from math import ceil
from typing import Optional
from typing import Tuple
from typing import cast
import torch
from torch import Tensor
from pfhedge._utils.doc import _set_attr_and_docstring
from pfhedge._utils.doc import _set_docstring
from pfhedge._utils.str import _format_float
from pfhedge._utils.typing import TensorOrScalar
from pfhedge.stochastic import generate_geometric_brownian
from .base import BasePrimary
[docs]class BrownianStock(BasePrimary):
r"""A stock of which spot prices follow the geometric Brownian motion.
.. seealso::
- :func:`pfhedge.stochastic.generate_geometric_brownian`:
The stochastic process.
Args:
sigma (float, default=0.2): The parameter :math:`\sigma`,
which stands for the volatility of the spot price.
mu (float, default=0.0): The parameter :math:`\mu`,
which stands for the drift of the spot price.
cost (float, default=0.0): The transaction cost rate.
dt (float, default=1/250): The intervals of the time steps.
dtype (torch.device, optional): Desired device of returned tensor.
Default: If None, uses a global default
(see :func:`torch.set_default_tensor_type()`).
device (torch.device, optional): Desired device of returned tensor.
Default: if None, uses the current device for the default tensor type
(see :func:`torch.set_default_tensor_type()`).
``device`` will be the CPU for CPU tensor types and
the current CUDA device for CUDA tensor types.
Buffers:
- spot (:class:`torch.Tensor`): The spot prices of the instrument.
This attribute is set by a method :meth:`simulate()`.
The shape is :math:`(N, T)` where
:math:`N` is the number of simulated paths and
:math:`T` is the number of time steps.
Examples:
>>> from pfhedge.instruments import BrownianStock
>>>
>>> _ = torch.manual_seed(42)
>>> stock = BrownianStock()
>>> stock.simulate(n_paths=2, time_horizon=5 / 250)
>>> stock.spot
tensor([[1.0000, 1.0016, 1.0044, 1.0073, 0.9930, 0.9906],
[1.0000, 0.9919, 0.9976, 1.0009, 1.0076, 1.0179]])
Using custom ``dtype`` and ``device``.
>>> stock = BrownianStock()
>>> stock.to(dtype=torch.float64, device="cuda:0")
BrownianStock(..., dtype=torch.float64, device='cuda:0')
"""
def __init__(
self,
sigma: float = 0.2,
mu: float = 0.0,
cost: float = 0.0,
dt: float = 1 / 250,
dtype: Optional[torch.dtype] = None,
device: Optional[torch.device] = None,
) -> None:
super().__init__()
self.sigma = sigma
self.mu = mu
self.cost = cost
self.dt = dt
self.to(dtype=dtype, device=device)
@property
def default_init_state(self) -> Tuple[float, ...]:
return (1.0,)
@property
def volatility(self) -> Tensor:
"""Returns the volatility of self.
It is a tensor filled with ``self.sigma``.
"""
return torch.full_like(self.get_buffer("spot"), self.sigma)
@property
def variance(self) -> Tensor:
"""Returns the volatility of self.
It is a tensor filled with the square of ``self.sigma``.
"""
return torch.full_like(self.get_buffer("spot"), self.sigma ** 2)
[docs] def simulate(
self,
n_paths: int = 1,
time_horizon: float = 20 / 250,
init_state: Optional[Tuple[TensorOrScalar]] = None,
) -> None:
"""Simulate the spot price and add it as a buffer named ``spot``.
The shape of the spot is :math:`(N, T)`, where :math:`N` is the number of
simulated paths and :math:`T` is the number of time steps.
The number of time steps is determinded from ``dt`` and ``time_horizon``.
Args:
n_paths (int, default=1): The number of paths to simulate.
time_horizon (float, default=20/250): The period of time to simulate
the price.
init_state (tuple[torch.Tensor | float], optional): The initial state of
the instrument.
This is specified by a tuple :math:`(S(0),)` where
:math:`S(0)` is the initial value of the spot price.
If ``None`` (default), it uses the default value
(See :attr:`default_init_state`).
It also accepts a :class:`float` or a :class:`torch.Tensor`.
Examples:
>>> _ = torch.manual_seed(42)
>>> stock = BrownianStock()
>>> stock.simulate(n_paths=2, time_horizon=5 / 250, init_state=(2.0,))
>>> stock.spot
tensor([[2.0000, 2.0031, 2.0089, 2.0146, 1.9860, 1.9812],
[2.0000, 1.9838, 1.9952, 2.0018, 2.0153, 2.0358]])
"""
if init_state is None:
init_state = cast(Tuple[float], self.default_init_state)
spot = generate_geometric_brownian(
n_paths=n_paths,
n_steps=ceil(time_horizon / self.dt + 1),
init_state=init_state,
sigma=self.sigma,
mu=self.mu,
dt=self.dt,
dtype=self.dtype,
device=self.device,
)
self.register_buffer("spot", spot)
def extra_repr(self) -> str:
params = ["sigma=" + _format_float(self.sigma)]
if self.mu != 0.0:
params.append("mu=" + _format_float(self.mu))
if self.cost != 0.0:
params.append("cost=" + _format_float(self.cost))
params.append("dt=" + _format_float(self.dt))
return ", ".join(params)
# Assign docstrings so they appear in Sphinx documentation
_set_docstring(BrownianStock, "default_init_state", BasePrimary.default_init_state)
_set_attr_and_docstring(BrownianStock, "to", BasePrimary.to)