VarianceSwap¶

class pfhedge.instruments.VarianceSwap(underlier, strike=0.04, maturity=0.08, dtype=None, device=None)[source]¶

Variance swap.

The payoff of a variance swap is given by

\[\mathrm{payoff} = \sigma^2 - K ,\]

where \(\sigma^2\) is the realized variance of the underlying asset until maturity and \(K\) is the strike.

See pfhedge.nn.functional.realized_variance() for the definition of the realized variance.

Parameters

underlier (BasePrimary) – The underlying instrument.
strike (float, default=0.04) – The strike variance of the swap.
maturity (float, default=20/250) – The maturity of the derivative.

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.nn.functional import realized_variance
>>> from pfhedge.instruments import BrownianStock
>>> from pfhedge.instruments import VarianceSwap
>>>
>>> _ = torch.manual_seed(42)
>>> derivative = VarianceSwap(BrownianStock(), strike=0.04, 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]])
>>> realized_variance(derivative.ul().spot, dt=derivative.ul().dt)
tensor([0.0114, 0.0129])
>>> derivative.payoff()
tensor([-0.0286, -0.0271])

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.

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().

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.