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

Idea

• 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

Results

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

Part 2

• 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

Idea

• 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

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