# -*- coding: utf-8 -*- """Baseline vs Alternative V2 Copy Automatically generated by Colaboratory. Original file is located at https://colab.research.google.com/drive/1NNPdiKfO3950MuAGyIXTNrr4OMliINKb # Parameters and Initialization """ import random import numpy as np import pandas as pd import plotly.graph_objects as go import plotly.express as px import matplotlib.pyplot as plt import scipy.stats from plotly.subplots import make_subplots #policy functions rate_issuance = 0.01 rate_redemption = 0.01 base_rate_initial = 0 #global variables period = 24*365 month=24*30 day=24 #ether price price_ether_initial = 1000 price_ether = [price_ether_initial] sd_ether=0.02 drift_ether = 0 #LQTY price & airdrop price_LQTY_initial = 1 price_LQTY = [price_LQTY_initial] sd_LQTY=0.005 drift_LQTY = 0.0035 #reduced for now. otherwise the initial return too high quantity_LQTY_airdrop = 500 supply_LQTY=[0] LQTY_total_supply=100000000 #PE ratio PE_ratio = 50 #natural rate natural_rate_initial = 0.2 natural_rate = [natural_rate_initial] sd_natural_rate=0.002 #stability pool initial_return=0.2 return_stability=[initial_return] sd_return=0.001 sd_stability=0.001 drift_stability=1.002 theta=0.001 #liquidity pool & redemption pool sd_liquidity=0.001 sd_redemption=0.001 drift_liquidity=1.0003 redemption_star = 0.8 delta = -20 #close troves sd_closetroves=0.5 #sensitivity to LUSD price beta = 0.2 #open troves distribution_parameter1_ether_quantity=10 distribution_parameter2_ether_quantity=500 distribution_parameter1_CR = 1.1 distribution_parameter2_CR = 0.1 distribution_parameter3_CR = 16 distribution_parameter1_inattention = 4 distribution_parameter2_inattention = 0.08 sd_opentroves=0.5 n_steady=0.5 initial_open=10 #sensitivity to LUSD price & issuance fee alpha = 0.3 #number of runs in simulation n_sim= 8640 """# Exogenous Factors Ether Price """ #ether price for i in range(1, period): random.seed(2019375+10000*i) shock_ether = random.normalvariate(0,sd_ether) price_ether.append(price_ether[i-1]*(1+shock_ether)*(1+drift_ether)) """Natural Rate""" #natural rate for i in range(1, period): random.seed(201597+10*i) shock_natural = random.normalvariate(0,sd_natural_rate) natural_rate.append(natural_rate[i-1]*(1+shock_natural)) """LQTY Price - First Month""" #LQTY price for i in range(1, month): random.seed(2+13*i) shock_LQTY = random.normalvariate(0,sd_LQTY) price_LQTY.append(price_LQTY[i-1]*(1+shock_LQTY)*(1+drift_LQTY)) """# Troves Liquidate Troves """ def liquidate_troves(troves, index, data): troves['CR_current'] = troves['Ether_Price']*troves['Ether_Quantity']/troves['Supply'] price_LUSD_previous = data.loc[index-1,'Price_LUSD'] price_LQTY_previous = data.loc[index-1,'price_LQTY'] stability_pool_previous = data.loc[index-1, 'stability'] troves_liquidated = troves[troves.CR_current < 1.1] troves = troves[troves.CR_current >= 1.1] debt_liquidated = troves_liquidated['Supply'].sum() ether_liquidated = troves_liquidated['Ether_Quantity'].sum() n_liquidate = troves_liquidated.shape[0] troves = troves.reset_index(drop = True) liquidation_gain = ether_liquidated*price_ether_current - debt_liquidated*price_LUSD_previous airdrop_gain = price_LQTY_previous * quantity_LQTY_airdrop np.random.seed(2+index) shock_return = np.random.normal(0,sd_return) if index <= day: return_stability = initial_return*(1+shock_return) elif index<=month: #min function to rule out the large fluctuation caused by the large but temporary liquidation gain in a particular period return_stability = min(0.5, 365*(data.loc[index-day:index, 'liquidation_gain'].sum()+data.loc[index-day:index, 'airdrop_gain'].sum())/(price_LUSD_previous*stability_pool_previous)) else: return_stability = (365/30)*(data.loc[index-month:index, 'liquidation_gain'].sum()+data.loc[index-month:index, 'airdrop_gain'].sum())/(price_LUSD_previous*stability_pool_previous) return[troves, return_stability, debt_liquidated, ether_liquidated, liquidation_gain, airdrop_gain, n_liquidate] """Close Troves""" def close_troves(troves, index2, price_LUSD_previous): np.random.seed(208+index2) shock_closetroves = np.random.normal(0,sd_closetroves) n_troves = troves.shape[0] if index2 <= 240: number_closetroves = np.random.uniform(0,1) elif price_LUSD_previous >=1: number_closetroves = max(0, n_steady * (1+shock_closetroves)) else: number_closetroves = max(0, n_steady * (1+shock_closetroves)) + beta*(1-price_LUSD_previous)*n_troves number_closetroves = int(round(number_closetroves)) random.seed(293+100*index2) drops = list(random.sample(range(len(troves)), number_closetroves)) troves = troves.drop(drops) troves = troves.reset_index(drop=True) if len(troves) < number_closetroves: number_closetroves = -999 return[troves, number_closetroves] """Adjust Troves""" def adjust_troves(troves, index): issuance_LUSD_adjust = 0 random.seed(57984-3*index) ratio = random.uniform(0,1) for i in range(0, troves.shape[0]): random.seed(187*index + 3*i) working_trove = troves.iloc[i,:] p = random.uniform(0,1) check = (working_trove['CR_current']-working_trove['CR_initial'])/(working_trove['CR_initial']*working_trove['Rational_inattention']) #A part of the troves are adjusted by adjusting debt if p >= ratio: if check<-1: working_trove['Supply'] = working_trove['Ether_Price']*working_trove['Ether_Quantity']/working_trove['CR_initial'] if check>2: supply_new = working_trove['Ether_Price']*working_trove['Ether_Quantity']/working_trove['CR_initial'] issuance_LUSD_adjust = issuance_LUSD_adjust + rate_issuance * (supply_new - working_trove['Supply']) working_trove['Supply'] = supply_new #Another part of the troves are adjusted by adjusting collaterals if p < ratio and (check < -1 or check > 2): working_trove['Ether_Quantity'] = working_trove['CR_initial']*working_trove['Supply']/working_trove['Ether_Price'] troves.loc[i] = working_trove return[troves, issuance_LUSD_adjust] """Open Troves""" def open_troves(troves, index1, price_LUSD_previous): random.seed(2019*index1) issuance_LUSD_open = 0 shock_opentroves = random.normalvariate(0,sd_opentroves) n_troves = troves.shape[0] if index1<=0: number_opentroves = initial_open elif price_LUSD_previous <=1 + rate_issuance: number_opentroves = max(0, n_steady * (1+shock_opentroves)) else: number_opentroves = max(0, n_steady * (1+shock_opentroves)) + alpha*(price_LUSD_previous-rate_issuance-1)*n_troves number_opentroves = int(round(float(number_opentroves))) for i in range(0, number_opentroves): price_ether_current = price_ether[index1] np.random.seed(2033 + index1 + i*i) CR_ratio = distribution_parameter1_CR + distribution_parameter2_CR * np.random.chisquare(df=distribution_parameter3_CR) np.random.seed(20 + 10 * i + index1) quantity_ether = np.random.gamma(distribution_parameter1_ether_quantity, scale=distribution_parameter2_ether_quantity) np.random.seed(209870- index1 + i*i) rational_inattention = np.random.gamma(distribution_parameter1_inattention, scale=distribution_parameter2_inattention) supply_trove = price_ether_current * quantity_ether / CR_ratio issuance_LUSD_open = issuance_LUSD_open + rate_issuance * supply_trove new_row = {"Ether_Price": price_ether_current, "Ether_Quantity": quantity_ether, "CR_initial": CR_ratio, "Supply": supply_trove, "Rational_inattention": rational_inattention, "CR_current": CR_ratio} troves = troves.append(new_row, ignore_index=True) return[troves, number_opentroves, issuance_LUSD_open] """# LUSD Market Stability Pool """ def stability_update(stability_pool_previous, return_previous, index): np.random.seed(27+3*index) shock_stability = np.random.normal(0,sd_stability) natural_rate_current = natural_rate[index] if index <= month: stability_pool = stability_pool_previous* (drift_stability+shock_stability)* (1+ return_previous- natural_rate_current)**theta else: stability_pool = stability_pool_previous* (1+shock_stability)* (1+ return_previous- natural_rate_current)**theta return[stability_pool] """LUSD Price, liquidity pool, and redemption""" def price_stabilizer(troves, index, data, stability_pool, n_open): issuance_LUSD_stabilizer = 0 redemption_fee = 0 n_redempt = 0 redempted = 0 redemption_pool = 0 #Calculating Price supply = troves['Supply'].sum() np.random.seed(20*index) shock_liquidity = np.random.normal(0,sd_liquidity) liquidity_pool_previous = float(data['liquidity'][index-1]) price_LUSD_previous = float(data['Price_LUSD'][index-1]) price_LUSD_current= price_LUSD_previous*((supply-stability_pool)/(liquidity_pool_previous*(drift_liquidity+shock_liquidity)))**(1/delta) #Liquidity Pool liquidity_pool = supply-stability_pool #Stabilizer #Ceiling Arbitrageurs if price_LUSD_current > 1.1 + rate_issuance: #supply_current = sum(troves['Supply']) supply_wanted=stability_pool+liquidity_pool_previous*(drift_liquidity+shock_liquidity)*((1.1+rate_issuance)/price_LUSD_previous)**delta supply_trove = supply_wanted - supply CR_ratio = 1.1 rational_inattention = 0.1 quantity_ether = supply_trove * CR_ratio / price_ether_current issuance_LUSD_stabilizer = rate_issuance * supply_trove new_row = {"Ether_Price": price_ether_current, "Ether_Quantity": quantity_ether, "CR_initial": CR_ratio, "Supply": supply_trove, "Rational_inattention": rational_inattention, "CR_current": CR_ratio} troves = troves.append(new_row, ignore_index=True) price_LUSD_current = 1.1 + rate_issuance #missing in the previous version liquidity_pool = supply_wanted-stability_pool n_open=n_open+1 #Floor Arbitrageurs if price_LUSD_current < 1 - rate_redemption: np.random.seed(30*index) shock_redemption = np.random.normal(0,sd_redemption) redemption_ratio = redemption_star * (1+shock_redemption) #supply_current = sum(troves['Supply']) supply_target=stability_pool+liquidity_pool_previous*(drift_liquidity+shock_liquidity)*((1-rate_redemption)/price_LUSD_previous)**delta supply_diff = supply - supply_target if supply_diff < redemption_ratio * liquidity_pool: redemption_pool=supply_diff #liquidity_pool = liquidity_pool - redemption_pool price_LUSD_current = 1 - rate_redemption else: redemption_pool=redemption_ratio * liquidity_pool #liquidity_pool = (1-redemption_ratio)*liquidity_pool price_LUSD_current= price_LUSD_previous * (liquidity_pool/(liquidity_pool_previous*(drift_liquidity+shock_liquidity)))**(1/delta) #Shutting down the riskiest troves troves = troves.sort_values(by='CR_current', ascending = True) quantity_working_trove = troves['Supply'][troves.index[0]] redempted = quantity_working_trove while redempted <= redemption_pool: troves = troves.drop(troves.index[0]) quantity_working_trove = troves['Supply'][troves.index[0]] redempted = redempted + quantity_working_trove n_redempt = n_redempt + 1 #Residuals redempted = redempted - quantity_working_trove residual = redemption_pool - redempted wk = troves.index[0] troves['Supply'][wk] = troves['Supply'][wk] - residual troves['Ether_Quantity'][wk] = troves['Ether_Quantity'][wk] - residual/price_ether_current troves['CR_current'][wk] = price_ether_current * troves['Ether_Quantity'][wk] / troves['Supply'][wk] #Redemption Fee redemption_fee = rate_redemption * redemption_pool troves = troves.reset_index(drop=True) return[price_LUSD_current, liquidity_pool, troves, issuance_LUSD_stabilizer, redemption_fee, n_redempt, redemption_pool, n_open] """# LQTY Market""" def LQTY_market(index, data): quantity_LQTY = (100000000/3)*(1-0.5**(index/period)) np.random.seed(2+3*index) if index <= month: price_LQTY_current = price_LQTY[index-1] annualized_earning = (index/month)**0.5*np.random.normal(200000000,500000) else: revenue_issuance = data.loc[index-month:index, 'issuance_fee'].sum() revenue_redemption = data.loc[index-month:index, 'redemption_fee'].sum() annualized_earning = 365*(revenue_issuance+revenue_redemption)/30 #discountin factor to factor in the risk in early days discount=index/period price_LQTY_current = discount*PE_ratio*annualized_earning/LQTY_total_supply MC_LQTY_current = price_LQTY_current * quantity_LQTY return[price_LQTY_current, annualized_earning, MC_LQTY_current] """# Simulation Program""" #Defining Initials initials = {"Price_LUSD":[1.00], "Price_Ether":[price_ether_initial], "n_open":[initial_open], "n_close":[0], "n_liquidate": [0], "n_redempt":[0], "n_troves":[initial_open], "stability":[0], "liquidity":[0], "redemption_pool":[0], "supply_LUSD":[0], "return_stability":[initial_return], "airdrop_gain":[0], "liquidation_gain":[0], "issuance_fee":[0], "redemption_fee":[0], "price_LQTY":[price_LQTY_initial], "MC_LQTY":[0], "annualized_earning":[0]} data = pd.DataFrame(initials) troves= pd.DataFrame({"Ether_Price":[], "Ether_Quantity":[], "CR_initial":[], "Supply":[], "Rational_inattention":[], "CR_current":[]}) result_open = open_troves(troves, 0, data['Price_LUSD'][0]) troves = result_open[0] issuance_LUSD_open = result_open[2] data.loc[0,'issuance_fee'] = issuance_LUSD_open * initials["Price_LUSD"][0] data.loc[0,'supply_LUSD'] = troves["Supply"].sum() data.loc[0,'liquidity'] = 0.5*troves["Supply"].sum() data.loc[0,'stability'] = 0.5*troves["Supply"].sum() #Simulation Process for index in range(1, n_sim): #exogenous ether price input price_ether_current = price_ether[index] troves['Ether_Price'] = price_ether_current price_LUSD_previous = data.loc[index-1,'Price_LUSD'] price_LQTY_previous = data.loc[index-1,'price_LQTY'] #trove liquidation & return of stability pool result_liquidation = liquidate_troves(troves, index, data) troves = result_liquidation[0] return_stability = result_liquidation[1] debt_liquidated = result_liquidation[2] ether_liquidated = result_liquidation[3] liquidation_gain = result_liquidation[4] airdrop_gain = result_liquidation[5] n_liquidate = result_liquidation[6] #close troves result_close = close_troves(troves, index, price_LUSD_previous) troves = result_close[0] n_close = result_close[1] #if n_close<0: # break #adjust troves result_adjustment = adjust_troves(troves, index) troves = result_adjustment[0] issuance_LUSD_adjust = result_adjustment[1] #open troves result_open = open_troves(troves, index, price_LUSD_previous) troves = result_open[0] n_open = result_open[1] issuance_LUSD_open = result_open[2] #Stability Pool stability_pool = stability_update(data.loc[index-1,'stability'], return_stability, index)[0] #Calculating Price, Liquidity Pool, and Redemption result_price = price_stabilizer(troves, index, data, stability_pool, n_open) price_LUSD_current = result_price[0] liquidity_pool = result_price[1] troves = result_price[2] issuance_LUSD_stabilizer = result_price[3] redemption_fee = result_price[4] n_redempt = result_price[5] redemption_pool = result_price[6] n_open=result_price[7] if liquidity_pool<0: break #LQTY Market result_LQTY = LQTY_market(index, data) price_LQTY_current = result_LQTY[0] annualized_earning = result_LQTY[1] MC_LQTY_current = result_LQTY[2] #Summary issuance_fee = price_LUSD_current * (issuance_LUSD_adjust + issuance_LUSD_open + issuance_LUSD_stabilizer) n_troves = troves.shape[0] supply_LUSD = troves['Supply'].sum() if index >= month: price_LQTY.append(price_LQTY_current) new_row = {"Price_LUSD":float(price_LUSD_current), "Price_Ether":float(price_ether_current), "n_open":float(n_open), "n_close":float(n_close), "n_liquidate":float(n_liquidate), "n_redempt": float(n_redempt), "n_troves":float(n_troves), "stability":float(stability_pool), "liquidity":float(liquidity_pool), "redemption_pool":float(redemption_pool), "supply_LUSD":float(supply_LUSD), "issuance_fee":float(issuance_fee), "redemption_fee":float(redemption_fee), "airdrop_gain":float(airdrop_gain), "liquidation_gain":float(liquidation_gain), "return_stability":float(return_stability), "annualized_earning":float(annualized_earning), "MC_LQTY":float(MC_LQTY_current), "price_LQTY":float(price_LQTY_current) } data = data.append(new_row, ignore_index=True) if price_LUSD_current < 0: break """#**Exhibition**""" data def linevis(data, measure): fig = px.line(data, x=data.index/720, y=measure, title= measure+' dynamics') fig.show() fig = make_subplots(specs=[[{"secondary_y": True}]]) fig.add_trace( go.Scatter(x=data.index/720, y=data['Price_LUSD'], name="LUSD Price"), secondary_y=False, ) fig.add_trace( go.Scatter(x=data.index/720, y=data['Price_Ether'], name="Ether Price"), secondary_y=True, ) fig.update_layout( title_text="Price Dynamics of LUSD and Ether" ) fig.update_xaxes(tick0=0, dtick=1, title_text="Month") fig.update_yaxes(title_text="LUSD Price", secondary_y=False) fig.update_yaxes(title_text="Ether Price", secondary_y=True) fig.show() fig = make_subplots(specs=[[{"secondary_y": True}]]) fig.add_trace( go.Scatter(x=data.index/720, y=data['n_troves'], name="Number of Troves"), secondary_y=False, ) fig.add_trace( go.Scatter(x=data.index/720, y=data['supply_LUSD'], name="LUSD Supply"), secondary_y=True, ) fig.update_layout( title_text="Dynamics of Trove Numbers and LUSD Supply" ) fig.update_xaxes(tick0=0, dtick=1, title_text="Month") fig.update_yaxes(title_text="Number of Troves", secondary_y=False) fig.update_yaxes(title_text="LUSD Supply", secondary_y=True) fig.show() fig = make_subplots(rows=2, cols=1) fig.add_trace( go.Scatter(x=data.index/720, y=data['n_open'], name="Number of Troves Opened", mode='markers'), row=1, col=1, secondary_y=False ) fig.add_trace( go.Scatter(x=data.index/720, y=data['n_close'], name="Number of Troves Closed", mode='markers'), row=2, col=1, secondary_y=False ) fig.update_layout( title_text="Dynamics of Number of Troves Opened and Closed" ) fig.update_xaxes(tick0=0, dtick=1, title_text="Month") fig.update_yaxes(title_text="Troves Opened", row=1, col=1) fig.update_yaxes(title_text="Troves Closed", row=2, col=1) fig.show() fig = make_subplots(specs=[[{"secondary_y": True}]]) fig.add_trace( go.Scatter(x=data.index/720, y=data['n_liquidate'], name="Number of Liquidated Troves", mode='markers'), secondary_y=False, ) fig.add_trace( go.Scatter(x=data.index/720, y=data['n_redempt'], name="Number of Redempted Troves", mode='markers'), secondary_y=False, ) fig.update_layout( title_text="Dynamics of Number of Liquidated and Redempted Troves" ) fig.update_xaxes(tick0=0, dtick=1, title_text="Month") fig.update_yaxes(title_text="Number of Liquidated Troves", secondary_y=False) fig.update_yaxes(title_text="Number of Redempted Troves", secondary_y=True) fig.show() fig = make_subplots(specs=[[{"secondary_y": True}]]) fig.add_trace( go.Scatter(x=data.index/720, y=data['liquidity'], name="Liquidity Pool"), secondary_y=False, ) fig.add_trace( go.Scatter(x=data.index/720, y=data['stability'], name="Stability Pool"), secondary_y=False, ) fig.add_trace( go.Scatter(x=data.index/720, y=100*data['redemption_pool'], name="100*Redemption Pool"), secondary_y=False, ) fig.add_trace( go.Scatter(x=data.index/720, y=data['return_stability'], name="Return of Stability Pool"), secondary_y=True, ) fig.update_layout( title_text="Dynamics of Liquidity, Stability, Redemption Pools and Return of Stability Pool" ) fig.update_xaxes(tick0=0, dtick=1, title_text="Month") fig.update_yaxes(title_text="Size of Pools", secondary_y=False) fig.update_yaxes(title_text="Return", secondary_y=True) fig.show() fig = make_subplots(specs=[[{"secondary_y": True}]]) fig.add_trace( go.Scatter(x=data.index/720, y=data['airdrop_gain'], name="Airdrop Gain"), secondary_y=False, ) fig.add_trace( go.Scatter(x=data.index/720, y=data['liquidation_gain'], name="Liquidation Gain"), secondary_y=True, ) fig.update_layout( title_text="Dynamics of Airdrop and Liquidation Gain" ) fig.update_xaxes(tick0=0, dtick=1, title_text="Month") fig.update_yaxes(title_text="Airdrop Gain", secondary_y=False) fig.update_yaxes(title_text="Liquidation Gain", secondary_y=True) fig.show() fig = make_subplots(specs=[[{"secondary_y": True}]]) fig.add_trace( go.Scatter(x=data.index/720, y=data['issuance_fee'], name="Issuance Fee"), secondary_y=False, ) fig.add_trace( go.Scatter(x=data.index/720, y=data['redemption_fee'], name="Redemption Fee"), secondary_y=True, ) fig.update_layout( title_text="Dynamics of Issuance Fee and Redemption Fee" ) fig.update_xaxes(tick0=0, dtick=1, title_text="Month") fig.update_yaxes(title_text="Issuance Fee", secondary_y=False) fig.update_yaxes(title_text="Redemption Fee", secondary_y=True) fig.show() #linevis(data, 'annualized_earning') fig = make_subplots(specs=[[{"secondary_y": True}]]) fig.add_trace( go.Scatter(x=data.index/720, y=data['price_LQTY'], name="LQTY Price"), secondary_y=False, ) fig.add_trace( go.Scatter(x=data.index/720, y=data['MC_LQTY'], name="LQTY Market Cap"), secondary_y=True, ) fig.update_layout( title_text="Dynamics of the Price and Market Cap of LQTY" ) fig.update_xaxes(tick0=0, dtick=1, title_text="Month") fig.update_yaxes(title_text="LQTY Price", secondary_y=False) fig.update_yaxes(title_text="LQTY Market Cap", secondary_y=True) fig.show() def trove_histogram(measure): fig = px.histogram(troves, x=measure, title='Distribution of '+measure, nbins=25) fig.show() troves trove_histogram('Ether_Quantity') trove_histogram('CR_initial') trove_histogram('Supply') trove_histogram('Rational_inattention') trove_histogram('CR_current') import matplotlib.pyplot as plt plt.plot(troves["Ether_Quantity"]) plt.show() plt.plot(troves["CR_initial"]) plt.show() plt.plot(troves["Supply"]) plt.show() plt.plot(troves["CR_current"]) plt.show() data.describe() """new policy function issuance fee = redemption fee = base rate #**Simulation with Policy Function** """ #Defining Initials initials = {"Price_LUSD":[1.00], "Price_Ether":[price_ether_initial], "n_open":[initial_open], "n_close":[0], "n_liquidate": [0], "n_redempt":[0], "n_troves":[initial_open], "stability":[0], "liquidity":[0], "redemption_pool":[0], "supply_LUSD":[0], "return_stability":[initial_return], "airdrop_gain":[0], "liquidation_gain":[0], "issuance_fee":[0], "redemption_fee":[0], "price_LQTY":[price_LQTY_initial], "MC_LQTY":[0], "annualized_earning":[0], "base_rate":[base_rate_initial]} data2 = pd.DataFrame(initials) troves2= pd.DataFrame({"Ether_Price":[], "Ether_Quantity":[], "CR_initial":[], "Supply":[], "Rational_inattention":[], "CR_current":[]}) result_open = open_troves(troves2, 0, data2['Price_LUSD'][0]) troves2 = result_open[0] issuance_LUSD_open = result_open[2] data2.loc[0,'issuance_fee'] = issuance_LUSD_open * initials["Price_LUSD"][0] data2.loc[0,'supply_LUSD'] = troves2["Supply"].sum() data2.loc[0,'liquidity'] = 0.5*troves2["Supply"].sum() data2.loc[0,'stability'] = 0.5*troves2["Supply"].sum() #Simulation Process for index in range(1, n_sim): #exogenous ether price input price_ether_current = price_ether[index] troves2['Ether_Price'] = price_ether_current price_LUSD_previous = data2.loc[index-1,'Price_LUSD'] price_LQTY_previous = data2.loc[index-1,'price_LQTY'] #policy function determines base rate base_rate_current = 0.98 * data2.loc[index-1,'base_rate'] + 0.5*(data2.loc[index-1,'redemption_pool']/troves2['Supply'].sum()) rate_issuance = base_rate_current rate_redemption = base_rate_current #trove liquidation & return of stability pool result_liquidation = liquidate_troves(troves2, index, data2) troves2 = result_liquidation[0] return_stability = result_liquidation[1] debt_liquidated = result_liquidation[2] ether_liquidated = result_liquidation[3] liquidation_gain = result_liquidation[4] airdrop_gain = result_liquidation[5] n_liquidate = result_liquidation[6] #close troves result_close = close_troves(troves2, index, price_LUSD_previous) troves2 = result_close[0] n_close = result_close[1] #if n_close<0: # break #adjust troves result_adjustment = adjust_troves(troves2, index) troves2 = result_adjustment[0] issuance_LUSD_adjust = result_adjustment[1] #open troves result_open = open_troves(troves2, index, price_LUSD_previous) troves2 = result_open[0] n_open = result_open[1] issuance_LUSD_open = result_open[2] #Stability Pool stability_pool = stability_update(data2.loc[index-1,'stability'], return_stability, index)[0] #Calculating Price, Liquidity Pool, and Redemption result_price = price_stabilizer(troves2, index, data2, stability_pool, n_open) price_LUSD_current = result_price[0] liquidity_pool = result_price[1] troves2 = result_price[2] issuance_LUSD_stabilizer = result_price[3] redemption_fee = result_price[4] n_redempt = result_price[5] redemption_pool = result_price[6] n_open=result_price[7] if liquidity_pool<0: break #LQTY Market result_LQTY = LQTY_market(index, data2) price_LQTY_current = result_LQTY[0] annualized_earning = result_LQTY[1] MC_LQTY_current = result_LQTY[2] #Summary issuance_fee = price_LUSD_current * (issuance_LUSD_adjust + issuance_LUSD_open + issuance_LUSD_stabilizer) n_troves = troves2.shape[0] supply_LUSD = troves2['Supply'].sum() if index >= month: price_LQTY.append(price_LQTY_current) new_row = {"Price_LUSD":float(price_LUSD_current), "Price_Ether":float(price_ether_current), "n_open":float(n_open), "n_close":float(n_close), "n_liquidate":float(n_liquidate), "n_redempt": float(n_redempt), "n_troves":float(n_troves), "stability":float(stability_pool), "liquidity":float(liquidity_pool), "redemption_pool":float(redemption_pool), "supply_LUSD":float(supply_LUSD), "issuance_fee":float(issuance_fee), "redemption_fee":float(redemption_fee), "airdrop_gain":float(airdrop_gain), "liquidation_gain":float(liquidation_gain), "return_stability":float(return_stability), "annualized_earning":float(annualized_earning), "MC_LQTY":float(MC_LQTY_current), "price_LQTY":float(price_LQTY_current), "base_rate":float(base_rate_current)} data2 = data2.append(new_row, ignore_index=True) if price_LUSD_current < 0: break data2 """#**Exhibition Part 2**""" fig = make_subplots(specs=[[{"secondary_y": True}]]) fig.add_trace( go.Scatter(x=data.index/720, y=data['Price_LUSD'], name="LUSD Price"), secondary_y=False, ) fig.add_trace( go.Scatter(x=data.index/720, y=data['Price_Ether'], name="Ether Price"), secondary_y=True, ) fig.add_trace( go.Scatter(x=data2.index/720, y=data2['Price_LUSD'], name="LUSD Price New", line = dict(dash='dot')), secondary_y=False, ) fig.update_layout( title_text="Price Dynamics of LUSD and Ether" ) fig.update_xaxes(tick0=0, dtick=1, title_text="Month") fig.update_yaxes(title_text="LUSD Price", secondary_y=False) fig.update_yaxes(title_text="Ether Price", secondary_y=True) fig.show() fig = make_subplots(specs=[[{"secondary_y": True}]]) fig.add_trace( go.Scatter(x=data.index/720, y=data['n_troves'], name="Number of Troves"), secondary_y=False, ) fig.add_trace( go.Scatter(x=data.index/720, y=data['supply_LUSD'], name="LUSD Supply"), secondary_y=True, ) fig.add_trace( go.Scatter(x=data2.index/720, y=data2['n_troves'], name="Number of Troves New", line = dict(dash='dot')), secondary_y=False, ) fig.add_trace( go.Scatter(x=data2.index/720, y=data2['supply_LUSD'], name="LUSD Supply New", line = dict(dash='dot')), secondary_y=True, ) fig.update_layout( title_text="Dynamics of Trove Numbers and LUSD Supply" ) fig.update_xaxes(tick0=0, dtick=1, title_text="Month") fig.update_yaxes(title_text="Number of Troves", secondary_y=False) fig.update_yaxes(title_text="LUSD Supply", secondary_y=True) fig.show() fig = make_subplots(rows=2, cols=2) fig.add_trace( go.Scatter(x=data.index/720, y=data['n_open'], name="Number of Troves Opened", mode='markers'), row=1, col=1, secondary_y=False ) fig.add_trace( go.Scatter(x=data.index/720, y=data['n_close'], name="Number of Troves Closed", mode='markers'), row=2, col=1, secondary_y=False ) fig.add_trace( go.Scatter(x=data2.index/720, y=data2['n_open'], name="Number of Troves Opened New", mode='markers'), row=1, col=2, secondary_y=False ) fig.add_trace( go.Scatter(x=data2.index/720, y=data2['n_close'], name="Number of Troves Closed New", mode='markers'), row=2, col=2, secondary_y=False ) fig.update_layout( title_text="Dynamics of Number of Troves Opened and Closed" ) fig.update_xaxes(tick0=0, dtick=1, title_text="Month") fig.update_yaxes(title_text="Troves Opened", row=1, col=1) fig.update_yaxes(title_text="Troves Closed", row=2, col=1) fig.show() fig = make_subplots(rows=2, cols=1) fig.add_trace( go.Scatter(x=data.index/720, y=data['n_liquidate'], name="Number of Liquidated Troves"), row=1, col=1, secondary_y=False ) fig.add_trace( go.Scatter(x=data.index/720, y=data['n_redempt'], name="Number of Redempted Troves"), row=2, col=1, secondary_y=False ) fig.add_trace( go.Scatter(x=data2.index/720, y=data2['n_liquidate'], name="Number of Liquidated Troves New", line = dict(dash='dot')), row=1, col=1, secondary_y=False ) fig.add_trace( go.Scatter(x=data2.index/720, y=data2['n_redempt'], name="Number of Redempted Troves New", line = dict(dash='dot')), row=2, col=1, secondary_y=False ) fig.update_layout( title_text="Dynamics of Number of Liquidated and Redempted Troves" ) fig.update_xaxes(tick0=0, dtick=1, title_text="Month") fig.update_yaxes(title_text="Troves Liquidated", row=1, col=1) fig.update_yaxes(title_text="Troves Redempted", row=2, col=1) fig.show() fig = make_subplots(specs=[[{"secondary_y": True}]]) fig.add_trace( go.Scatter(x=data.index/720, y=data['liquidity'], name="Liquidity Pool"), secondary_y=False, ) fig.add_trace( go.Scatter(x=data.index/720, y=data['stability'], name="Stability Pool"), secondary_y=False, ) fig.add_trace( go.Scatter(x=data.index/720, y=100*data['redemption_pool'], name="100*Redemption Pool"), secondary_y=False, ) fig.add_trace( go.Scatter(x=data2.index/720, y=data2['liquidity'], name="Liquidity Pool New", line = dict(dash='dot')), secondary_y=False, ) fig.add_trace( go.Scatter(x=data2.index/720, y=data2['stability'], name="Stability Pool New", line = dict(dash='dot')), secondary_y=False, ) fig.add_trace( go.Scatter(x=data2.index/720, y=100*data2['redemption_pool'], name="100*Redemption Pool New", line = dict(dash='dot')), secondary_y=False, ) fig.update_layout( title_text="Dynamics of Liquidity, Stability, Redemption Pools and Return of Stability Pool" ) fig.update_xaxes(tick0=0, dtick=1, title_text="Month") fig.update_yaxes(title_text="Size of Pools", secondary_y=False) fig.show() fig = make_subplots(specs=[[{"secondary_y": True}]]) fig.add_trace( go.Scatter(x=data.index/720, y=data['return_stability'], name="Return of Stability Pool"), secondary_y=False, ) fig.add_trace( go.Scatter(x=data2.index/720, y=data2['return_stability'], name="Return of Stability Pool New", line = dict(dash='dot')), secondary_y=False, ) fig.update_layout( title_text="Dynamics of Liquidity, Stability, Redemption Pools and Return of Stability Pool" ) fig.update_xaxes(tick0=0, dtick=1, title_text="Month") fig.update_yaxes(title_text="Return", secondary_y=False) fig.show() fig = make_subplots(specs=[[{"secondary_y": True}]]) fig.add_trace( go.Scatter(x=data.index/720, y=data['airdrop_gain'], name="Airdrop Gain"), secondary_y=False, ) fig.add_trace( go.Scatter(x=data.index/720, y=data['liquidation_gain'], name="Liquidation Gain"), secondary_y=True, ) fig.add_trace( go.Scatter(x=data2.index/720, y=data2['airdrop_gain'], name="Airdrop Gain New", line = dict(dash='dot')), secondary_y=False, ) fig.add_trace( go.Scatter(x=data2.index/720, y=data2['liquidation_gain'], name="Liquidation Gain New", line = dict(dash='dot')), secondary_y=True, ) fig.update_layout( title_text="Dynamics of Airdrop and Liquidation Gain" ) fig.update_xaxes(tick0=0, dtick=1, title_text="Month") fig.update_yaxes(title_text="Airdrop Gain", secondary_y=False) fig.update_yaxes(title_text="Liquidation Gain", secondary_y=True) fig.show() fig = make_subplots(rows=2, cols=1) fig.add_trace( go.Scatter(x=data.index/720, y=data['issuance_fee'], name="Issuance Fee"), row=1, col=1 ) fig.add_trace( go.Scatter(x=data.index/720, y=data['redemption_fee'], name="Redemption Fee"), row=2, col=1 ) fig.add_trace( go.Scatter(x=data2.index/720, y=data2['issuance_fee'], name="Issuance Fee New", line = dict(dash='dot')), row=1, col=1 ) fig.add_trace( go.Scatter(x=data2.index/720, y=data2['redemption_fee'], name="Redemption Fee New", line = dict(dash='dot')), row=2, col=1 ) fig.update_layout( title_text="Dynamics of Issuance Fee and Redemption Fee" ) fig.update_xaxes(tick0=0, dtick=1, title_text="Month") fig.update_yaxes(title_text="Issuance Fee", secondary_y=False, row=1, col=1) fig.update_yaxes(title_text="Redemption Fee", secondary_y=False, row=2, col=1) fig.show() fig = make_subplots(specs=[[{"secondary_y": True}]]) fig.add_trace( go.Scatter(x=data.index/720, y=data['annualized_earning'], name="Annualized Earning"), secondary_y=False, ) fig.add_trace( go.Scatter(x=data2.index/720, y=data2['annualized_earning'], name="Annualized Earning New", line = dict(dash='dot')), secondary_y=False, ) fig.update_layout( title_text="Dynamics of Annualized Earning" ) fig.update_xaxes(tick0=0, dtick=1, title_text="Month") fig.update_yaxes(title_text="Annualized Earning", secondary_y=False) fig.show() fig = make_subplots(specs=[[{"secondary_y": True}]]) fig.add_trace( go.Scatter(x=data.index/720, y=data['price_LQTY'], name="LQTY Price"), secondary_y=False, ) fig.add_trace( go.Scatter(x=data.index/720, y=data['MC_LQTY'], name="LQTY Market Cap"), secondary_y=True, ) fig.add_trace( go.Scatter(x=data2.index/720, y=data2['price_LQTY'], name="LQTY Price New", line = dict(dash='dot')), secondary_y=False, ) fig.add_trace( go.Scatter(x=data2.index/720, y=data2['MC_LQTY'], name="LQTY Market Cap New", line = dict(dash='dot')), secondary_y=True, ) fig.update_layout( title_text="Dynamics of the Price and Market Cap of LQTY" ) fig.update_xaxes(tick0=0, dtick=1, title_text="Month") fig.update_yaxes(title_text="LQTY Price", secondary_y=False) fig.update_yaxes(title_text="LQTY Market Cap", secondary_y=True) fig.show() fig = make_subplots(specs=[[{"secondary_y": True}]]) fig.add_trace( go.Scatter(x=data.index/720, y=[0.01] * n_sim, name="Base Rate"), secondary_y=False, ) fig.add_trace( go.Scatter(x=data2.index/720, y=data2['base_rate'], name="Base Rate New"), secondary_y=False, ) fig.update_layout( title_text="Dynamics of Issuance Fee and Redemption Fee" ) fig.update_xaxes(tick0=0, dtick=1, title_text="Month") fig.update_yaxes(title_text="Issuance Fee", secondary_y=False) fig.update_yaxes(title_text="Redemption Fee", secondary_y=True) fig.show() def trove2_histogram(measure): fig = px.histogram(troves2, x=measure, title='Distribution of '+measure, nbins=25) fig.show() trove2_histogram('Ether_Quantity') trove2_histogram('CR_initial') trove2_histogram('Supply') trove2_histogram('Rational_inattention') trove2_histogram('CR_current')