fin0

Various financial mathematics codes in Python for testing purposes.
See comment in files for what each does, but explanation is very limited.
Includes:

• Analytical pricing of European options under Black-Scholes-Merton, with Greeks
• Implied volatility calculation
• Monte Carlo simulation (and European option pricing) for
  • Black-Scholes-Merton (with and without importance sampling)
  • Cox-Ingersoll-Ross
  • Heston (with and without importance sampling and antithetic variates)
  • gamma
  • variance gamma
  • bilateral gamma
  • Poisson
• American option pricing
  • binomial tree
  • Longstaff-Schwartz
  • de-Americanization
• Carr-Madan FFT pricing of European options for
  • Black-Scholes-Merton
  • variance gamma
  • bilateral gamma
• PDE pricing
  • Black-Scholes PDE

Some notes

While not necessary, full paths are always generated in Monte Carlo simulations for pricing, so that path-dependent options may be priced also.
Scripts should be ran from within this directory.
Plots are written to the out folder in this directory.

Some plots

Implied volatility calculation

American option pricing under Black-Scholes-Merton via the binomial tree

Black-Scholes-Merton Monte Carlo simulation

Cox-Ingersoll-Ross Monte Carlo simulation

Heston Monte Carlo simulation

Variance gamma Monte Carlo simulation

Bilateral gamma Monte Carlo simulation