Multilevel Monte Carlo for Option Pricing

This repository contains the code generate the plots in the report.

Installation

To install the project on a new machine, follow these steps:

1. Clone the project and navigate to the project directory.
2. Create a new python environment, cf. docs, and activate it.
3. Install the required packages using

   pip install -r requirements. txt
   

4. Install the package using

   pip install .
   

   or using

   pip install --editable .
   

   if you want to edit the project.

Running the experiments

To run the experiments in the different sections of the report, follow these instructions. All the scripts come with an argument parser, that allows the variation of the input arguments. For help about a script script.py, call

python script.py --help

For the plotting scripts, add the --usetex flag for LaTeX support.

Section IV.A - standard estimator

To vary the number of samples, call

python nsamp_variation.py

and then

python plot_nsamp_variation.py

To vary the time step size $h$, call

python h_variation.py

and then

python plot_h_variation.py

Section IV.B - two-level estimator

For the two-level experiments, call

python two_level.py

and then

python plot_two_level.py

Section IV.C - multi-level estimator

For the multi-level experiments with the Asian option, call first

python multi_level_asian.py

and then

python plot_multi_level_asian.py

Section V. - barrier call option

For the multi-level experiments with the barrier option, call first

python multi_level_barrier.py

and then

python plot_multi_level_barrier.py

Section VI. - variance reduction

For the experiments on variance reduction for high strike prices, run For the multi-level experiments with the Asian option, call first

python higher_strike.py

License

This project is licensed under the MIT License.