*Last updated: 2023-03-16.*
# tf_quant_finance.experimental.svi.total_variance_from_raw_svi_parameters
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Computes modeled total variance using raw SVI parameters.
```python
tf_quant_finance.experimental.svi.total_variance_from_raw_svi_parameters(
*, svi_parameters, log_moneyness=None, forwards=None, strikes=None, dtype=None,
name=None
)
```
The SVI volatility model parameterizes an option's total implied variance,
defined as w(k,t) := sigmaBS(k,t)^2 * t, where k := log(K/F) is the options's
log-moneyness, t is the time to expiry, and sigmaBS(k,t) is the Black-Scholes
market implied volatility. For a fixed timeslice (i.e. given expiry t), the
raw SVI parameterization consists of 5 parameters (a,b,rho,m,sigma), and
the model approximation formula for w(k,t) as a function of k is (cf.[1]):
```None
w(k) = a + b * (rho * (k - m) + sqrt{(k - m)^2 + sigma^2)}
```
The raw parameters have the following interpretations (cf.[2]):
a vertically shifts the variance graph
b controls the angle between the left and right asymptotes
rho controls the rotation of the variance graph
m horizontally shifts the variance graph
sigma controls the graph smoothness at the vertex (ATM)
#### 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.])
strikes = np.array([[1800., 2000., 2200., 2400., 2600., 2800., 3000.]])
total_var = tff.experimental.svi.total_variance_from_raw_svi_parameters(
svi_parameters=svi_parameters, forwards=forwards, strikes=strikes)
# Expected: total_var tensor (rounded to 4 decimal places) should contain
# [[0.0541, 0.0363, 0.02452, 0.0178, 0.0153, 0.0161, 0.0194]]
```
#### References:
[1] Gatheral J., Jaquier A., Arbitrage-free SVI volatility surfaces.
https://arxiv.org/pdf/1204.0646.pdf
[2] Gatheral J, A parsimonious arbitrage-free implied volatility
parameterization with application to the valuation of volatility derivatives.
http://faculty.baruch.cuny.edu/jgatheral/madrid2004.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 option.
* `forwards`: A rank 2 real `Tensor` of shape [batch_size, num_strikes]. The
forward price of the option at expiry.
* `strikes`: A rank 2 real `Tensor` of shape [batch_size, num_strikes]. The
option's strike price.
* `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_total_variance`.
#### 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.