AMPL Simulation Script

import math
import statistics as stat
import random
import numpy as np
import matplotlib.pyplot as plt

'''
Most recent update: 2020-10-16

Code written by Hikaru Sunakawa (@shammoo25 on Telegram), 2020-07-16, Japan.

This script simulates AMPL economics with user-defined initial conditions. You are able to configure the initial
AMPL price, AMPL supply and the amount of AMPL in your wallet. You must also choose how many days you want to simulate,
and how many simulations you want to perform. You may also choose to plot the results, by configuring the plot_results
and max_plots parameters. At the end of the script, when all simulations have been performed, statistics about the
simulations will be printed to the console.

The volatiltiy and demand coefficients used in this configuration produce "adequately similar" price action (based
purely on a qualitative assessment of the output simulation plots versus the actual AMPL data plots over the last 90
days), but these coefficients can be changed to whatever you like for the purpose of experimentation.

AMPL and Oracle price changes are random, determined using volatility ranges and dynamically changing weights which
favour either an up or down price movement.

Note that the random number functions do not have defined seeds, meaning that the results will be different every time
the script is run

Please modify the code as you see fit if you feel that it can be improved or corrected. Please let me know on my
telegram handle above if you have any interesting suggestions
'''

############################################ MODIFY THE FOLLOWING VALUES ###############################################
sim_number = 10000  # Number of simulations to perform (if doing more than 1000 simulations, set print_daily and plot_results to False to vastly improve performance)
days = 90  # Number of days per simulation
print_daily = False  # Print the daily stats to the console during each simulation? Will improve performance if False
plot_results = False  # Plot simulation results? True or False. Will output the maximum number of figures determined by max_plots
max_plots = 20  # Maximum number of plot figures to output (1 plot figure per simulation)
init_ampl_balance = 1000  # Initial amount of AMPL in wallet
init_ampl_price = 0.92  # [USD] Initial price of AMPL
init_supply = 166929000.0  # Initial TOTAL supply of AMPL
price_target = 1.014  # [USD] Price target used in rebase calculation
demand_threshold = 0.05  # [USD] The difference between AMPL price and $1.00, used for changing demand coefficients
equal_chance = False  # If this is True, then every day there is the same chance of a upward or downward price movement, and the demand coefficients below are not used
low_price_demand = 1.70  # The higher this coefficient, the higher the chance of an upward price movement when price is within demand_threshold of $1.00
high_price_demand = 1.20  # The higher this coefficient, the higher the chance of an upward price movement when price is outside demand_threshold of $1.00
min_low_volatility = 0.02  # The higher this value, the higher the minimum possible value of the daily AMPL and Oracle price swings when price is within demand_threshold of $1.00
max_low_volatility = 0.08  # The higher this value, the higher the maximum possible value of the daily AMPL and Oracle price swings when price is within demand_threshold of $1.00
min_high_volatility = 0.10  # The higher this value, the higher the minimum possible value of the daily AMPL and Oracle price swings when price is outside demand_threshold of $1.00
max_high_volatility = 0.30  # The higher this value, the higher the maximum possible value of the daily AMPL and Oracle price swings when price is outside demand_threshold of $1.00
########################################################################################################################

# Constants
rebase_lag = 10  # [days] Lag used in rebase calculation
contraction_threshold = price_target * 0.95  # [USD] Oracle rate window lower value. Between this value and expansion_threshold, rebase will not take place
expansion_threshold = price_target * 1.05  # [USD] Oracle rate window higher value

# Initialize
days += 1
ampl_price = np.zeros((days, sim_number))
supply = np.zeros((days, sim_number))
my_balance = np.zeros((days, sim_number))
rebase = np.zeros((days, sim_number))
market_cap = np.zeros((days, sim_number))
ampl_value = np.zeros((days, sim_number))
init_ampl_value = init_ampl_price * init_ampl_balance
init_market_cap = init_supply * init_ampl_price

################################################### SIMULATE ###########################################################
for s in range(sim_number):
    for x in range(days):
        if x == 0:
            ampl_price[0, s] = init_ampl_price
            supply[0, s] = init_supply
            my_balance[0, s] = init_ampl_balance
            rebase[0, s] = 0.0
            market_cap[0, s] = init_market_cap
            ampl_value[0, s] = init_ampl_value
        else:
            # Determine demand strength and volatility
            if math.fabs(ampl_price[x - 1, s] - 1.00) < demand_threshold:
                demand_strength = random.uniform(1.0, low_price_demand)
                volatility = random.uniform(min_low_volatility, max_low_volatility)
            else:
                demand_strength = random.uniform(min(low_price_demand, high_price_demand),
                                                 max(low_price_demand, high_price_demand))
                volatility = random.uniform(min_high_volatility, max_high_volatility)
            # Determine direction of movement
            direction_list = [1.0] + [-1.0]
            if equal_chance:
                up_weight = 50
                down_weight = 50
            else:
                up_weight = demand_strength
                down_weight = 1 / demand_strength
            direction = random.choices(direction_list, weights=(up_weight, down_weight), k=1)
            direction = float(direction[0])
            # Calculate price, balance, supply and market cap
            ampl_price[x, s] = ampl_price[x - 1, s] * (1.0 + (volatility * direction))  # Calculate pre-rebase AMPL price
            # Determine Oracle rate based on average AMPL price (using previous post-rebase price and current pre-rebase price), then calculate  subsequent rebase amount
            oracle_price = (ampl_price[x - 1, s] + ampl_price[x, s]) / 2
            if contraction_threshold <= oracle_price <= expansion_threshold:
                rebase[x, s] = 0.0
            else:
                rebase[x, s] = (oracle_price - price_target) / price_target / rebase_lag
            ampl_price[x, s] *= (1 - rebase[x - 1, s])  # Calculate post-rebase AMPL price
            my_balance[x, s] = my_balance[x - 1, s] * (1 + rebase[x, s])
            supply[x, s] = supply[x - 1, s] * (1 + rebase[x, s])
            market_cap[x, s] = ampl_price[x, s] * supply[x, s]
            ampl_value[x, s] = my_balance[x, s] * ampl_price[x, s]

        if print_daily:
            print("Sim " + str(s + 1),
                  "| Day " + str(x),
                  "| AMPL price = $" + str('%.2f' % (ampl_price[x, s])),
                  "| AMPL Balance = " + f'{my_balance[x, s]:,.0f}',
                  "| AMPL Value = $" + str('%.3f' % (ampl_value[x, s])),
                  "| Rebase = " + str('%.3f' % (100 * rebase[x, s])) + "%",
                  "| Supply = " + f'{supply[x, s]:,.0f}',
                  "| Market Cap = $" + f'{market_cap[x, s]:,.0f}')

    if plot_results and s < max_plots:
        fig, (ax1, ax2, ax3, ax4, ax5) = plt.subplots(5, figsize=(10, 8), constrained_layout=True)
        fig.suptitle('Simulation ' + str(s + 1))
        ax1.plot(ampl_price[:, s])
        ax1.set_title('AMPL Price (USD)')
        ax1.grid(b=True, which='both', axis='both')
        ax2.plot(market_cap[:, s], 'tab:orange')
        ax2.set_title('Market Cap')
        ax2.grid(b=True, which='both', axis='both')
        ax3.plot(supply[:, s], 'tab:cyan')
        ax3.set_title('Supply')
        ax3.grid(b=True, which='both', axis='both')
        ax4.plot(my_balance[:, s], 'tab:green')
        ax4.set_title('Amount of AMPL Held in Wallet')
        ax4.grid(b=True, which='both', axis='both')
        ax5.plot(ampl_value[:, s], 'tab:red')
        ax5.set_title('USD Value of AMPL in Wallet')
        ax5.grid(b=True, which='both', axis='both')

    if print_daily == False:
        percent_complete = s / sim_number * 100
        if percent_complete % 1 == 0:
            print('\r', str(int(percent_complete)) + '% of simulations performed', end='')
    else:
        print('-------------------------------------------------------------------------------------------------------'
              '-----------------------------------------------------------------------------')

print('\r', 'All simulations performed', end='')

###############################################  CALCULATE STATISTICS ##################################################
price_up = 0
supply_up = 0
balance_up = 0
value_up = 0
mc_up = 0
price_diff_percent = np.zeros(sim_number)
price_diff_dollar = np.zeros(sim_number)
supply_diff = np.zeros(sim_number)
supply_diff_percent = np.zeros(sim_number)
balance_diff_percent = np.zeros(sim_number)
balance_diff = np.zeros(sim_number)
value_diff_percent = np.zeros(sim_number)
value_diff_dollar = np.zeros(sim_number)
mc_diff_percent = np.zeros(sim_number)
mc_diff_dollar = np.zeros(sim_number)
drawdown = np.zeros(sim_number)
recovery = np.zeros(sim_number)
for s in range(sim_number):
    if ampl_price[-1, s] > ampl_price[0, s]:
        price_up += 1
    if supply[-1, s] > supply[0, s]:
        supply_up += 1
    if my_balance[-1, s] > my_balance[0, s]:
        balance_up += 1
    if ampl_value[-1, s] > ampl_value[0, s]:
        value_up += 1
    if market_cap[-1, s] > market_cap[0, s]:
        mc_up += 1
    price_diff_percent[s] = (ampl_price[-1, s] / ampl_price[0, s] * 100) - 100
    price_diff_dollar[s] = ampl_price[-1, s] - ampl_price[0, s]
    supply_diff_percent[s] = (supply[-1, s] / [supply[0, s]] * 100) - 100
    supply_diff[s] = supply[-1, s] - supply[0, s]
    balance_diff_percent[s] = (my_balance[-1, s] / my_balance[0, s] * 100) - 100
    balance_diff[s] = my_balance[-1, s] - my_balance[0, s]
    value_diff_percent[s] = (ampl_value[-1, s] / ampl_value[0, s] * 100) - 100
    value_diff_dollar[s] = ampl_value[-1, s] - ampl_value[0, s]
    mc_diff_percent[s] = (market_cap[-1, s] / market_cap[0, s] * 100) - 100
    mc_diff_dollar[s] = market_cap[-1, s] - market_cap[0, s]
    min_market_cap = min(market_cap[:, s])
    drawdown[s] = max(0, 100 - (min_market_cap / init_market_cap * 100))
max_drawdown_index = np.argmax(drawdown)

print(f'\n**************************************** OVERALL STATISTICS *****************************************')
print(str(price_up) + ' out of ' + str(sim_number) + ' (' + str(price_up / sim_number * 100)
      + '%) simulations ended with AMPL price higher than the initial price')
print(str(supply_up) + ' out of ' + str(sim_number) + ' (' + str(supply_up / sim_number * 100)
      + '%) simulations ended with AMPL supply higher than the initial amount')
print(str(mc_up) + ' out of ' + str(sim_number) + ' (' + str(mc_up / sim_number * 100)
      + '%) simulations ended with market cap higher than the initial value')
print(str(balance_up) + ' out of ' + str(sim_number) + ' (' + str(balance_up / sim_number * 100)
      + '%) simulations ended with amount of AMPL in wallet higher than the initial amount')
print(str(value_up) + ' out of ' + str(sim_number) + ' (' + str(value_up / sim_number * 100)
      + '%) simulations ended with value of AMPL (USD) in wallet higher than the initial value')

# AMPL Price
print(f'\nAMPL Price Changes:\n' + 'The mean price on the last day was $' + f'{stat.mean(ampl_price[-1, :]):,.2f}'
      + str('. This is a difference of $')
      + str('%.2f' % stat.mean(price_diff_dollar)) + ' ('
      + str('%.2f' % stat.mean(price_diff_percent)) + '%) from the initial price of $' + str('%.2f' % init_ampl_price))

print('The median price on the last day was $' + f'{stat.median(ampl_price[-1, :]):,.2f}'
      + str('. This is a difference of $')
      + str('%.2f' % stat.median(price_diff_dollar)) + ' ('
      + str('%.2f' % stat.median(price_diff_percent)) + '%) from the initial price of $'
      + str('%.2f' % init_ampl_price))

# AMPL Supply
print(f'\nAMPL Supply Changes:\n'
      + 'The mean supply at the end of ' + str(days - 1) + ' days was ' + f'{stat.mean(supply[-1, :]):,.0f}'
      + '. This is a change of ' + f'{stat.mean(supply_diff):,.0f}'
      + ' (' + f'{stat.mean(supply_diff_percent):,.2f}'
      + '%) from the initial supply of ' + f'{init_supply:,.0f}')

print('The median supply at the end of ' + str(days - 1)
      + ' days was ' + f'{stat.median(supply[-1, :]):,.0f}'
      + '. This is a change of ' + f'{stat.median(supply_diff):,.0f}'
      + ' (' + f'{stat.median(supply_diff_percent):,.2f}'
      + '%) from the initial supply of ' + f'{init_supply:,.0f}')

# Market Cap
print(f'\nMarket Cap Changes:\n'
      + 'The mean market cap at the end of ' + str(days - 1) + ' days was $' + f'{stat.mean(market_cap[-1, :]):,.0f}'
      + '. This is a change of $' + f'{stat.mean(mc_diff_dollar):,.0f}'
      + ' (' + f'{stat.mean(mc_diff_percent):,.2f}'
      + '%) from the initial amount of $' + f'{init_market_cap:,.0f}')

print('The median market cap at the end of ' + str(days - 1) + ' days was $' + f'{stat.median(market_cap[-1, :]):,.0f}'
      + '. This is a change of $' + f'{stat.median(mc_diff_dollar):,.0f}'
      + ' (' + f'{stat.median(mc_diff_percent):,.2f}'
      + '%) from the initial amount of $' + f'{init_market_cap:,.0f}')

# Amount of AMPL in Wallet
print(f'\nAMPL Wallet Balance Changes:\n' + 'The mean amount of held AMPL at the end of ' + str(
    days - 1) + ' days was ' + f'{stat.mean(my_balance[-1, :]):,.2f}'
      + ' AMPL. This is a change of ' + f'{stat.mean(balance_diff):,.2f}'
      + ' (' + f'{stat.mean(balance_diff_percent):,.2f}'
      + '%) from the initial amount of ' + f'{init_ampl_balance:,.2f}' + ' AMPL.')

print('The median amount of held AMPL at the end of ' + str(
    days - 1) + ' days was ' + f'{stat.median(my_balance[-1, :]):,.2f}'
      + ' AMPL. This is a change of ' + f'{stat.median(balance_diff):,.2f}'
      + ' (' + f'{stat.median(balance_diff_percent):,.2f}'
      + '%) from the initial amount of ' + f'{init_ampl_balance:,.2f}' + ' AMPL')

# USD Value of AMPL in Wallet
print(f'\nAMPL Wallet USD Value Changes:\n' + 'The mean amount of USD value of held AMPL at the end of ' + str(
    days - 1) + ' days was $' + f'{stat.mean(ampl_value[-1, :]):,.2f}'
      + '. This is a change of $' + f'{stat.mean(value_diff_dollar):,.2f}'
      + ' (' + f'{stat.mean(value_diff_percent):,.2f}'
      + '%) from the initial amount of $' + f'{init_ampl_value:,.2f}')

print('The median amount of USD value held AMPL at the end of ' + str(days - 1) + ' days was $'
      + f'{stat.median(ampl_value[-1, :]):,.2f}'
      + '. This is a change of $' + f'{stat.median((ampl_value[-1, :]) - init_ampl_value):,.2f}'
      + ' (' + f'{stat.median(value_diff_percent):,.2f}'
      + '%) from the initial amount of $' + f'{init_ampl_value:,.2f}')

# Drawdown
print(f'\nMarket Cap Drawdown % from the Initial USD Value (equivalent to drawdown % of USD value of AMPL in wallet):\n'
      + 'The mean percentage drawdown during the ' + str(days - 1)
      + ' day period was -' + f'{stat.mean(drawdown):,.2f}' + '%')
print('The median percentage drawdown during the ' + str(days - 1)
      + ' day period was -' + f'{stat.median(drawdown):,.2f}' + '%')
print('The largest drawndown out of all the simulations was -' + f'{(max(drawdown)):,.2f}' + '%'
      + ' in simulation #' + str(max_drawdown_index + 1))
print('Simulation #' + str(max_drawdown_index + 1) + ' ended with a market cap of $'
      + f'{market_cap[-1, max_drawdown_index]:,.0f}' + ' which is a change of $'
      + f'{market_cap[-1, max_drawdown_index] - init_market_cap:,.0f}'
      + ' (' + f'{(market_cap[-1, max_drawdown_index] / market_cap[0, max_drawdown_index] * 100) - 100:,.2f}'
      + '%) from the initial market cap of $'  + f'{init_market_cap:,.0f}')

if plot_results:
    plt.show()