def __init__(self, pct_drift=None, pct_vol=None, time_unit=dt.timedelta(days=1)): if pct_drift is None and pct_vol is None: pct_drift = 0.; pct_vol = 1. self._pct_drift, self._pct_vol = None, None if pct_drift is not None: self._pct_drift = npu.to_ndim_2(pct_drift, ndim_1_to_col=True, copy=True) process_dim = npu.nrow(self._pct_drift) if pct_vol is not None: self._pct_vol = npu.to_ndim_2(pct_vol, ndim_1_to_col=True, copy=True) process_dim = npu.nrow(self._pct_vol) if self._pct_drift is None: self._pct_drift = npu.col_of(process_dim, 0.) if self._pct_vol is None: self._pct_vol = np.eye(process_dim) npc.check_col(self._pct_drift) npc.check_nrow(self._pct_drift, process_dim) npc.check_nrow(self._pct_vol, process_dim) noise_dim = npu.ncol(self._pct_vol) self._pct_cov = stats.vol_to_cov(self._pct_vol) npu.make_immutable(self._pct_drift) npu.make_immutable(self._pct_vol) npu.make_immutable(self._pct_cov) self._to_string_helper_GeometricBrownianMotion = None self._str_GeometricBrownianMotion = None super(GeometricBrownianMotion, self).__init__(process_dim=process_dim, noise_dim=noise_dim, drift=lambda t, x: self._pct_drift * x, diffusion=lambda t, x: x * self._pct_vol, time_unit=time_unit)
def __init__(self, mean=None, vol=None, time_unit=dt.timedelta(days=1)): if mean is None and vol is None: mean = 0.; vol = 1. self._mean, self._vol = None, None if mean is not None: self._mean = npu.to_ndim_2(mean, ndim_1_to_col=True, copy=True) process_dim = npu.nrow(self._mean) if vol is not None: self._vol = npu.to_ndim_2(vol, ndim_1_to_col=True, copy=True) process_dim = npu.nrow(self._vol) if self._mean is None: self._mean = npu.col_of(process_dim, 0.) if self._vol is None: self._vol = np.eye(process_dim) npc.check_col(self._mean) npc.check_nrow(self._mean, process_dim) npc.check_nrow(self._vol, process_dim) noise_dim = npu.ncol(self._vol) self._cov = stats.vol_to_cov(self._vol) npu.make_immutable(self._mean) npu.make_immutable(self._vol) npu.make_immutable(self._cov) self._to_string_helper_WienerProcess = None self._str_WienerProcess = None super(WienerProcess, self).__init__(process_dim=process_dim, noise_dim=noise_dim, drift=lambda t, x: self._mean, diffusion=lambda t, x: self._vol, time_unit=time_unit)
def __init__(self, initial_value=None, final_value=None, initial_time=0., final_time=1., vol=None, time_unit=dt.timedelta(days=1)): process_dim = 1 self.__initial_value = None self.__final_value = None if initial_value is not None: self.__initial_value = npu.to_ndim_2(initial_value, ndim_1_to_col=True, copy=True) process_dim = npu.nrow(self.__initial_value) if final_value is not None: self.__final_value = npu.to_ndim_2(final_value, ndim_1_to_col=True, copy=True) process_dim = npu.nrow(self.__final_value) if self.__initial_value is None: self.__initial_value = npu.col_of(process_dim, 0.) if self.__final_value is None: self.__final_value = npu.col_of(process_dim, 0.) self.__vol = None if vol is not None: self.__vol = npu.to_ndim_2(vol, ndim_1_to_col=True, copy=True) process_dim = npu.nrow(self.__vol) if self.__vol is None: self.__vol = np.eye(process_dim) self.__initial_time = initial_time self.__final_time = final_time npc.check_col(self.__initial_value) npc.check_col(self.__final_value) npc.check_nrow(self.__initial_value, process_dim) npc.check_nrow(self.__final_value, process_dim) noise_dim = npu.ncol(self.__vol) self.__cov = stats.vol_to_cov(self.__vol) npu.make_immutable(self.__initial_value) npu.make_immutable(self.__final_value) npu.make_immutable(self.__vol) npu.make_immutable(self.__cov) self._to_string_helper_BrownianBridge = None self._str_BrownianBridge = None super(BrownianBridge, self).__init__(process_dim=process_dim, noise_dim=noise_dim, drift=lambda t, x: (self.__final_value - x) / (self.__final_time - t), diffusion=lambda t, x: self.__vol, time_unit=time_unit)
def __init__(self, transition=None, mean=None, vol=None, time_unit=dt.timedelta(days=1)): if transition is None and mean is None and vol is None: transition = 1.; mean = 0.; vol = 1. self._transition, self._mean, self._vol = None, None, None if transition is not None: self._transition = npu.to_ndim_2(transition, ndim_1_to_col=True, copy=True) process_dim = npu.nrow(self._transition) if mean is not None: self._mean = npu.to_ndim_2(mean, ndim_1_to_col=True, copy=True) process_dim = npu.nrow(self._mean) if vol is not None: self._vol = npu.to_ndim_2(vol, ndim_1_to_col=True, copy=True) process_dim = npu.nrow(self._vol) if self._transition is None: self._transition = np.eye(process_dim) if self._mean is None: self._mean = npu.col_of(process_dim, 0.) if self._vol is None: self._vol = np.eye(process_dim) npc.check_square(self._transition) npc.check_nrow(self._transition, process_dim) npc.check_col(self._mean) npc.check_nrow(self._mean, process_dim) npc.check_nrow(self._vol, process_dim) noise_dim = npu.ncol(self._vol) self._transition_x_2 = npu.kron_sum(self._transition, self._transition) self._transition_x_2_inverse = np.linalg.inv(self._transition_x_2) self._cov = stats.vol_to_cov(self._vol) self._cov_vec = npu.vec(self._cov) self._cached_mean_reversion_factor = None self._cached_mean_reversion_factor_time_delta = None self._cached_mean_reversion_factor_squared = None self._cached_mean_reversion_factor_squared_time_delta = None npu.make_immutable(self._transition) npu.make_immutable(self._transition_x_2) npu.make_immutable(self._transition_x_2_inverse) npu.make_immutable(self._mean) npu.make_immutable(self._vol) npu.make_immutable(self._cov) npu.make_immutable(self._cov_vec) self._to_string_helper_OrnsteinUhlenbeckProcess = None self._str_OrnsteinUhlenbeckProcess = None super(OrnsteinUhlenbeckProcess, self).__init__(process_dim=process_dim, noise_dim=noise_dim, drift=lambda t, x: -np.dot(self._transition, x - self._mean), diffusion=lambda t, x: self._vol, time_unit=time_unit)
def __init__(self, mean_of_log=None, cov_of_log=None, vol_of_log=None, dim=None, copy=True): if mean_of_log is not None and dim is not None and np.size(mean_of_log) == 1: mean_of_log = npu.col_of(dim, npu.to_scalar(mean_of_log)) if mean_of_log is None and vol_of_log is None and cov_of_log is None: self._dim = 1 if dim is None else dim mean_of_log = npu.col_of(self._dim, 0.) cov_of_log = np.eye(self._dim) vol_of_log = np.eye(self._dim) self._dim, self._mean_of_log, self._vol_of_log, self._cov_of_log = None, None, None, None # TODO We don't currently check whether cov_of_log and vol_of_log are consistent, i.e. that cov_of_log = np.dot(vol_of_log, vol_of_log.T) -- should we? if mean_of_log is not None: self._mean_of_log = npu.to_ndim_2(mean_of_log, ndim_1_to_col=True, copy=copy) self._dim = npu.nrow(self._mean_of_log) if cov_of_log is not None: self._cov_of_log = npu.to_ndim_2(cov_of_log, ndim_1_to_col=True, copy=copy) self._dim = npu.nrow(self._cov_of_log) if vol_of_log is not None: self._vol_of_log = npu.to_ndim_2(vol_of_log, ndim_1_to_col=True, copy=copy) self._dim = npu.nrow(self._vol_of_log) if self._mean_of_log is None: self._mean_of_log = npu.col_of(self._dim, 0.) if self._cov_of_log is None and self._vol_of_log is None: self._cov_of_log = np.eye(self._dim) self._vol_of_log = np.eye(self._dim) npc.check_col(self._mean_of_log) npc.check_nrow(self._mean_of_log, self._dim) if self._cov_of_log is not None: npc.check_nrow(self._cov_of_log, self._dim) npc.check_square(self._cov_of_log) if self._vol_of_log is not None: npc.check_nrow(self._vol_of_log, self._dim) if self._cov_of_log is None: self._cov_of_log = stats.vol_to_cov(self._vol_of_log) if self._vol_of_log is None: self._vol_of_log = stats.cov_to_vol(self._cov_of_log) npu.make_immutable(self._mean_of_log) npu.make_immutable(self._cov_of_log) npu.make_immutable(self._vol_of_log) mean = np.exp(self._mean_of_log + .5 * npu.col(*[self._cov_of_log[i,i] for i in range(self._dim)])) cov = np.array([[np.exp(self._mean_of_log[i,0] + self._mean_of_log[j,0] + .5 * (self._cov_of_log[i,i] + self._cov_of_log[j,j])) * (np.exp(self._cov_of_log[i,j]) - 1.) for j in range(self._dim)] for i in range(self._dim)]) vol = stats.cov_to_vol(cov) self._to_string_helper_LogNormalDistr = None self._str_LogNormalDistr = None super().__init__(mean, cov, vol, self._dim, copy)
def cov(self): if self._cov is None: self._cov = stats.vol_to_cov(self._vol) return self._cov