Financial Engineering in IRFX in C++

Following structure of this course.

Topics Include:

• Binomial tree/pricer
• American & path-dependent options
• Monte Carlo methods
• Non linear solvers for implied vol
• Curve construction
• Short rate modelling
• HJM
• LMM
• SABR
• etc...
  

Contributions are more than welcome!

The current format/set-up is largely based on this repo. Special thanks to Kelvin for letting me copy his set up.

Features

• Python binding of c++ code via pybind11 (see this readme file for more info)
• Unit test suite supported by googletest
• CI via Github Actions
• Code review of jupyter notebooks via ReviewNB App
• Auto formatting via clang-format

Requirements

• CMake
• C++11 compliant compiler
• Python3.7 or above
• Gtest

Install, Build & Run

All commands below are assumed to be run from root of the repo, unless specified otherwise.

Build

cmake -S ./ -B build
cmake --build build
./build/exec

Run tests

ctest --test-dir ./build --output-on-failure

Build and run tests

The following script only works for linux/macOS users:

./build_and_test_proj.sh

Set up & using pybind11

See this separate readme file for details

The following scripts only work for linux/macOS users (and assumes dependencies have been installed) - best to refer to this readme file for set up.

Install our c++ python binding fineng_irfx into the virtual env .venv:

./deploy_cpp_module.sh

Now, you can also launch a jupyter lab session with the required virtual env:

./launch_jupyter.sh

Project Structure

• The C++ code can be found here
• The Python code can be found here
• Example tests can be found here
• Project to-do list are here

Lecture 1

• Binomial tree option pricing
  • using function pointers to switch payoffs
  • different choices of tree structure
  • analysing prob distribution generated by binomial tree
  • computing Binomial coeff using recurrsion

Lecture 2

• Binomial tree option pricing continued:
  • improve code design by using OO design patterns
  • pricing path-dependent (knock-out) options
  • CRR model, numerical/analytical implementation
  • connection to Black Scholes
  • risks computation via finite differencing

Lecture 3

• Binomial tree option pricing continued:

  • pricing early excerise payoffs (American/Bermudans)
  • introduction of C++ templates
  • multiple inheritance in C++
  • numerical stability and convergence analysis

• Monte Carlo methods:

  • pricing vanilla options
  • using Box-muller as RNG
  • discretisation via the Euler–Maruyama scheme
  • pricing path-dependent payoffs (barrier/Asian)
  • discretisation error in long stepping (terminal correlation)

Lecture 4

• Monte Carlo methods continued:
  • Monte Carlo error analysis and convergence
  • variance reduction techniques
  • pricing arithmetic Asian with geometric asian as control variate
  • pricing barrier with vanilla option as control variate
  • error analysis continued
  • risks computation & error analysis

Lecture 5

• Monte Carlo methods continued:

  • American Options - Longstaff-Schwartz method
  • multi-asset simulation
  • pricing basket options

• 1 factor short rate modelling:

  • introduction to short rate models - 1 factor models
  • Merton Model - bond pricing
  • Merton Model - implied yield curve

Lecture 6

• 1 factor short rate modelling continued:
  • Vasicek Model - bond pricing
  • Vasicek Model - implied yield curve
  • calibration of the Vasicek model to the day-0 yield curve
  • intro to the Hull White model
  • calibration of the Hull White model to the day-0 yield curve