Portfolio with Multi-Risk Derivatives
from dx import *
# constant short rate
r = constant_short_rate('r', 0.02)
# market environments
me_gbm = market_environment('gbm', dt.datetime(2015, 1, 1))
me_jd = market_environment('jd', dt.datetime(2015, 1, 1))
me_sv = market_environment('sv', dt.datetime(2015, 1, 1))
# geometric Brownian motion
me_gbm.add_constant('initial_value', 36.)
me_gbm.add_constant('volatility', 0.2)
me_gbm.add_constant('currency', 'EUR')
me_gbm.add_constant('model', 'gbm')
# jump diffusion
me_jd.add_constant('initial_value', 36.)
me_jd.add_constant('volatility', 0.2)
me_jd.add_constant('lambda', 0.5)
# probability for jump p.a.
me_jd.add_constant('mu', -0.75)
# expected jump size [%]
me_jd.add_constant('delta', 0.1)
# volatility of jump
me_jd.add_constant('currency', 'EUR')
me_jd.add_constant('model', 'jd')
# stochastic volatility model
me_sv.add_constant('initial_value', 36.)
me_sv.add_constant('volatility', 0.2)
me_sv.add_constant('vol_vol', 0.1)
me_sv.add_constant('kappa', 2.5)
me_sv.add_constant('theta', 0.4)
me_sv.add_constant('rho', -0.5)
me_sv.add_constant('lambda', 0.0)
# probability for jump p.a.
me_sv.add_constant('mu', 0.0)
# expected jump size [%]
me_sv.add_constant('delta', 0.0)
# volatility of jump
me_sv.add_constant('currency', 'EUR')
me_sv.add_constant('model', 'svjd')
# valuation environment
val_env = market_environment('val_env', dt.datetime(2015, 1, 1))
val_env.add_constant('paths', 10000)
val_env.add_constant('frequency', 'M')
val_env.add_curve('discount_curve', r)
val_env.add_constant('starting_date', dt.datetime(2015, 1, 1))
val_env.add_constant('final_date', dt.datetime(2015, 12, 31))
# add valuation environment to market environments
me_gbm.add_environment(val_env)
me_jd.add_environment(val_env)
me_sv.add_environment(val_env)
underlyings = {'gbm' : me_gbm, 'jd' : me_jd, 'sv' : me_sv}
correlations = [['gbm', 'jd', 0.66], ['jd', 'sv', -0.75]]
gbm = geometric_brownian_motion('gbm_obj', me_gbm)
me_put = market_environment('put', dt.datetime(2015, 1, 1))
me_put.add_constant('maturity', dt.datetime(2015, 12, 31))
me_put.add_constant('strike', 40.)
me_put.add_constant('currency', 'EUR')
me_put.add_environment(val_env)
am_put = valuation_mcs_american_single('am_put', mar_env=me_put, underlying=gbm,
payoff_func='np.maximum(strike - instrument_values, 0)')
am_put.present_value(fixed_seed=True, bf=3)
jd = jump_diffusion('jd_obj', me_jd)
me_max_call = market_environment('put', dt.datetime(2015, 1, 1))
me_max_call.add_constant('maturity', dt.datetime(2015, 9, 15))
me_max_call.add_constant('currency', 'EUR')
me_max_call.add_environment(val_env)
payoff_call = "np.maximum(np.maximum(maturity_value['gbm'], maturity_value['jd']) - 34., 0)"
assets = {'gbm' : me_gbm, 'jd' : me_jd}
asset_corr = [correlations[0]]
asset_corr
max_call = valuation_mcs_european_multi('max_call', me_max_call, assets, asset_corr,
payoff_func=payoff_call)
max_call.present_value(fixed_seed=False)
max_call.delta('jd')
max_call.delta('gbm')
sv = jump_diffusion('sv_obj', me_sv)
me_min_put = market_environment('min_put', dt.datetime(2015, 1, 1))
me_min_put.add_constant('maturity', dt.datetime(2015, 6, 17))
me_min_put.add_constant('currency', 'EUR')
me_min_put.add_environment(val_env)
payoff_put = "np.maximum(32. - np.minimum(instrument_values['jd'], instrument_values['sv']), 0)"
assets = {'jd' : me_jd, 'sv' : me_sv}
asset_corr = [correlations[1]]
asset_corr
min_put = valuation_mcs_american_multi('min_put', val_env=me_min_put, assets=assets,
correlations=asset_corr, payoff_func=payoff_put)
min_put.present_value(fixed_seed=True)
min_put.delta('jd')
min_put.delta('sv')
am_put_pos = derivatives_position('am_put_pos', 2, ['gbm'], me_put, 'American single',
'np.maximum(instrument_values - 36., 0)')
max_call_pos = derivatives_position('max_call_pos', 3, ['gbm', 'jd'], me_max_call, 'European multi',
payoff_call)
min_put_pos = derivatives_position('min_put_pos', 5, ['sv', 'jd'], me_min_put, 'American multi',
payoff_put)
positions = {'am_put_pos' : am_put_pos, 'max_call_pos' : max_call_pos,
'min_put_pos' : min_put_pos}
port = derivatives_portfolio('portfolio', positions, val_env, underlyings, correlations)
port.time_grid
port.get_statistics()
path_no = 1
paths1 = port.underlying_objects['sv'].get_instrument_values()[:, path_no]
paths2 = port.underlying_objects['jd'].get_instrument_values()[:, path_no]
paths1
paths2
import matplotlib.pyplot as plt
%matplotlib inline
plt.plot(port.time_grid, paths1, 'r', label='sv')
plt.plot(port.time_grid, paths2, 'b', label='jd')
plt.gcf().autofmt_xdate()
plt.legend(loc=0); plt.grid(True)
# negatively correlated underlyings