BrownianStock

class pfhedge.instruments.BrownianStock(sigma=0.2, mu=0.0, cost=0.0, dt=0.004, dtype=None, device=None)

A stock of which spot prices follow the geometric Brownian motion.

See also

• pfhedge.stochastic.generate_geometric_brownian(): The stochastic process.

Parameters

• sigma (float, default=0.2) – The parameter $\sigma$, which stands for the volatility of the spot price.

• mu (float, default=0.0) – The parameter $\mu$, 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 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 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 (torch.Tensor): The spot prices of the instrument. This attribute is set by a method simulate(). The shape is $(N,T)$ where $N$ is the number of simulated paths and $T$ 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')

property default_init_state

Returns the default initial state of simulation.

simulate(n_paths=1, time_horizon=0.08, init_state=None)

Simulate the spot price and add it as a buffer named spot.

The shape of the spot is $(N,T)$, where $N$ is the number of simulated paths and $T$ is the number of time steps. The number of time steps is determinded from dt and time_horizon.

Parameters

• 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 $(S(0),)$ where $S(0)$ is the initial value of the spot price. If None (default), it uses the default value (See default_init_state). It also accepts a float or a 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]])

to(*args, **kwargs)

Moves and/or casts the buffers of the instrument.

This can be called as

to(device=None, dtype=None)

to(tensor)

to(instrument)

Its signature is similar to torch.nn.Module.to(). It only accepts floating point dtypes. See Instrument dtype and device for details.

Note

This method modifies the instrument in-place.

See also

• float(): Cast to torch.float32.

• double(): Cast to torch.float64.

• half(): Cast to torch.float16.

• bfloat16(): Cast to torch.bfloat16.

• cuda(): Move to CUDA memory.

• cpu(): Move to CPU memory.

Parameters

• dtype (torch.dtype) – The desired floating point dtype of the buffers in this instrument.

• device (torch.device) – The desired device of the buffers in this instrument.

• tensor (torch.Tensor) – Tensor whose dtype and device are the desired dtype and device of the buffers in this instrument.

• instrument (BaseInstrument) – Instrument whose dtype and device are the desired dtype and device of the buffers in this instrument.

Returns

self

property variance

Returns the volatility of self.

It is a tensor filled with the square of self.sigma.

property volatility

Returns the volatility of self.

It is a tensor filled with self.sigma.