Running the Code

To run Part 1, type python part1.py
- This will output the average payoff for a block of 100 options
- It will also create a graph of the price paths for the stock
To run Part 2, type python part2.py
- This will fit stock1.csv and stock2.csv to distributions
  - It will then plot the distributions against the histograms for stock 1 and stock 2
- The program will then output the average payoff for 100 options when the value of each option is calculated by outperforming the average value of the distributions.
- The program does the same for outperforming the max value of the distributions.

Part 1

Refactor the europeanMonteCarlo.py to use np.beta(14,6) - 0.65 instead of the Brownian Motion.
Instead of 100 paths, do 5000.
Change Volatility and drift

The ideal price of the option is approximately $900 (for a block of 100 options).

After fitting the data to all distributions (using get_distributions()), the results were as follows:
For stock 1, an f distribution did the best, with a sum square error of 0.029197
- Best 5: f, levy_stable, chi, geninvgauss, powernorm
For stock 2, an alpha distribution fit best, with a sum square error of 0.022781
- Best 5: alpha, genhyperbolic, chi2, invgamma, skewnorm
From the common distributions, the lognormal distribution fits both datasets best, with a sum square error of 0.029207 and 0.022877 respectively
For simplicity, we will use the lognormal distribution as the fit distribution to calculate option value

Fit the stock data to its best distribution
- f distribution for stock 1, alpha distribution for stock 2
- Each stock gets its own distribution (2 total)
Pull down 365 values from each distribution as the estimated prices for each stock
For outperforming the average of the two stocks:
- If the value of the option at expiry is greater than the average value of the two stocks AT EXPIRY (last element in price list), then the payoff is option_price - average(stock1_expiry_price, stock2_expiry_price)
- Else, the payoff of the option is 0
For outperforming the max of the two stocks:
- If the value of the option at expiry is greater than the max value of the two stocks AT EXPIRY (last element in price list), then the payoff is option_price - max(stock1_expiry_price, stock2_expiry_price)
- Else, the payoff of the option is 0

Results according to distributions fit for stocks 1 and 2:

The average payoff has a large volatility, varying between about $500 and $1500 when computed using the average value and varying from about $200 to $1200 when computed using the max value. This is because the payoff of the option all depends on the random draws obtained for the stock prices at expiry