code: def adesi_whaley(
      *,
      volatilities: types.RealTensor,
      strikes: types.RealTensor,
      expiries: types.RealTensor,
      spots: types.RealTensor = None,
      forwards: types.RealTensor = None,
      discount_rates: types.RealTensor = None,
      dividend_rates: types.RealTensor = None,
      discount_factors: types.RealTensor = None,
      is_call_options: types.BoolTensor = None,
      max_iterations: int = 100,
      tolerance: types.RealTensor = 1e-8,
      dtype: tf.DType = None,
      name: str = None,
  ) -> Tuple[types.RealTensor, types.BoolTensor, types.BoolTensor]:
      """Computes American option prices using the Baron-Adesi Whaley approximation.
  
      #### Example
  
      ```python
      spots = [80.0, 90.0, 100.0, 110.0, 120.0]
      strikes = [100.0, 100.0, 100.0, 100.0, 100.0]
      volatilities = [0.2, 0.2, 0.2, 0.2, 0.2]
      expiries = 0.25
      dividends = 0.12
      discount_rates = 0.08
      computed_prices = adesi_whaley(
          volatilities=volatilities,
          strikes=strikes,
          expiries=expiries,
          discount_rates=discount_rates,
          dividend_rates=dividends,
          spots=spots,
          dtype=tf.float64)
      # Expected print output of computed prices:
      # [0.03, 0.59, 3.52, 10.31, 20.0]
      ```
  
      #### References:
      [1] Baron-Adesi, Whaley, Efficient Analytic Approximation of American Option
        Values, The Journal of Finance, Vol XLII, No. 2, June 1987
        https://deriscope.com/docs/Barone_Adesi_Whaley_1987.pdf
  
      Args:
        volatilities: Real `Tensor` of any shape and real 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. 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`. If not `None`, discount factors are calculated as e^(-rT),
          where r are the discount rates, or risk free rates.
          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`. The continuous dividend rate on the underliers. May be
          negative (to indicate costs of holding the underlier).
          Default value: `None`, equivalent to zero dividends.
        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_rate. 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 `-log(discount_factors) / expiries`
        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.
        max_iterations: positive `int`. The maximum number of iterations of Newton's
          root finding method to find the critical spot price above and below which
          the pricing formula is different.
          Default value: 100
        tolerance: Positive scalar `Tensor`. As with `max_iterations`, used with the
          Newton root finder to find the critical spot price. The root finder will
          judge an element to have converged if `|f(x_n) - a|` is less than
          `tolerance` (where `f` is the target function as defined in [1] and `x_n`
          is the estimated critical value), or if `x_n` becomes `nan`. When an
          element is judged to have converged it will no longer be updated. If all
          elements converge before `max_iterations` is reached then the root finder
          will return early.
          Default value: 1e-8
        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 `adesi_whaley`.
  
      Returns:
        A 3-tuple containing the following items in order:
           (a) option_prices: A `Tensor` of the same shape as `forwards`. The Black
             Scholes price of the options.
           (b) converged: A boolean `Tensor` of the same shape as `option_prices`
             above. Indicates whether the corresponding adesi-whaley approximation
             has converged to within tolerance.
           (c) failed: A boolean `Tensor` of the same shape as `option_prices`
             above. Indicates whether the corresponding options price is NaN or not
             a finite number. Note that converged being True implies that failed
             will be false. However, it may happen that converged is False but
             failed is not True. This indicates the search did not converge in the
             permitted number of iterations but may converge if the iterations are
             increased.
  
      Raises:
        ValueError:
          (a) If both `forwards` and `spots` are supplied or if neither is supplied.
      """
      if (spots is None) == (forwards is None):
          raise ValueError(
              "Either spots or forwards must be supplied but not both."
          )
      if (discount_rates is not None) and (
          discount_factors is not None
      ):
          raise ValueError(
              "At most one of discount_rates and discount_factors may "
              "be supplied"
          )
      with tf.name_scope(name or "adesi_whaley"):
          volatilities = tf.convert_to_tensor(
              volatilities, dtype=dtype, name="volatilities"
          )
          dtype = (
              volatilities.dtype
          )  # This dtype should be common for all inputs
          strikes = tf.convert_to_tensor(
              strikes, dtype=dtype, name="strikes"
          )
          expiries = tf.convert_to_tensor(
              expiries, dtype=dtype, name="expiries"
          )
          if discount_rates is not None:
              discount_rates = tf.convert_to_tensor(
                  discount_rates, dtype=dtype, name="discount_rates"
              )
          elif discount_factors is not None:
              discount_factors = tf.convert_to_tensor(
                  discount_factors, dtype=dtype, name="discount_factors"
              )
              discount_rates = -tf.math.log(discount_factors) / expiries
          else:
              discount_rates = tf.constant(
                  0.0, dtype=dtype, name="discount_rates"
              )
  
          if dividend_rates is not None:
              dividend_rates = tf.convert_to_tensor(
                  dividend_rates, dtype=dtype, name="dividend_rates"
              )
          else:
              dividend_rates = 0
          # Set forwards and spots
          if forwards is not None:
              spots = tf.convert_to_tensor(
                  forwards
                  * tf.exp(
                      -(discount_rates - dividend_rates) * expiries
                  ),
                  dtype=dtype,
                  name="spots",
              )
          else:
              spots = tf.convert_to_tensor(
                  spots, dtype=dtype, name="spots"
              )
          if is_call_options is not None:
              is_call_options = tf.convert_to_tensor(
                  is_call_options, dtype=tf.bool, name="is_call_options"
              )
          else:
              is_call_options = tf.constant(
                  True, name="is_call_options"
              )
  
          am_prices, converged, failed = _adesi_whaley(
              sigma=volatilities,
              x=strikes,
              t=expiries,
              s=spots,
              r=discount_rates,
              d=dividend_rates,
              is_call_options=is_call_options,
              dtype=dtype,
              max_iterations=max_iterations,
              tolerance=tolerance,
          )
  
          # For call options where b >= r as per reference [1], only the European
          # option price should be calclated, while for the rest the american price
          # formula should be used. For this reason, the vanilla European price is
          # calculated for all the spot prices, (assuming they are all call options),
          # and a subset of these will be used further down, if any of the date points
          # fit the criteria that they are all call options with b >= r.
          eu_prices = vanilla_prices.option_price(
              volatilities=volatilities,
              strikes=strikes,
              expiries=expiries,
              spots=spots,
              discount_rates=discount_rates,
              dividend_rates=dividend_rates,
              dtype=dtype,
              name=name,
          )
          calculate_eu = is_call_options & (dividend_rates <= 0)
          converged = tf.where(calculate_eu, True, converged)
          failed = tf.where(calculate_eu, False, failed)
          return (
              tf.where(calculate_eu, eu_prices, am_prices),
              converged,
              failed,
          )
  
imports: from typing import Tuple
  import numpy
  import tensorflow.compat.v2
  from tf_quant_finance import types
  from tf_quant_finance.black_scholes import vanilla_prices
  from tf_quant_finance.math import gradient
  from tf_quant_finance.math import integration
  from tf_quant_finance.math.root_search import newton
label_desc: Use image node_id 1 for calling a global function with example usage: adesi_whaley() and returns: tf,  converged,  failed