*Last updated: 2023-03-16.*
# tf_quant_finance.models.heston.approximations.asian_option_price
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Computes the Heston price for a batch of asian options.
```python
tf_quant_finance.models.heston.approximations.asian_option_price(
*, variances, mean_reversion, theta, volvol, rho, strikes, expiries, spots=None,
forwards=None, sampling_times=None, past_fixings=None, discount_rates=None,
dividend_rates=None, discount_factors=None, is_call_options=None,
averaging_type=tf_quant_finance.black_scholes.AveragingType.GEOMETRIC,
averaging_frequency=tf_quant_finance.black_scholes.AveragingFrequency.DISCRETE,
integration_method=None, dtype=None, name=None, **kwargs
)
```
Discrete and continuous geometric asian options can be priced using a
semi-analytical expression in the Heston model.
#### Example
```python
# Price a batch of seasoned discrete geometric asians in Heston model
# This example reproduces some prices from the reference paper
variances = 0.09
mean_reversion = 1.15
volvol = 0.39
theta = 0.0348
rho = -0.64
spots = 100.0
strikes = [90.0, 100.0, 110.0]
discount_rates = 0.05
T = 0.5
expiries = T
sampling_times = np.linspace(1/365, T, 182)[:, np.newaxis]
computed_prices_asians = asian_option_price(
variances=variances,
mean_reversion=mean_reversion,
theta=theta,
volvol=volvol,
rho=rho,
strikes=strikes,
expiries=expiries,
spots=spots,
sampling_times=sampling_times,
discount_rates=discount_rates
)
# Expected print output of computed prices:
# [[11.884178 ], [ 5.080889 ], [ 1.3527349]]
```
#### References:
[1] B. Kim, J. Kim, J. Kim & I. S. Wee, "A Recursive Method for Discretely
Monitored Geometric Asian Option Prices", Bull. Korean Math. Soc. 53,
733-749 (2016)
#### Args:
* `variances`: Real `Tensor` of any shape compatible with a `batch_shape` and
and any real dtype. The initial value of the variance.
* `mean_reversion`: A real `Tensor` of the same dtype and compatible shape as
`variances`. Corresponds to the mean reversion rate.
* `theta`: A real `Tensor` of the same dtype and compatible shape as
`variances`. Corresponds to the long run price variance.
* `volvol`: A real `Tensor` of the same dtype and compatible shape as
`variances`. Corresponds to the volatility of the volatility.
* `rho`: A real `Tensor` of the same dtype and compatible shape as
`variances`. Corresponds to the correlation between dW_{X}` and `dW_{V}`.
* `strikes`: A real `Tensor` of the same dtype and compatible shape as
`variances`. The strikes of the options to be priced.
* `expiries`: A real `Tensor` of same dtype and compatible shape as
`variances`. The expiry of each option. The units should be such that
`expiry * volatility**2` is dimensionless.
* `spots`: A real `Tensor` of any shape that broadcasts to the shape of the
`variances`. The current spot price of the underlying. Either this
argument or the `forwards` (but not both) must be supplied.
* `forwards`: A real `Tensor` of any shape that broadcasts to the shape of
`variances`. The forwards to maturity. Either this argument or the
`spots` must be supplied but both must not be supplied.
* `sampling_times`: A real `Tensor` of same dtype as expiries and shape
`[n] + batch_shape` where `n` is the number of sampling times for
the asian options
Default value: `None`, which will raise an error for discrete sampling
asian options
* `past_fixings`: A real `Tensor` of same dtype as spots or forwards and shape
`[n] + batch_shape` where n is the number of past fixings that have
already been observed
Default value: `None`, equivalent to no past fixings (ie. unseasoned)
* `discount_rates`: An optional real `Tensor` of same dtype as the
`variances` and of the shape that broadcasts with `variances`.
If not `None`, discount factors are calculated as e^(-rT),
where r are the discount rates, or risk free rates. At most one of
`discount_rates` and `discount_factors` can be supplied.
Default value: `None`, equivalent to r = 0 and discount factors = 1 when
`discount_factors` also not given.
* `dividend_rates`: An optional real `Tensor` of same dtype as the
`variances` and of the shape that broadcasts with `variances`.
Default value: `None`, equivalent to q = 0.
* `discount_factors`: An optional real `Tensor` of same dtype as the
`variances`. If not `None`, these are the discount factors to expiry
(i.e. e^(-rT)). Mutually exclusive with `discount_rates`. If neither is
given, no discounting is applied (i.e. the undiscounted option price is
returned). If `spots` is supplied and `discount_factors` is not `None`
then this is also used to compute the forwards to expiry. At most one of
`discount_rates` and `discount_factors` can be supplied.
Default value: `None`, which maps to e^(-rT) calculated from
discount_rates.
* `is_call_options`: A boolean `Tensor` of a shape compatible with
`variances`. Indicates whether the option is a call (if True) or a put
(if False). If not supplied, call options are assumed.
* `averaging_type`: Enum value of AveragingType to select the averaging method
for the payoff calculation
Default value: AveragingType.GEOMETRIC
* `averaging_frequency`: Enum value of AveragingFrequency to select the
averaging type for the payoff calculation (discrete vs continuous)
Default value: AveragingFrequency.DISCRETE
* `integration_method`: An instance of math.integration.IntegrationMethod.
Default value: `None` which maps to Gaussian quadrature.
* `dtype`: Optional `tf.DType`. If supplied, the dtype to be used for conversion
of any supplied non-`Tensor` arguments to `Tensor`.
Default value: `None` which maps to the default dtype inferred by
TensorFlow.
* `name`: str. The name for the ops created by this function.
Default value: `None` which is mapped to the default name
`asian_option_price`.
* `**kwargs`: Additional parameters for the underlying integration method.
If not supplied, uses bounds `lower=1e-9`, `upper=100`.
#### Returns:
* `option_prices`: A `Tensor` of the same shape as `strikes`. The Heston price
of the options.
#### Raises:
* `ValueError`: If both `forwards` and `spots` are supplied or if neither is
supplied.
* `ValueError`: If both `discount_rates` and `discount_factors` is supplied.
* `ValueError`: If option is arithmetic.
* `NotImplementedError`: if option is continuous averaging.
* `NotImplementedError`: if any of the Heston model parameters are of type
PiecewiseConstantFunc.