This README is intended to guide the user in how to use HW-05.
The assignment is hosted on github here:
https://github.com/DavisVaughan/uncc-math-6204/tree/master/assignments/hw-05
The purpose of this module is to calculate the Monte Carlo value of American options using the regression 2 approach from the Tools for Computational Finance book.
Regression 2 differs from regression 1 by only considering in the money points at the regression and update steps.
I think that the values in HW5 are MUCH more accurate than those in HW4. With our computational constraints, only considering the in the money values allows our numerical method to converge to the true value of the option much faster.
The Euler discretization of GBM was used to simulate the sample paths.
This method prices the American option using a regression method. The continuation value at time t is calculated by regressing the discounted value of the option at time t+1 on the price at time t. The continuation value is then compared to the value of the payoff at time t, and the max is chosen as the value of the option at t.
Notably, this is regression method 2, which only considers points that are in the money when running the regression and making updating decisions.
main.py - (DRIVER) Simulates the GBM and calculates the American option values at different degrees of accuracy.
gbm_simulator.py - The functions that generate the stock price simulations using Euler methods.
option_value.py - The price_option() function in this file is the interface that prices the option based on the user’s inputs. It dispatches to find the correct pricing function using the functions in option_value_dispatch.py.
option_value_dispatch.py - These function support option_value.py and are used to return the correct option pricing function (European VS American and Call VS Put).
Because the main.py file includes the code:
if __name__ == "__main__":
print(main())the easiest way to run the example is from the terminal.
Within your command line / terminal, navigate to the folder containing the main.py script, and just run:
python2 main.py^ Make sure you are using python2.
A pandas data frame should output:
MC_option_value call_put dt option_type
0 31.389674 call .01 american
1 28.906298 put .01 american
2 15.292809 call .001 american
3 29.552257 put .001 american