*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.
```python
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
```python
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 `Tensor`s.
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.