import numpy as np import matplotlib.pyplot as plt # model parameters class ModelParams: def __init__(self): self.D = 0.1 # base fee decay factor self.A = 1.5 # weighting for price change in token demand self.B = 1.5 # weighting for momentum change in token demand self.T = 5 # weighting for price change in trove issuance self.F = 5 # weighting for momentum change in trove issuance self.lookback = 5 # Lookback parameter for ETH price momentum self.max_redemption_fraction = 0.5 # Maximum fraction of supply that can be redeemed in a timestep # time series data class Data: def __init__(self): self.ETH_price = [500.0] self.momentum = [0.0] self.base_fee = [0.0] self.redeemed_amount = [0.0] self.token_price = [1.0] self.token_demand = [100.0] self.trove_issuance = [100.0] self.token_supply = [100.0] self.innate_token_demand = 100.0 ### Functions def get_new_momentum(data, params, ETH_price): lookback = params.lookback if lookback == 0: return 0 ETH_price_past = get_past_ETH_price(data, params) new_momentum = (ETH_price - ETH_price_past) / ETH_price_past return new_momentum def get_past_ETH_price(data, params): length = len(data.ETH_price) ETH_price_past = None if (params.lookback > length): ETH_price_past = data.ETH_price[0] else: ETH_price_past = data.ETH_price[length - params.lookback - 1] if ETH_price_past == 0: return 1 return ETH_price_past def get_new_redeemed_amount(data, params): max_redeemable = data.token_supply[-1] * params.max_redemption_fraction if max_redeemable == 0: return 0 redeemed = (1 - data.token_price[-1] - data.base_fee[-1]) * data.token_supply[-1] / 2 if redeemed < 0: return 0 else: return max(redeemed, max_redeemable) # Decay base fee correctly def get_new_base_fee(data, redeemed_amount): if data.token_supply[-1] == 0: return 0 base_fee = data.base_fee[-1]*params.D + (redeemed_amount / (2 * data.token_supply[-1])) return base_fee # return the innate component of market demand for holding LQTY tokens. Could be a function of: # - demand for a safe-haven $1-pegged asset # - trader needs for liquidity # - def get_innate_token_demand(): return 100.0 # compute price based on setting token supply = trove demand, and clearing the market def get_new_token_price(data, params, redeemed_amount, momentum): B = params.B F = params.F A = params.A T = params.T factor = - 1 /(A + T) print(f'factor: {factor}') # price = (data.trove_issuance[-1] - data.token_demand[-1] - ((A + T) * data.token_price[-1]) + ((B + F) * momentum) - redeemed_amount) * factor price = (data.trove_issuance[-1] - data.innate_token_demand - (A * data.token_price[-1] ) -T + ((B + F) * momentum) - redeemed_amount) * factor if price < 0: return 0 elif price > 1.1: return 1.1 else: return price # return price def get_new_token_demand(data, params, token_price, momentum): demand = data.innate_token_demand - params.A*(token_price - data.token_price[-1]) - params.B*(momentum) if demand < 0: return 0 else: return demand def get_new_trove_issuance(data, params, token_price, momentum ): trove_issuance = data.trove_issuance[-1] + params.T*(token_price - 1) + params.F*(momentum) if trove_issuance < 0: return 0 else: return trove_issuance def get_new_token_supply(trove_issuance, redeemed): new_supply = trove_issuance - redeemed if new_supply < 0: return 0 else: return new_supply ### Various ETH price functions def constant_ETH_price(last_price): return last_price # ETH price generator is a random walk (normal dist.), with occasional large +ve and -ve jumps def randomwalk_ETH_price(last_price): big_event = 0 big_event_chance = np.random.normal() if (big_event_chance > 1.5) or (big_event_chance < -1.5): big_event = big_event_chance * 20 new_price = last_price + np.random.normal(scale=5) + big_event if new_price < 0: return 0 else: return new_price def linear_increasing_ETH_price(last_price, gradient): return last_price + gradient def oscillating_ETH_price(min, magnitude, i): return min + magnitude + magnitude*np.sin(i) def linear_decreasing_ETH_price(last_price, gradient): return last_price - gradient def quadratic_ETH_price(scale, i): return scale*(i**2) def sublinear_ETH_price(last_price, steepness, i): return last_price + 1/(2*np.sqrt(steepness*(i+1))) # ### Script params = ModelParams() data = Data() # initialize data timeseries for i in range(1, 100): # update exogenous ETH price last_ETH_price = data.ETH_price[-1] # ETH_price = last_ETH_price # ETH_price = randomwalk_ETH_price(last_ETH_price) # ETH_price = oscillating_ETH_price(500, 10, i) # ETH_price = quadratic_ETH_price(10, i) # ETH_price = linear_increasing_ETH_price(last_ETH_price, 100) # ETH_price = linear_decreasing_ETH_price(last_ETH_price, 1) ETH_price = sublinear_ETH_price(last_ETH_price, 10, i) # print(ETH_price) momentum = get_new_momentum(data, params, ETH_price) redeemed_amount = get_new_redeemed_amount(data, params) base_fee = get_new_base_fee(data, redeemed_amount) data.innate_token_demand = get_innate_token_demand() # clear the market token_price = get_new_token_price(data, params, redeemed_amount, momentum) token_demand = get_new_token_demand(data, params, token_price, momentum) trove_issuance = get_new_trove_issuance(data, params, token_price, momentum) token_supply = get_new_token_supply(trove_issuance, redeemed_amount) # display all new data print(f'step: {i}') print(f'ETH price: {ETH_price}') print(f'momentum: {momentum}') print(f'redeemed amount: {redeemed_amount}') print(f'base fee: {base_fee}') print(f'token price: {token_price}') print(f'token demand: {token_demand}') print(f'trove_issuance: {trove_issuance}') print(f'token_supply: {token_supply}') # update all time series data.ETH_price.append(ETH_price) data.momentum.append(momentum) data.redeemed_amount.append(redeemed_amount) data.base_fee.append(base_fee) data.token_price.append(token_price) data.token_demand.append(token_demand) data.trove_issuance.append(trove_issuance) data.token_supply.append(token_supply) # print(f'length redeemed amt is + {len(data.redeemed_amount)}') # print(*data.redeemed_amount) # print(*data.base_fee) # print(*data.token_price) # print(*data.momentum) # Plot results fig = plt.figure() ax1 = fig.add_subplot(221) ax1.set_title('Token price') plt.plot(data.token_price) ax2 = fig.add_subplot(222) ax2.set_title('Redeemed amount') plt.plot(data.redeemed_amount) ax3 = fig.add_subplot(223) ax3.set_title('ETH Price') plt.plot(data.ETH_price) ax4 = fig.add_subplot(224) ax4.set_title('Base Fee') plt.plot(data.base_fee) # plt.plot(data.momentum) # plt.plot(data.token_demand) plt.show()