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Financial Recipes

Running Jupyter Locally

The easiest is probably to install Docker and use the provided Dockerfile.

The Makefile is set up to do just this, so once you have docker installed, just type:

make

And open your browser at address localhost:8888. The changes you make will be stored to the notebooks folder in the current directory, which you can then commit to git.

Models and Pricing

  • Heston stochastic volatility model
  • Black-Scholes
  • Vasicek
  • Hull-White for interest rates [1-factor, 2-factor]
  • Garman-Kohlhagen for FX
  • CEV (constant elasticity of variance) model
  • Bachelier model
  • SABR model
  • A DSL for models (and basis for stochastic sampling)

Computational ingredients/components

  • Brownian bridge
  • Quasirandom number generation
    • Sobol numbers
    • van der Corput numbers
  • Pseudorandom number generation
  • Monte-Carlo simulation
  • Longstaff-Schwartz (for American options);

Finite differencing for PDE solving

  • binomial trees, lattices

Risk

  • Value at Risk
  • “Greeks” — sensitivities to designated parameters (risk factors)
    • Automatic differentiation

Date/time

  • Day count conventions
  • Data conversion

Notes on Parallelism

  • Vectorisation

Related Work

  1. Paolo Brandimarte. Numerical methods in finance and economics: a MATLAB-based introduction. John Wiley & Sons, Inc., 2006. Available via REX: http://onlinelibrary.wiley.com.ep.fjernadgang.kb.dk/book/10.1002/0470080493

  2. Seydel, Rüdiger. Tools for computational finance. Berlin: Springer, 2006. Available via REX: http://link.springer.com.ep.fjernadgang.kb.dk/book/10.1007%2F3-540-27926-1