LookbackOption¶

class pfhedge.instruments.LookbackOption(underlier, call=True, strike=1.0, maturity=0.08, dtype=None, device=None)[source]¶

Lookback option with fixed strike.

The payoff of a lookback call option is given by

\[\mathrm{payoff} = \max(\mathrm{Max} - K, 0) ,\]

where \(\mathrm{Max}\) is the maximum of the underlier’s spot price until maturity and \(K\) is the strike.

The payoff of a lookback put option is given by

\[\mathrm{payoff} = \max(K - \mathrm{Min}, 0) ,\]

where \(\mathrm{Max}\) is the minimum of the underlier’s spot price until maturity.

See also

pfhedge.nn.functional.lookback_payoff()

Parameters

underlier (BasePrimary) – The underlying instrument of the option.
call (bool, default=True) – Specifies whether the option is call or put.
strike (float, default=1.0) – The strike price of the option.
maturity (float, default=20/250) – The maturity of the option.

dtype¶

The dtype with which the simulated time-series are represented.

Type: torch.dtype

device¶

The device where the simulated time-series are.

Type: torch.device

Examples

>>> import torch
>>> from pfhedge.instruments import BrownianStock
>>> from pfhedge.instruments import LookbackOption
>>>
>>> _ = torch.manual_seed(42)
>>> derivative = LookbackOption(BrownianStock(), maturity=5/250)
>>> derivative.simulate(n_paths=2)
>>> derivative.underlier.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]])
>>> derivative.payoff()
tensor([0.0073, 0.0179])

list(pricer, cost=0.0)¶

Make self a listed derivative.

After this method self will be a exchange-traded derivative which can be transacted at any time with the spot price given by self.spot.

See an example in EuropeanOption for a usage.

Parameters

pricer (Callable[[BaseDerivative], Tensor]]) – A function that takes self and returns the spot price tensor of self.
cost (float, optional) – The transaction cost rate.

log_moneyness(time_step=None)¶

Returns log-moneyness of self.

Log-moneyness reads \(\log(S / K)\) where \(S\) is the spot price of the underlying instrument and \(K\) is the strike of the derivative.

Returns: torch.Tensor

moneyness(time_step=None, log=False)¶

Returns the moneyness of self.

Moneyness reads \(S / K\) where \(S\) is the spot price of the underlying instrument and \(K\) is the strike of the derivative.

Parameters

time_step (int, optional) – The time step to calculate the moneyness. If None (default), the moneyness is calculated at all time steps.
log (bool, default=False) – If True, returns log moneyness.

Shape:

Output: \((N, T)\) where \(N\) is the number of paths and \(T\) is the number of time steps. If time_step is given, the shape is \((N, 1)\).

Returns: torch.Tensor

simulate(n_paths=1, init_state=None)¶

Simulate time series associated with the underlier.

Parameters

n_paths (int) – The number of paths to simulate.
init_state (tuple[torch.Tensor | float], optional) – The initial state of the underlier.
**kwargs – Other parameters passed to self.underlier.simulate().

time_to_maturity(time_step=None)¶

Returns the time to maturity of self.

Parameters: time_step (int, optional) – The time step to calculate the time to maturity. If None (default), the time to maturity is calculated at all time steps.

Shape:

Output: \((N, T)\) where \(N\) is the number of paths and \(T\) is the number of time steps. If time_step is given, the shape is \((N, 1)\).

Returns: torch.Tensor

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.