theory,Stochastic Calculus, SDE, Martingals Theory, Ito Calculus, Feymann-Kac, Girsanov (Willmot, Pliska, Steven Shreve, Neftci, Oskendal)
Malliavin Calculus
Review Monte Carlo methods in Finance (Jaeckel, Glasserman, Mike Giles)
Solves PDE numerically using Finite Differences
Solves PDE numerically using Fourier Transform
Radial Functions Option Pricing, Radial Basis Functions & Fourier Transform (Alonso Pegna)
Hagan numerical interpolation
Study Numerical Optimization Techniques (Nocedal)
Asyntotic Analysis, Spectral Methods, Topology & Differential Geometry (Spivak, Gilbert Strang)
Study Monte Carlo method variance reduction methods
Dive depth on Calibration, Correlation and Volatility
Implement Local Volatility Model and Stochastic Volatility Models [Heston Model, SABR Model, CEV Model] (Dupire, Jim Gatheral, Lorenzo Bergomi, Xen Chuli)
Hagan LIBOR Market Model with SABR Volatility (HAGAN)
Price/Study FX products
Baruch Course on Interest Rate and Credit Models (MTH-9877) (Brigo, Rebonato, Pallacini, Hagan)
Price Bermuda Swaptions (Garetek)
Study Machine Learning and Deep Learning (Christopher Bishop, TEOSTL, Ian Good Fellow, Tensor Flow)
Implement Rough Volatility paper with Deep Learning / Tensor Flow
American Options
Multi-Asset (rainbow) options
Marginal (MVA), Collateral, XVA (Green)
Skills Gained (Andrew Green)
1 - Develop a new XVA platform
2 - CUDA GPU / C++ (11) CPU Hybrid Compute environment
3 - Grid Computing
4 - Adjoint Algorithmic Differentiation (AAD): CPU/GPU implementation using NAG dco/dco_map
5 - Multi-asset platform: IR & FX, later inflation, commodities and equity derivatives
6 - stochastic volatility modelling, correlation & calibration
7 - Deep Learning applications in XVA