def generate_paths(self, fixed_seed=False, day_count=365.):
if self.time_grid == None:
self.generate_time_grid()
#number of dates in time grid
M = len(self.time_grid)
#number of paths
I = self.paths
#array initalization for path simulation
paths = np.zeros((M, I))
paths_ = np.zeros_like(paths)
paths[0] = self.initial_value
paths_[0] = self.initial_value
if not self.correlated:
#If not correlated, generate random numbers
rand = sn_random_numbers((1, M, I), fixed_seed=fixed_seed)
else:
#if not correlated, use random numbers in market env
rand = self.random_numbers
#get short rate for drift of processes
short_rate = self.discount_curve.short_rate
for t in range(1, len(self.time_grid)):
#select the right time slice from the relevant time sets
if not self.correlated:
ran = rand[t]
else:
ran = np.dot(self.cholesky_matrix, rand[:, t, :])
ran = ran[self.rn_set]
dt = (self.time_grid[t] - self.time_grid[t - 1]).days / day_count
#diff between two dates as year fraction
paths_[t] = (paths_[t - 1] + self.kappa *
(self.theta - np.maximum(0, paths_[t - 1, :])) * dt +
np.sqrt(np.maximum(0, paths_[t - 1, :])) *
self.volatility * np.sqrt(dt) * ran)
paths[t] = np.maximum(0, paths_[t])
self.instrument_values = paths
def generate_paths(self, fixed_seed=False, day_count=365.):
if self.time_grid is None:
self.generate_time_grid()
#number of dates in time grid
M = len(self.time_grid)
#number of paths
I = self.paths
#array initalization for path simulation
paths = np.zeros((M, I))
paths[0] = self.initial_value
if not self.correlated:
#If not correlated, generate random numbers
sn1 = sn_random_numbers((1, M, I), fixed_seed=fixed_seed)
else:
#if not correlated, use random numbers in market env
sn1 = self.random_numbers
#for the jump component
sn2 = sn_random_numbers((1, M, I), fixed_seed=fixed_seed)
rj = self.lamb * (np.exp(self.mu + 0.5 * self.delt**2) - 1)
#get short rate for drift of processes
short_rate = self.discount_curve.short_rate
for t in range(1, len(self.time_grid)):
#select the right time slice from the relevant time sets
if not self.correlated:
ran = sn1[t]
else:
ran = np.dot(self.cholesky_matrix, sn1[:, t, :])
ran = ran[self.rn_set]
dt = (self.time_grid[t] - self.time_grid[t - 1]).days / day_count
#diff between two dates as year fraction
poi = np.random.poisson(self.lamb * dt, I)
#poisson distrubited jump numbers
paths[t] = paths[t - 1] * (
np.exp((short_rate - rj - 0.5 * self.volatility**2) * dt +
self.volatility * np.sqrt(dt) * ran) +
(np.exp(self.mu + self.delt * sn2[t]) - 1) * poi)
self.instrument_values = paths