def sim_synthetic_bubble(seed):
"""
Simulate model once with a shock and return accompanying info on
- bubble_type
- bubble-episode price
- wealth_start
- wealth_end
+ wealth_gini_over_time
+ palma_over_time
+ twentytwenty_over_time
"""
BURN_IN = 200
SHOCK = 12000.0
SHOCK_PERIOD = 400
params = {
"spread_max": 0.004087,
"fundamental_value": 166,
"fundamentalist_horizon_multiplier": 0.73132061,
"n_traders": 500,
"w_fundamentalists": 37.20189844,
"base_risk_aversion": 11.65898537,
"mutation_probability": 0.30623129,
"init_stocks": 50,
"trader_sample_size": 19,
"ticks": 700,
"std_fundamental": 0.0530163128919286,
"std_noise": 0.29985649,
"trades_per_tick": 5,
"average_learning_ability": 0.57451773,
"w_momentum": 0.01,
"horizon": 200,
"w_random": 1.0
}
# simulate model once
obs = []
obs_no_shock = []
# run model with parameters
print('Simulate once')
traders, orderbook = init_objects_distr(params, seed)
traders, orderbook = pb_distr_model_shock(traders, orderbook, params,
SHOCK, SHOCK_PERIOD, seed)
obs.append(orderbook)
traders_no_shock, orderbook_no_shock = init_objects_distr(params, seed)
traders_no_shock, orderbook_no_shock = pb_distr_model_shock(
traders_no_shock, orderbook_no_shock, params, 0.0, SHOCK_PERIOD, seed)
obs_no_shock.append(orderbook)
# store simulated stylized facts
mc_prices, mc_returns, mc_autocorr_returns, mc_autocorr_abs_returns, mc_volatility, mc_volume, mc_fundamentals = organise_data(
obs, burn_in_period=BURN_IN)
mc_prices_ns, mc_returns_ns, mc_autocorr_returns_ns, mc_autocorr_abs_returns_ns, mc_volatility_ns, mc_volume_ns, mc_fundamentals_ns = organise_data(
obs_no_shock, burn_in_period=BURN_IN)
y = pd.Series(mc_prices[0][:-1] / mc_fundamentals[0])
y_ns = pd.Series(mc_prices_ns[0][:-1] / mc_fundamentals_ns[0])
obs = len(y)
r0 = 0.01 + 1.8 / np.sqrt(obs)
swindow0 = int(math.floor(r0 * obs))
dim = obs - swindow0 + 1
IC = 2
adflag = 6
yr = 2
Tb = 12 * yr + swindow0 - 1
nboot = 99
# calc bubbles
bsadfs = PSY(y, swindow0, IC, adflag)
quantilesBsadf = cvPSYwmboot(y, swindow0, IC, adflag, Tb, nboot=99)
monitorDates = y.iloc[swindow0 - 1:obs].index
quantile95 = np.dot(np.array([quantilesBsadf]).T, np.ones([1, dim]))
ind95 = (bsadfs.T[0] > quantile95[1, ])
periods = monitorDates[ind95]
bubble_types = []
bubble_prices = []
wealth_starts = []
wealth_ends = []
ginis_ot = []
palmas_ot = []
twtws_ot = []
bubble_prices_ns = []
wealth_ends_ns = []
ginis_ot_ns = []
palmas_ot_ns = []
twtws_ot_ns = []
if True in ind95:
bubbly_dates = find_sequences_ints(periods, monitorDates)
proper_bubbles = bubbly_dates.iloc[p_bubbles(bubbly_dates)]
# classify the bubbles
start_dates = []
end_dates = []
# then add the first bubble episodes
start_dates.append(proper_bubbles.iloc[0]['start_date'])
end_dates.append(proper_bubbles.iloc[0]['end_date'])
if abs(y[end_dates[0]] - y[start_dates[0]]) > y[:end_dates[0]].std():
# classify as boom or bust
if y[start_dates[0]] > y[end_dates[0]]:
bubble_type = 'bust'
else:
bubble_type = 'boom'
else:
if y[start_dates[0]:end_dates[0]].mean() > y[start_dates[0]]:
# classify as boom-bust or bust-boom
bubble_type = 'boom-bust'
else:
bubble_type = 'bust-boom'
bubble_types.append(bubble_type)
# determine the start and end wealth of the bubble
money_start = np.array(
[x.var.money[BURN_IN + start_dates[0]] for x in traders])
stocks_start = np.array(
[x.var.stocks[BURN_IN + start_dates[0]] for x in traders])
wealth_start = money_start + (stocks_start *
mc_prices[0].iloc[start_dates[0]])
money_end = np.array(
[x.var.money[BURN_IN + end_dates[0]] for x in traders])
stocks_end = np.array(
[x.var.stocks[BURN_IN + end_dates[0]] for x in traders])
wealth_end = money_end + (stocks_end * mc_prices[0].iloc[end_dates[0]])
# track money + wealth no shocks TODO check if this works
money_end_ns = np.array(
[x.var.money[BURN_IN + end_dates[0]] for x in traders_no_shock])
stocks_end_ns = np.array(
[x.var.stocks[BURN_IN + end_dates[0]] for x in traders_no_shock])
wealth_end_ns = money_end_ns + (stocks_end_ns *
mc_prices_ns[0].iloc[end_dates[0]])
wealth_gini_over_time = []
palma_over_time = []
twentytwenty_over_time = []
# also record the gini etc. over time without the shock
wealth_gini_over_time_ns = []
palma_over_time_ns = []
twentytwenty_over_time_ns = []
for t in range(BURN_IN + start_dates[0], BURN_IN + end_dates[0]):
money = np.array([x.var.money[t] for x in traders])
stocks = np.array([x.var.stocks[t] for x in traders])
wealth = money + (stocks * orderbook.tick_close_price[t])
share_top_10 = sum(
np.sort(wealth)[int(len(wealth) * 0.9):]) / sum(wealth)
share_bottom_40 = sum(
np.sort(wealth)[:int(len(wealth) * 0.4)]) / sum(wealth)
palma_over_time.append(share_top_10 / share_bottom_40)
share_top_20 = sum(
np.sort(wealth)[int(len(wealth) * 0.8):]) / sum(wealth)
share_bottom_20 = sum(
np.sort(wealth)[:int(len(wealth) * 0.2)]) / sum(wealth)
twentytwenty_over_time.append(share_top_20 / share_bottom_20)
wealth_gini_over_time.append(gini(wealth))
# No shocks
money_ns = np.array([x.var.money[t] for x in traders_no_shock])
stocks_ns = np.array([x.var.stocks[t] for x in traders_no_shock])
wealth_ns = money_ns + (stocks_ns *
orderbook_no_shock.tick_close_price[t])
share_top_10_ns = sum(
np.sort(wealth_ns)[int(len(wealth_ns) *
0.9):]) / sum(wealth_ns)
share_bottom_40_ns = sum(
np.sort(wealth_ns)[:int(len(wealth_ns) *
0.4)]) / sum(wealth_ns)
palma_over_time_ns.append(share_top_10_ns / share_bottom_40_ns)
share_top_20_ns = np.mean(
np.sort(wealth_ns)[int(len(wealth_ns) * 0.8):])
share_bottom_20_ns = np.mean(
np.sort(wealth_ns)[:int(len(wealth_ns) * 0.2)])
twentytwenty_over_time_ns.append(share_top_20_ns /
share_bottom_20_ns)
wealth_gini_over_time_ns.append(gini(wealth_ns))
bubble_prices.append(
list(mc_prices[0].iloc[start_dates[0]:end_dates[0]]))
wealth_starts.append(list(wealth_start))
wealth_ends.append(list(wealth_end))
ginis_ot.append(wealth_gini_over_time)
palmas_ot.append(palma_over_time)
twtws_ot.append(twentytwenty_over_time)
bubble_prices_ns.append(
list(mc_prices_ns[0].iloc[start_dates[0]:end_dates[0]]))
wealth_ends_ns.append(list(wealth_end_ns))
ginis_ot_ns.append(wealth_gini_over_time_ns)
palmas_ot_ns.append(palma_over_time_ns)
twtws_ot_ns.append(twentytwenty_over_time_ns)
return bubble_types, bubble_prices, wealth_starts, wealth_ends, ginis_ot, palmas_ot, twtws_ot, bubble_prices_ns, wealth_ends_ns, ginis_ot_ns, palmas_ot_ns, twtws_ot_ns
def simulate_params_efast(NRUNS, parameter_set, fixed_parameters):
"""
Simulate the model for different parameter sets. Record the difference in Gini inequality.
:param NRUNS: integer amount of Monte Carlo simulations
:param parameter_set: list of parameters which have been sampled for Sobol sensitivity analysis
:param fixed_parameters: list of parameters which will remain fixed
:return: numpy array of average stylized facts outcome values for all parameter combinations
"""
gini_avs = []
real_gini_avs = []
palma_avs = []
real_palma_avs = []
av_profits = []
av_volatilities = []
for parameters in parameter_set:
# combine individual parameters with fixed parameters
params = fixed_parameters.copy()
params.update(parameters)
# simulate the model
trdrs = []
orbs = []
for seed in range(NRUNS):
traders, orderbook = init_objects.init_objects(params, seed)
traders, orderbook = exuberance_inequality_model(traders,
orderbook,
params,
seed=seed)
trdrs.append(traders)
orbs.append(orderbook)
mc_prices, mc_returns, mc_autocorr_returns, \
mc_autocorr_abs_returns, mc_volatility, mc_volume, mc_fundamentals = organise_data(orbs, burn_in_period=0)
av_volatility = mc_volatility.mean().mean()
ginis_ot = []
palmas_ot = []
real_ginis_ot = []
real_palmas_ot = []
profits = []
# determine the start and end wealth
for seed, traders in enumerate(trdrs):
money_start = np.array([x.var.money[0] for x in traders])
stocks_start = np.array([x.var.stocks[0] for x in traders])
wealth_start = money_start + (stocks_start *
orbs[seed].tick_close_price[0])
money_end = np.array([x.var.money[-1] for x in traders])
stocks_end = np.array([x.var.stocks[-1] for x in traders])
wealth_end = money_end + (stocks_end *
orbs[seed].tick_close_price[-1])
profits.append((np.array(wealth_end) - np.array(wealth_start)) /
np.array(wealth_start))
wealth_gini_over_time = []
palma_over_time = []
real_wealth_gini_over_time = []
real_palma_over_time = []
for t in range(params['ticks'] - 1):
money = np.array([x.var.money[t] for x in traders])
stocks = np.array([x.var.stocks[t] for x in traders])
wealth = money + (stocks * orbs[seed].tick_close_price[t])
real_wealth = np.array([x.var.real_wealth[t] for x in traders])
share_top_10 = sum(
np.sort(wealth)[int(len(wealth) * 0.9):]) / sum(wealth)
share_bottom_40 = sum(
np.sort(wealth)[:int(len(wealth) * 0.4)]) / sum(wealth)
palma_over_time.append(share_top_10 / share_bottom_40)
real_share_top_10 = sum(
np.sort(real_wealth)[int(len(real_wealth) *
0.9):]) / sum(real_wealth)
real_share_bottom_40 = sum(
np.sort(real_wealth)[:int(len(real_wealth) *
0.4)]) / sum(real_wealth)
real_palma_over_time.append(real_share_top_10 /
real_share_bottom_40)
wealth_gini_over_time.append(gini(wealth))
real_wealth_gini_over_time.append(gini(real_wealth))
ginis_ot.append(wealth_gini_over_time)
palmas_ot.append(palma_over_time)
real_ginis_ot.append(real_wealth_gini_over_time)
real_palmas_ot.append(real_palma_over_time)
gini_avs.append(np.mean(ginis_ot))
real_gini_avs.append(np.mean(real_ginis_ot))
palma_avs.append(np.mean(palmas_ot))
real_palma_avs.append(np.mean(real_palmas_ot))
av_profits.append(np.mean(profits))
av_volatilities.append(av_volatility)
return gini_avs, real_gini_avs, palma_avs, real_palma_avs, av_profits, av_volatilities
def sim_bubble_info(seed):
"""
Simulate model once and return accompanying info on
Inequality:
- bubble_type
- bubble-episode price
- wealth_start
- wealth_end
+ wealth_gini_over_time
+ palma_over_time
+ twentytwenty_over_time
Information on agent characteristics
- risk aversion
- horizon
- learning ability
- chartist expectation
- fundamentalist expectation
"""
BURN_IN = 400
with open('parameters.json', 'r') as f:
params = json.loads(f.read())
# simulate model once
#traders = []
obs = []
# run model with parameters
print('Simulate once')
traders, orderbook = init_objects_distr(params, seed)
traders, orderbook = pb_distr_model(traders, orderbook, params, seed)
#traders.append(traders)
obs.append(orderbook)
# store simulated stylized facts
mc_prices, mc_returns, mc_autocorr_returns, mc_autocorr_abs_returns, mc_volatility, mc_volume, mc_fundamentals = organise_data(
obs, burn_in_period=BURN_IN)
y = pd.Series(mc_prices[0][:-1] / mc_fundamentals[0])
obs = len(y)
r0 = 0.01 + 1.8 / np.sqrt(obs)
swindow0 = int(math.floor(r0 * obs))
dim = obs - swindow0 + 1
IC = 2
adflag = 6
yr = 2
Tb = 12 * yr + swindow0 - 1
nboot = 99
# calc bubbles
bsadfs = PSY(y, swindow0, IC, adflag)
quantilesBsadf = cvPSYwmboot(y, swindow0, IC, adflag, Tb, nboot=99)
monitorDates = y.iloc[swindow0 - 1:obs].index
quantile95 = np.dot(np.array([quantilesBsadf]).T, np.ones([1, dim]))
ind95 = (bsadfs.T[0] > quantile95[1, ])
periods = monitorDates[ind95]
bubble_types = []
bubble_prices = []
wealth_starts = []
wealth_ends = []
ginis_ot = []
palmas_ot = []
twtws_ot = []
risk_aversions = []
horizons = []
learning_abilities = []
chartist_expectations = []
fundamentalist_expectations = []
if True in ind95:
bubbly_dates = find_sequences_ints(periods, monitorDates)
proper_bubbles = bubbly_dates.iloc[p_bubbles(bubbly_dates)]
# classify the bubbles
start_dates = []
end_dates = []
# add bubble episodes
for l in range(len(proper_bubbles)):
start_dates.append(proper_bubbles.iloc[l]['start_date'])
end_dates.append(proper_bubbles.iloc[l]['end_date'])
if abs(y[end_dates[l]] -
y[start_dates[l]]) > y[:end_dates[l]].std():
# classify as boom or bust
if y[start_dates[l]] > y[end_dates[l]]:
bubble_type = 'bust'
else:
bubble_type = 'boom'
else:
if y[start_dates[l]:end_dates[l]].mean() > y[start_dates[l]]:
# classify as boom-bust or bust-boom
bubble_type = 'boom-bust'
else:
bubble_type = 'bust-boom'
bubble_types.append(bubble_type)
# determine the start and end wealth of the bubble
money_start = np.array(
[x.var.money[BURN_IN + start_dates[l]] for x in traders])
stocks_start = np.array(
[x.var.stocks[BURN_IN + start_dates[l]] for x in traders])
wealth_start = money_start + (stocks_start *
mc_prices[0].iloc[start_dates[l]])
money_end = np.array(
[x.var.money[BURN_IN + end_dates[l]] for x in traders])
stocks_end = np.array(
[x.var.stocks[BURN_IN + end_dates[l]] for x in traders])
wealth_end = money_end + (stocks_end *
mc_prices[0].iloc[end_dates[l]])
# determine characteristics of the agents
risk_aversions.append([x.par.risk_aversion for x in traders])
horizons.append([x.par.horizon for x in traders])
learning_abilities.append(
[x.par.learning_ability for x in traders])
chartist_expectations.append([
list(
np.array(x.var.weight_chartist)[BURN_IN +
start_dates[l]:BURN_IN +
end_dates[l]] *
x.var.forecast_adjust) for x in traders
])
fundamentalist_expectations.append([
list(
np.array(x.var.weight_fundamentalist)
[BURN_IN + start_dates[l]:BURN_IN + end_dates[l]] *
x.var.forecast_adjust) for x in traders
])
wealth_gini_over_time = []
palma_over_time = []
twentytwenty_over_time = []
for t in range(BURN_IN + start_dates[l], BURN_IN + end_dates[l]):
money = np.array([x.var.money[t] for x in traders])
stocks = np.array([x.var.stocks[t] for x in traders])
wealth = money + (stocks * orderbook.tick_close_price[t])
share_top_10 = sum(
np.sort(wealth)[int(len(wealth) * 0.9):]) / sum(wealth)
share_bottom_40 = sum(
np.sort(wealth)[:int(len(wealth) * 0.4)]) / sum(wealth)
palma_over_time.append(share_top_10 / share_bottom_40)
share_top_20 = np.mean(
np.sort(wealth)[int(len(wealth) * 0.8):])
share_bottom_20 = np.mean(
np.sort(wealth)[:int(len(wealth) * 0.2)])
twentytwenty_over_time.append(share_top_20 / share_bottom_20)
wealth_gini_over_time.append(gini(wealth))
bubble_prices.append(
list(mc_prices[0].iloc[start_dates[l]:end_dates[l]]))
wealth_starts.append(list(wealth_start))
wealth_ends.append(list(wealth_end))
ginis_ot.append(wealth_gini_over_time)
palmas_ot.append(palma_over_time)
twtws_ot.append(twentytwenty_over_time)
return bubble_types, bubble_prices, wealth_starts, wealth_ends, ginis_ot, palmas_ot, twtws_ot, risk_aversions, horizons, learning_abilities, chartist_expectations, fundamentalist_expectations