def generate_cva_merton(Exposures, Z_M, rhos_merton, Q_default, name_saved_file=''):
PD = Q_default(time_exposure)
DiscountFactorXdefault = PD * discount_factor(time_exposure)
@jit
def calc_cva_merton(rho):
result = zeros(Z_M.shape[0])
for k in range(0, len(Exposures)):
for t in range_exposure:
result[k] = result[k] + DiscountFactorXdefault[t] * \
sum(Exposures[k][t] * Merton(Z_M[k][t], rho, PD[t], tolerance=0.001))
return result
# it is faster with jit (but just a little bit)
# def calc_cva_merton0(rho, Z_M=Z_M):
# weightsMerton = [[Merton(Z_M[k][t], rho, PD[t], tolerance=0.001)
# for t in range_exposure] for k in range_portfolio]
# resultsDWR = array([[sum(Z_M[k][t] * weightsMerton[k][t]) for t in range_exposure] for k in range_portfolio])
# return [sum(resultsDWR[k, :] * DiscountFactorXdefault) for k in range_portfolio]
@jit
def curve_cva(rhos):
L = empty((len(rhos), Z_M.shape[0]))
for r in range(0, len(rhos)):
L[r, :] = calc_cva_merton(rhos[r])
return L
cva = curve_cva(rhos_merton)
if name_saved_file != '':
save_array(name_saved_file, cva)
return array(cva)
def generate_cva_indep(Exposures, Q_default, name_saved_file='', n_jobs=4):
PD = Q_default(time_exposure)
DiscountFactorXdefault = PD * discount_factor(time_exposure)
###################
### Compute cva
###################
resultsDWR = mean(Exposures, axis=2)
cva = Parallel(n_jobs=n_jobs, backend="threading")(
delayed(sum)(resultsDWR[k, :] * DiscountFactorXdefault) for k in range(0, len(Exposures)))
# cva = [sum(resultsDWR[k, :] * DiscountFactorXdefault) for k in range(0, len(Exposures))]
if name_saved_file != '':
save_array(name_saved_file, cva)
return array(cva)
def generate_cva_twofactors_hull(Exposures, Z_M1, Z_M2, bs1, bs2, Q_default, name_saved_file='', max_iter=100000,
tol=1e-3, n_jobs=4):
# cva = [Parallel(n_jobs=n_jobs, backend="threading")(delayed(generate_cva_generalized_hull)
# (Exposures, b1 * Z_M1 + b2 * Z_M2, Q_default, max_iter=max_iter,
# tol=tol, threading=False)
# for b2 in bs2)
# for b1 in bs1]
cva = Parallel(n_jobs=n_jobs, backend="threading")(delayed(_partial_cva_twofactors_hull)
(Exposures, Z_M1, Z_M2, b1, bs2, Q_default, name_saved_file='',
max_iter=100000, tol=1e-3)
for b1 in bs1)
# cva = [[generate_cva_generalized_hull(Exposures, b1 * Z_M1 + b2 * Z_M2,Q_default, max_iter=max_iter, tol=tol)
# for b2 in bs2] for b1 in bs1]
if name_saved_file != '':
save_array(name_saved_file, cva)
return array(cva)
def generate_cvas(model):
############################
### Independent
############################
if model == 1:
generate_cva_indep(Exposures=exposures['exposures'], Q_default=Q_default, name_saved_file='cva_indep')
generate_cva_twofactors_hull(Exposures=exposures['exposures'],
Z_M1=market_factor['Z_S'], bs1=bS,
Z_M2=market_factor['Z_V'], bs2=bV,
Q_default=Q_default, name_saved_file='cva_hull', max_iter=100000, tol=1e-3)
if model == 2:
cva_indep_shift_S_pos = generate_cva_indep(Exposures=exposures['exposures_shift_S_pos'], Q_default=Q_default)
cva_indep_shift_S_neg = generate_cva_indep(Exposures=exposures['exposures_shift_S_neg'], Q_default=Q_default)
delta_S_cva_indep = (cva_indep_shift_S_pos - cva_indep_shift_S_neg) / (2 * shift_S)
save_array('delta_S_cva_indep', delta_S_cva_indep)
if model == 3:
cva_indep_shift_intensity_pos = generate_cva_indep(Exposures=exposures['exposures'],
Q_default=Q_default_shift_pos)
cva_indep_shift_intensity_neg = generate_cva_indep(Exposures=exposures['exposures'],
Q_default=Q_default_shift_neg)
delta_intensity_cva_indep = (cva_indep_shift_intensity_pos - cva_indep_shift_intensity_neg) / (
2 * shift_intensity)
save_array('delta_intensity_cva_indep', delta_intensity_cva_indep)
# delta_S
if model == 4:
cva_hull_shift_S_pos = generate_cva_twofactors_hull(Exposures=exposures['exposures_shift_S_pos'],
Z_M1=market_factor['Z_S_shift_S_pos'], bs1=bS,
Z_M2=market_factor['Z_V_shift_S_pos'], bs2=bV,
Q_default=Q_default, max_iter=100000, tol=1e-3)
cva_hull_shift_S_neg = generate_cva_twofactors_hull(Exposures=exposures['exposures_shift_S_neg'],
Z_M1=market_factor['Z_S_shift_S_neg'], bs1=bS,
Z_M2=market_factor['Z_V_shift_S_neg'], bs2=bV,
Q_default=Q_default, max_iter=100000, tol=1e-3)
delta_S_cva_hull = (cva_hull_shift_S_pos - cva_hull_shift_S_neg) / (2 * shift_S)
save_array('delta_S_cva_hull', delta_S_cva_hull)
# delta_intensity
if model == 5:
cva_hull_shift_intensity_pos = generate_cva_twofactors_hull(Exposures=exposures['exposures'],
Z_M1=market_factor['Z_S'], bs1=bS,
Z_M2=market_factor['Z_V'], bs2=bV,
Q_default=Q_default_shift_pos, max_iter=100000,
tol=1e-3)
cva_hull_shift_intensity_neg = generate_cva_twofactors_hull(Exposures=exposures['exposures'],
Z_M1=market_factor['Z_S'], bs1=bS,
Z_M2=market_factor['Z_V'], bs2=bV,
Q_default=Q_default_shift_neg, max_iter=100000,
tol=1e-3)
delta_intensity_cva_hull = (cva_hull_shift_intensity_pos - cva_hull_shift_intensity_neg) / (2 * shift_intensity)
save_array('delta_intensity_cva_hull', delta_intensity_cva_hull)
def generate_cva_hull(Exposures, Z_M, bs_hull, Q_default, name_saved_file='', max_iter=100000, tol=1e-3):
cva = [generate_cva_generalized_hull(Exposures, b * Z_M, Q_default, max_iter=max_iter, tol=tol, threading=True)
for b in bs_hull]
if name_saved_file != '':
save_array(name_saved_file, cva)
return array(cva)
def launch_simulation(S_ini=S0, delta_ini=delta0, shift_str=''):
###################
### Initialize
###################
model = load_model()
book, time_exposure, timeline, contract_names = portfolio()
index_exposure = [list(timeline).index(t) for t in time_exposure]
range_exposure = range(0, len(time_exposure))
range_book = range(0, len(contract_names))
range_timeline = range(0, len(timeline))
###################
### Simulation
###################
# market sensitivities
simulated_paths = simulate_path(timeline,
S_ini=S_ini,
delta_ini=delta_ini,
reset_seed=True)
S = simulated_paths[0]
convenience_yield = simulated_paths[1]
###################
### Portfolio
###################
contracts_alltimes = array([[
instrument(timeline[t], S[t, :], convenience_yield[t, :])
for t in range_timeline
] for instrument in book])
contract_ini = array(
[instrument(0, S_ini, delta_ini) for instrument in book])
contracts = contracts_alltimes[:, index_exposure, :]
###################
### Exposure
###################
exposure_alltimes = exposure_function(contracts_alltimes)
exposures = exposure_alltimes[:, index_exposure, :]
###################
### Market Factor for hull()
###################
Z_S = S / S_ini
Z_V = array(
[contracts_alltimes[k] / abs(contract_ini[k]) for k in range_book])
Z_E = array(
[exposure_alltimes[k] / abs(contract_ini[k]) for k in range_book])
save_array('spot_prices' + shift_str, S)
save_array('convenience_yields' + shift_str, convenience_yield)
save_array('contracts' + shift_str, contracts)
save_array('exposures' + shift_str, exposures)
# save_array('contracts_alltimes'+shift_str, contracts_alltimes)
# save_array('exposures_alltimes'+shift_str, exposure_alltimes)
save_array('Z_S' + shift_str, Z_S)
save_array('Z_V' + shift_str, Z_V)
save_array('Z_E' + shift_str, Z_E)
save_array('timeline', timeline)
save_array('time_exposure', time_exposure)
save_array('contract_names', contract_names)