*Last updated: 2023-03-16.*
# tf_quant_finance.experimental.svi.implied_volatility_from_raw_svi_parameters
View source
Computes modeled implied volatility using raw SVI parameters.
```python
tf_quant_finance.experimental.svi.implied_volatility_from_raw_svi_parameters(
*, svi_parameters, log_moneyness=None, forwards=None, strikes=None,
expiries=None, dtype=None, name=None
)
```
The SVI volatility model parameterizes an option's total implied variance. For
a fixed timeslice (i.e. given expiry t), raw SVI parameters (a,b,rho,m,sigma)
and option's log-moneyness k:=log(K/F), the modeled total variance is
```None
w(k) = a + b * (rho * (k - m) + sqrt{(k - m)^2 + sigma^2)}
```
The modeled Black-Scholes implied volatility sigmaBS is computed from w(k)
and the option's expiry t from the equation
```None
w(k,t) = sigmaBS(k,t)^2 * t
```
See [1] and documentation for `total_variance_from_raw_svi_parameters` for
additional details.
#### Example
```python
import numpy as np
import tensorflow as tf
import tf_quant_finance as tff
svi_parameters = np.array([-0.1825, 0.3306, -0.0988, 0.0368, 0.6011])
forwards = np.array([2402.])
expiries = np.array([0.23])
strikes = np.array([[1800., 2000., 2200., 2400., 2600., 2800., 3000.]])
implied_vol = tff.experimental.svi.implied_volatility_from_raw_svi_parameters(
svi_parameters=svi_parameters,
forwards=forwards,
strikes=strikes,
expiries=expiries)
# Expected: implied_vol tensor (rounded to 4 decimal places) should contain
# [[0.4849, 0.3972, 0.3265, 0.2785, 0.2582, 0.2647, 0.2905]]
```
#### References:
[1] Gatheral J., Jaquier A., Arbitrage-free SVI volatility surfaces.
https://arxiv.org/pdf/1204.0646.pdf
#### Args:
* `svi_parameters`: A rank 2 real `Tensor` of shape [batch_size, 5]. The raw SVI
parameters for each volatility skew.
* `log_moneyness`: A rank 2 real `Tensor` of shape [batch_size, num_strikes].
The log-moneyness of the options.
* `forwards`: A rank 2 real `Tensor` of shape [batch_size, num_strikes]. The
forward prices of the options at expiries.
* `strikes`: A rank 2 real `Tensor` of shape [batch_size, num_strikes]. The
options strike prices.
* `expiries`: A rank 1 real `Tensor` of shape [batch_size]. The options
expiries.
* `dtype`: Optional `tf.Dtype`. If supplied, the dtype for the input and output
`Tensor`s will be converted to this.
Default value: `None` which maps to the dtype inferred from
`log_moneyness`.
* `name`: Python str. The name to give to the ops created by this function.
Default value: `None` which maps to `svi_implied_volatility`.
#### Returns:
A rank 2 real `Tensor` of shape [batch_size, num_strikes].
#### Raises:
* `ValueError`: If exactly one of `forwards` and `strikes` is supplied.
* `ValueError`: If both `log_moneyness' and `forwards` are supplied or if
neither is supplied.