tf_quant_finance.models.sabr.approximations.european_option_price

Last updated: 2023-03-16.

tf_quant_finance.models.sabr.approximations.european_option_price#

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Computes the approximate European option price under the SABR model.

tf_quant_finance.models.sabr.approximations.european_option_price(
    *, strikes, expiries, forwards, is_call_options, alpha, beta, volvol, rho,
    shift=0.0, volatility_type=tf_quant_finance.models.sabr.approximations.SabrImpli
    edVolatilityType.LOGNORMAL, approximation_type=tf_quant_finance.models.sabr.appr
    oximations.SabrApproximationType.HAGAN, dtype=None, name=None
)

For a review of the SABR model and the conventions used, please see the docstring for implied_volatility.

Example#

import tf_quant_finance as tff
import tensorflow as tf

prices = tff.models.sabr.approximations.european_option_price(
  strikes=np.array([90.0, 100.0]),
  expiries=np.array([0.5, 1.0]),
  forwards=np.array([100.0, 110.0]),
  is_call_options=np.array([True, False]),
  alpha=3.2,
  beta=0.2,
  volvol=1.4,
  rho=0.0005,
  dtype=tf.float64)

# Expected: [10.41244961, 1.47123225]

Args:#

  • strikes: Real Tensor of arbitrary shape, specifying the strike prices. Values must be strictly positive.

  • expiries: Real Tensor of shape compatible with that of strikes, specifying the corresponding time-to-expiries of the options. Values must be strictly positive.

  • forwards: Real Tensor of shape compatible with that of strikes, specifying the observed forward prices of the underlying. Values must be strictly positive.

  • is_call_options: Boolean Tensor of shape compatible with that of forward, indicating whether the option is a call option (true) or put option (false).

  • alpha: Real Tensor of shape compatible with that of strikes, specifying the initial values of the stochastic volatility. Values must be strictly positive.

  • beta: Real Tensor of shape compatible with that of strikes, specifying the model exponent beta. Values must satisfy 0 <= beta <= 1.

  • volvol: Real Tensor of shape compatible with that of strikes, specifying the model vol-vol multipliers. Values must satisfy 0 <= volvol.

  • rho: Real Tensor of shape compatible with that of strikes, specifying the correlation factors between the Wiener processes modeling the forward and the volatility. Values must satisfy -1 < rho < 1.

  • shift: Optional Tensor of shape compatible with that of strkies, specifying the shift parameter(s). In the shifted model, the process modeling the forward is modified as: dF = sigma * (F + shift) ^ beta * dW. With this modification, negative forward rates are valid as long as F > -shift. Default value: 0.0

  • volatility_type: Either SabrImpliedVolatility.NORMAL or LOGNORMAL. Default value: LOGNORMAL.

  • approximation_type: Instance of SabrApproxmationScheme. Default value: HAGAN.

  • dtype: Optional: tf.DType. If supplied, the dtype to be used for converting values to Tensors. Default value: None, which means that the default dtypes inferred from strikes is used.

  • name: str. The name for the ops created by this function. Default value: ‘sabr_approx_eu_option_price’.

Returns:#

A real Tensor of the same shape as strikes, containing the corresponding options price.

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