*Last updated: 2023-03-16.*
# tf_quant_finance.black_scholes.asset_or_nothing_price
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Computes the Black Scholes price for a batch of asset-or-nothing options.
```python
tf_quant_finance.black_scholes.asset_or_nothing_price(
*, volatilities, strikes, expiries, spots=None, forwards=None,
discount_rates=None, dividend_rates=None, discount_factors=None,
is_call_options=None, is_normal_volatility=False, dtype=None, name=None
)
```
The asset-or-nothing call (resp. put) pays out one unit of the underlying
asset if the spot is above (resp. below) the strike at maturity.
#### Example
```python
# Price a batch of 5 asset_or_nothing call and put options.
volatilities = np.array([0.0001, 102.0, 2.0, 0.1, 0.4])
forwards = np.array([1.0, 2.0, 3.0, 4.0, 5.0])
# Strikes will automatically be broadcasted to shape [5].
strikes = np.array([3.0])
# Expiries will be broadcast to shape [5], i.e. each option has strike=3
# and expiry = 1.
expiries = 1.0
computed_prices = tff.black_scholes.asset_or_nothing_price(
volatilities=volatilities,
strikes=strikes,
expiries=expiries,
forwards=forwards)
# Expected print output of prices:
# [0., 2., 2.52403424, 3.99315108, 4.65085383]
```
#### References:
[1] Hull, John C., Options, Futures and Other Derivatives. Pearson, 2018.
[2] https://en.wikipedia.org/wiki/Binary_option#Asset-or-nothing_call
#### Args:
* `volatilities`: Real `Tensor` of any shape and dtype. The volatilities to
expiry of the options to price.
* `strikes`: A real `Tensor` of the same dtype and compatible shape as
`volatilities`. The strikes of the options to be priced.
* `expiries`: A real `Tensor` of same dtype and compatible shape as
`volatilities`. The expiry of each option.
* `spots`: A real `Tensor` of any shape that broadcasts to the shape of the
`volatilities`. 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
`volatilities`. The forwards to maturity. Either this argument or the
`spots` must be supplied but both must not be supplied.
* `discount_rates`: An optional real `Tensor` of same dtype as the
`volatilities` and of the shape that broadcasts with `volatilities`. 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
`volatilities` and of the shape that broadcasts with `volatilities`.
Default value: `None`, equivalent to q = 0.
* `discount_factors`: An optional real `Tensor` of same dtype as the
`volatilities`. 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
`volatilities`. Indicates whether the option is a call (if True) or a put
(if False). If not supplied, call options are assumed.
* `is_normal_volatility`: An optional Python boolean specifying whether the
`volatilities` correspond to lognormal Black volatility (if False) or
normal Black volatility (if True).
Default value: False, which corresponds to lognormal volatility.
* `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
`asset_or_nothing_price`.
#### Returns:
* `option_prices`: A `Tensor` of the same shape as `forwards`. The Black
Scholes 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.