This research project applies an object oriented approach to compute the prices of American and European Call and Put options using different pricing methods such as Monte Carlo, the analytical Black-Scholes formula and the Binomial tree method.
This project applies an object oriented approach to compute the prices of American and European Call and Put options using different pricing methods such as Monte Carlo, the analytical Black-Scholes formula and the Binomial tree method.
Generates a binomial option pricing tree based on the parameters one inputs in order to achieve the price of the option premium. Applicable to European as well as American options.
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:
Some reduction variance methods have been implemented:
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).
git clone https://github.com/RedwanBouizi/MC.gitcd MCmkdir buildcd buildcmake ../makeBoth 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 -3Option 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.
