*Last updated: 2023-03-16.*
# tf_quant_finance.experimental.american_option_pricing.andersen_lake.calculate_exercise_boundary
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Calculates the exercise boundary function of an American option.
```python
tf_quant_finance.experimental.american_option_pricing.andersen_lake.calculate_exercise_boundary(
tau_grid, k, r, q, sigma, max_iterations=20, tolerance=1e-08,
integration_num_points=32, dtype=None
)
```
Iteratively calculates the exercise boundary function of an American option.
This corresponds to `B` in formula (3.9) in the paper [1].
#### References
[1] Leif Andersen, Mark Lake and Dimitri Offengenden. High-performance
American option pricing. 2015
https://engineering.nyu.edu/sites/default/files/2019-03/Carr-adjusting-exponential-levy-models.pdf#page=55
#### Example
```python
tau = tf.constant([0.01, 0.02, 1], dtype=tf.float64)
k = tf.constant([1, 2, 3], dtype=tf.float64)
r = tf.constant([0.01, 0.02, 0.035], dtype=tf.float64)
q = tf.constant([0.01, 0.02, 0.07], dtype=tf.float64)
sigma = tf.constant([0.1, 0.15, 0.32], dtype=tf.float64)
grid_num_points = 40
max_iterations = 600
tolerance = 1e-8
integration_num_points = 32
tau_grid = tf.linspace(tf.constant(0.0001, dtype=tf.float64), tau,
grid_num_points, axis=-1)
exercise_boundary(tau_grid, k, r, q, sigma, max_iterations, tolerance,
integration_num_points)
# Returns a tensor of shape [3, 40].
```
#### Args:
* `tau_grid`: Grid of values of shape `[num_options, grid_num_points]`
indicating the time left until option maturity.
* `k`: Same dtype as `tau_grid` with shape `num_options` representing the strike
price of the option.
* `r`: Same shape and dtype as `k` representing the annualized risk-free
interest rate, continuously compounded.
* `q`: Same shape and dtype as `k` representing the dividend rate.
* `sigma`: Same shape and dtype as `k` representing the volatility of the
option's returns.
* `max_iterations`: Maximum number of iterations for calculating the exercise
boundary if it doesn't converge earlier. Default value: 20.
* `tolerance`: Represents the tolerance for the relative difference between the
old and new exercise boundary function values, at which to stop further
calculating a new exercise boundary function.
* `integration_num_points`: The number of points used in the integration
approximation method.
Default value: 32.
* `dtype`: If supplied, the dtype for all input tensors. Result will have the
same dtype.
Default value: None which maps to dtype of `tau`.
#### Returns:
`Callable` expecting `Tensor` of shape `[num_options, n]` as input (where
`n` is an arbitrary integer) and returning `Tensor` of the same shape.
Represents the exercise boundary function of an American option pricing
algorithm.