*Last updated: 2023-03-16.*
# tf_quant_finance.models.hull_white.swaption_price
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Calculates the price of European Swaptions using the Hull-White model.
```python
tf_quant_finance.models.hull_white.swaption_price(
*, expiries, floating_leg_start_times, floating_leg_end_times,
fixed_leg_payment_times, floating_leg_daycount_fractions,
fixed_leg_daycount_fractions, fixed_leg_coupon, reference_rate_fn,
mean_reversion, volatility, notional=None, is_payer_swaption=True,
use_analytic_pricing=True, num_samples=100, random_type=None, seed=None, skip=0,
time_step=None, dtype=None, name=None
)
```
A European Swaption is a contract that gives the holder an option to enter a
swap contract at a future date at a prespecified fixed rate. A swaption that
grants the holder to pay fixed rate and receive floating rate is called a
payer swaption while the swaption that grants the holder to receive fixed and
pay floating payments is called the receiver swaption. Typically the start
date (or the inception date) of the swap concides with the expiry of the
swaption. Mid-curve swaptions are currently not supported (b/160061740).
Analytic pricing of swaptions is performed using the Jamshidian decomposition
[1].
#### References:
[1]: D. Brigo, F. Mercurio. Interest Rate Models-Theory and Practice.
Second Edition. 2007.
#### Example
The example shows how value a batch of 1y x 1y and 1y x 2y swaptions using the
Hull-White model.
````python
import numpy as np
import tensorflow as tf
import tf_quant_finance as tff
dtype = tf.float64
expiries = [1.0, 1.0]
float_leg_start_times = [[1.0, 1.25, 1.5, 1.75, 2.0, 2.0, 2.0, 2.0],
[1.0, 1.25, 1.5, 1.75, 2.0, 2.25, 2.5, 2.75]]
float_leg_end_times = [[1.25, 1.5, 1.75, 2.0, 2.0, 2.0, 2.0, 2.0],
[1.25, 1.5, 1.75, 2.0, 2.25, 2.5, 2.75, 3.0]]
fixed_leg_payment_times = [[1.25, 1.5, 1.75, 2.0, 2.0, 2.0, 2.0, 2.0],
[1.25, 1.5, 1.75, 2.0, 2.25, 2.5, 2.75, 3.0]]
float_leg_daycount_fractions = [[0.25, 0.25, 0.25, 0.25, 0.0, 0.0, 0.0, 0.0],
[0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25]]
fixed_leg_daycount_fractions = [[0.25, 0.25, 0.25, 0.25, 0.0, 0.0, 0.0, 0.0],
[0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25]]
fixed_leg_coupon = [[0.011, 0.011, 0.011, 0.011, 0.0, 0.0, 0.0, 0.0],
[0.011, 0.011, 0.011, 0.011, 0.011, 0.011, 0.011, 0.011]]
zero_rate_fn = lambda x: 0.01 * tf.ones_like(x, dtype=dtype)
price = tff.models.hull_white.swaption_price(
expiries=expiries,
floating_leg_start_times=float_leg_start_times,
floating_leg_end_times=float_leg_end_times,
fixed_leg_payment_times=fixed_leg_payment_times,
floating_leg_daycount_fractions=float_leg_daycount_fractions,
fixed_leg_daycount_fractions=fixed_leg_daycount_fractions,
fixed_leg_coupon=fixed_leg_coupon,
reference_rate_fn=zero_rate_fn,
notional=100.,
dim=1,
mean_reversion=[0.03],
volatility=[0.02],
dtype=dtype)
# Expected value: [0.7163243383624043, 1.4031415262337608] # shape = (2,1)
````
#### Args:
* `expiries`: A real `Tensor` of any shape and dtype. The time to
expiration of the swaptions. The shape of this input determines the number
(and shape) of swaptions to be priced and the shape of the output.
* `floating_leg_start_times`: A real `Tensor` of the same dtype as `expiries`.
The times when accrual begins for each payment in the floating leg. The
shape of this input should be `expiries.shape + [m]` where `m` denotes
the number of floating payments in each leg.
* `floating_leg_end_times`: A real `Tensor` of the same dtype as `expiries`.
The times when accrual ends for each payment in the floating leg. The
shape of this input should be `expiries.shape + [m]` where `m` denotes
the number of floating payments in each leg.
* `fixed_leg_payment_times`: A real `Tensor` of the same dtype as `expiries`.
The payment times for each payment in the fixed leg. The shape of this
input should be `expiries.shape + [n]` where `n` denotes the number of
fixed payments in each leg.
* `floating_leg_daycount_fractions`: A real `Tensor` of the same dtype and
compatible shape as `floating_leg_start_times`. The daycount fractions
for each payment in the floating leg.
* `fixed_leg_daycount_fractions`: A real `Tensor` of the same dtype and
compatible shape as `fixed_leg_payment_times`. The daycount fractions
for each payment in the fixed leg.
* `fixed_leg_coupon`: A real `Tensor` of the same dtype and compatible shape
as `fixed_leg_payment_times`. The fixed rate for each payment in the
fixed leg.
* `reference_rate_fn`: A Python callable that accepts expiry time as a real
`Tensor` and returns a `Tensor` of either shape `input_shape` or
`input_shape`. Returns the continuously compounded zero rate at
the present time for the input expiry time.
* `mean_reversion`: A real positive scalar `Tensor` or a Python callable. The
callable can be one of the following:
(a) A left-continuous piecewise constant object (e.g.,
`tff.math.piecewise.PiecewiseConstantFunc`) that has a property
`is_piecewise_constant` set to `True`. In this case the object should
have a method `jump_locations(self)` that returns a `Tensor` of shape
`[num_jumps]`. The return value of `mean_reversion(t)` should return a
`Tensor` of shape `t.shape`, `t` is a rank 1 `Tensor` of the same `dtype`
as the output. See example in the class docstring.
(b) A callable that accepts scalars (stands for time `t`) and returns a
scalar `Tensor` of the same `dtype` as `strikes`.
Corresponds to the mean reversion rate.
* `volatility`: A real positive `Tensor` of the same `dtype` as
`mean_reversion` or a callable with the same specs as above.
Corresponds to the long run price variance.
* `notional`: An optional `Tensor` of same dtype and compatible shape as
`strikes`specifying the notional amount for the underlying swap.
Default value: None in which case the notional is set to 1.
* `is_payer_swaption`: A boolean `Tensor` of a shape compatible with `expiries`.
Indicates whether the swaption is a payer (if True) or a receiver
(if False) swaption. If not supplied, payer swaptions are assumed.
* `use_analytic_pricing`: A Python boolean specifying if analytic valuation
should be performed. Analytic valuation is only supported for constant
`mean_reversion` and piecewise constant `volatility`. If the input is
`False`, then valuation using Monte-Carlo simulations is performed.
Default value: The default value is `True`.
* `num_samples`: Positive scalar `int32` `Tensor`. The number of simulation
paths during Monte-Carlo valuation. This input is ignored during analytic
valuation.
Default value: The default value is 1.
* `random_type`: Enum value of `RandomType`. The type of (quasi)-random
number generator to use to generate the simulation paths. This input is
relevant only for Monte-Carlo valuation and ignored during analytic
valuation.
Default value: `None` which maps to the standard pseudo-random numbers.
* `seed`: Seed for the random number generator. The seed is only relevant if
`random_type` is one of
`[STATELESS, PSEUDO, HALTON_RANDOMIZED, PSEUDO_ANTITHETIC,
STATELESS_ANTITHETIC]`. For `PSEUDO`, `PSEUDO_ANTITHETIC` and
`HALTON_RANDOMIZED` the seed should be an Python integer. For
`STATELESS` and `STATELESS_ANTITHETIC `must be supplied as an integer
`Tensor` of shape `[2]`. This input is relevant only for Monte-Carlo
valuation and ignored during analytic valuation.
Default value: `None` which means no seed is set.
* `skip`: `int32` 0-d `Tensor`. The number of initial points of the Sobol or
Halton sequence to skip. Used only when `random_type` is 'SOBOL',
'HALTON', or 'HALTON_RANDOMIZED', otherwise ignored.
Default value: `0`.
* `time_step`: Scalar real `Tensor`. Maximal distance between time grid points
in Euler scheme. Relevant when Euler scheme is used for simulation. This
input is ignored during analytic valuation.
Default value: `None`.
* `dtype`: The default dtype to use when converting values to `Tensor`s.
Default value: `None` which means that default dtypes inferred by
TensorFlow are used.
* `name`: Python string. The name to give to the ops created by this function.
Default value: `None` which maps to the default name
`hw_swaption_price`.
#### Returns:
A `Tensor` of real dtype and shape `expiries.shape` containing the
computed swaption prices. For swaptions that have. reset in the past
(expiries<0), the function sets the corresponding option prices to 0.0.