In this project we have implemented some Monte-Carlo simulations around the Black-Scholes and Heston models. Given some parameters of an european call option, this code computes for {100, 10000, 100000} simulations the following quantities:
- price
- delta
- gamma
- vega
Some reduction variance methods have been implemented:
- Antithetic Variables
- Control Variates
- Importance Sampling
All of them show great improvements in the estimator accuracy.
We have also plotted the price and greeks on a same scale against the spot, maturity and volatility (only for the Black-Scholes model in the latter).
- gnuplot > 5.2 (tested with qt terminal) http://www.gnuplot.info/download.html
- gnuplot-iostream interface http://stahlke.org/dan/gnuplot-iostream/
- boost > 1.63.0 http://www.boost.org/users/download/
- cmake > 3.8 https://cmake.org/download/
- clone the git repository:
git clone https://github.com/RedwanBouizi/MC.git - go to MC directory:
cd MC - create a build directory:
mkdir build - go to build directory:
cd build cmake ../make
Both the library and executable should now be built respectively in /src and /tests. To run the executable, follow these commands:
cd tests./example -1 -2 -3
Option 1: performs price and greeks computation using the Black-Scholes and Heston models.
Option 2: outputs several graphs telling about the influence of spot, maturity, volatility over the price and greeks computations.
Option 3: shows how the asymmetry (price and greeks) evolves as the correlation between brownian motions in the Heston model increases.
The latter is quite long, which is why we have included the outputs below.
