*Last updated: 2023-03-16.*
# tf_quant_finance.black_scholes.option_price_binomial
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Computes the BS price for a batch of European or American options.
```python
tf_quant_finance.black_scholes.option_price_binomial(
*, volatilities, strikes, expiries, spots, discount_rates=None,
dividend_rates=None, is_call_options=None, is_american=None, num_steps=100,
dtype=None, name=None
)
```
Uses the Cox-Ross-Rubinstein version of the binomial tree method to compute
the price of American or European options. Supports batching of the options
and allows mixing of European and American style exercises in a batch.
For more information about the binomial tree method and the
Cox-Ross-Rubinstein method in particular see the references below.
#### Example
```python
# Prices 5 options with a mix of Call/Put, American/European features
# in a single batch.
dtype = np.float64
spots = np.array([1.0, 2.0, 3.0, 4.0, 5.0], dtype=dtype)
strikes = np.array([3.0, 3.0, 3.0, 3.0, 3.0], dtype=dtype)
volatilities = np.array([0.1, 0.22, 0.32, 0.01, 0.4], dtype=dtype)
is_call_options = np.array([True, True, False, False, False])
is_american = np.array([False, True, True, False, True])
discount_rates = np.array(0.035, dtype=dtype)
dividend_rates = np.array([0.02, 0.0, 0.07, 0.01, 0.0], dtype=dtype)
expiries = np.array(1.0, dtype=dtype)
prices = option_price_binomial(
volatilities=volatilities,
strikes=strikes,
expiries=expiries,
spots=spots,
discount_rates=discount_rates,
dividend_rates=dividend_rates,
is_call_options=is_call_options,
is_american=is_american,
dtype=dtype)
# Prints [0., 0.0098847, 0.41299509, 0., 0.06046989]
```
#### References
[1] Hull, John C., Options, Futures and Other Derivatives. Pearson, 2018.
[2] Wikipedia contributors. Binomial Options Pricing Model. Available at:
https://en.wikipedia.org/wiki/Binomial_options_pricing_model
#### 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. 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
`volatilities`. The current spot price of the underlying.
* `discount_rates`: An optional real `Tensor` of same dtype as the
`volatilities`. The risk free discount rate. If None the rate is assumed
to be 0.
Default value: None, equivalent to discount rates = 0..
* `dividend_rates`: An optional real `Tensor` of same dtype as the
`volatilities`. If None the rate is assumed to be 0.
Default value: None, equivalent to discount rates = 1.
* `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.
Default value: None, equivalent to is_call_options = True.
* `is_american`: A boolean `Tensor` of a shape compatible with `volatilities`.
Indicates whether the option exercise style is American (if True) or
European (if False). If not supplied, European style exercise is assumed.
Default value: None, equivalent to is_american = False.
* `num_steps`: A positive scalar int32 `Tensor`. The size of the time
discretization to use.
Default value: 100.
* `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
(float32).
* `name`: str. The name for the ops created by this function.
Default value: None which is mapped to the default name `option_price`.
#### Returns:
A `Tensor` of the same shape as the inferred batch shape of the input data.
The Black Scholes price of the options computed on a binomial tree.