tf_quant_finance.experimental.svi.implied_volatility_from_raw_svi_parameters

Last updated: 2023-03-16.

tf_quant_finance.experimental.svi.implied_volatility_from_raw_svi_parameters#

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Computes modeled implied volatility using raw SVI parameters.

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

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

w(k,t) = sigmaBS(k,t)^2 * t

See [1] and documentation for total_variance_from_raw_svi_parameters for additional details.

Example#

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 Tensors 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.

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