tf_quant_finance.models.hull_white.swaption_price

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.

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.

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 strikesspecifying 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 Tensors. 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.

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