tf_quant_finance.experimental.american_option_pricing.andersen_lake.calculate_exercise_boundary

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.

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#

  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.

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