tf_quant_finance.models.hjm.bond_option_price

Last updated: 2023-03-16.

tf_quant_finance.models.hjm.bond_option_price#

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Calculates European bond option prices using the HJM model.

tf_quant_finance.models.hjm.bond_option_price(
    *, strikes, expiries, maturities, discount_rate_fn, dim, mean_reversion,
    volatility, corr_matrix=None, is_call_options=True, num_samples=1,
    random_type=None, seed=None, skip=0, time_step=None, dtype=None, name=None
)

Bond options are fixed income securities which give the holder a right to exchange at a future date (the option expiry) a zero coupon bond for a fixed price (the strike of the option). The maturity date of the bond is after the the expiry of the option. If P(t,T) denotes the price at time t of a zero coupon bond with maturity T, then the payoff from the option at option expiry, T0, is given by:

payoff = max(P(T0, T) - X, 0)

where X is the strike price of the option.

Example#

import numpy as np
import tensorflow as tf
import tf_quant_finance as tff

dtype = tf.float64

discount_rate_fn = lambda x: 0.01 * tf.ones_like(x, dtype=dtype)
expiries = np.array([1.0])
maturities = np.array([5.0])
strikes = np.exp(-0.01 * maturities) / np.exp(-0.01 * expiries)
price = tff.models.hjm.bond_option_price(
    strikes=strikes,
    expiries=expiries,
    maturities=maturities,
    dim=1,
    mean_reversion=[0.03],
    volatility=[0.02],
    discount_rate_fn=discount_rate_fn,
    dtype=dtype)
# Expected value: [[0.02817777]]

Args:#

  • strikes: A real Tensor of any shape and dtype. The strike price of the options. The shape of this input determines the number (and shape) of the options to be priced and the output.

  • expiries: A real Tensor of the same dtype and compatible shape as strikes. The time to expiry of each bond option.

  • maturities: A real Tensor of the same dtype and compatible shape as strikes. The time to maturity of the underlying zero coupon bonds.

  • discount_rate_fn: A Python callable that accepts expiry time as a real Tensor and returns a Tensor of shape input_shape. Computes the zero coupon bond yield at the present time for the input expiry time.

  • dim: A Python scalar which corresponds to the number of factors within a single HJM model.

  • mean_reversion: A real positive Tensor of shape [dim]. Corresponds to the mean reversion rate of each factor.

  • volatility: A real positive Tensor of the same dtype and shape as mean_reversion or a callable with the following properties: (a) The callable should accept a scalar Tensor t and a 1-D Tensor r(t) of shape [num_samples] and returns a 2-D Tensor of shape [num_samples, dim]. The variable t stands for time and r(t) is the short rate at time t. The function returns instantaneous volatility sigma(t) = sigma(t, r(t)). When volatility is specified is a real Tensor, each factor is assumed to have a constant instantaneous volatility and the model is effectively a Gaussian HJM model. Corresponds to the instantaneous volatility of each factor.

  • corr_matrix: A Tensor of shape [dim, dim] and the same dtype as mean_reversion. Corresponds to the correlation matrix Rho. Default value: None, meaning the factors are uncorrelated.

  • is_call_options: A boolean Tensor of a shape compatible with strikes. Indicates whether the option is a call (if True) or a put (if False). If not supplied, call options are assumed.

  • num_samples: Positive scalar int32 Tensor. The number of simulation paths during Monte-Carlo 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. 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]. 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. 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 class. Default value: None which maps to the default name hw_bond_option_price.

Returns:#

A Tensor of real dtype and shape strikes.shape containing the computed option prices.

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