code: def replicating_weights(
      ordered_strikes,
      reference_strikes,
      expiries,
      validate_args=False,
      dtype=None,
      name=None,
  ):
      """Calculates the weights for options to recreate the variance swap payoff.
  
      This implements the approach in Appendix A of Demeterfi et al for calculating
      the weight of European options required to replicate the payoff of a variance
      swap given traded strikes. In particular this function calculates the weights
      for the put option part of the portfolio (when `ordered_strikes` is descending
      ) or for the call option part of the portfolio (when `ordered_strikes`
      is ascending). See the fair strike docstring for further details on variance
      swaps.
  
      #### Example
  
      ```python
      dtype = tf.float64
      ordered_put_strikes = [100, 95, 90, 85]
      reference_strikes = ordered_put_strikes[0]
      expiries = 0.25
      # Contains weights for put options at ordered_put_strikes[:-1]
      put_weights = variance_replicating_weights(
        ordered_put_strikes, reference_strikes, expiries, dtype=dtype)
      # [0.00206927, 0.00443828, 0.00494591]
      ```
  
      #### References
  
      [1] Demeterfi, K., Derman, E., Kamal, M. and Zou, J., 1999. More Than You Ever
        Wanted To Know About Volatility Swaps. Goldman Sachs Quantitative Strategies
        Research Notes.
  
      Args:
        ordered_strikes: A real `Tensor` of liquidly traded strikes of shape
          `batch_shape + [num_strikes]`. The last entry will not receive a weight in
          the portfolio. The values must be sorted ascending if the strikes are for
          calls, or descending if the strikes are for puts. The final value in
          `ordered_strikes` will not itself receive a weight.
        reference_strikes: A `Tensor` of the same dtype as `ordered_strikes` and of
          shape compatible with `batch_shape`. An arbitrarily chosen strike
          representing an at the money strike price.
        expiries: A `Tensor` of the same dtype as `ordered_strikes` and of shape
          compatible with `batch_shape`. Represents the time to maturity of the
          options.
        validate_args: Python `bool`. When `True`, input `Tensor`s are checked for
          validity. The checks verify that `ordered_strikes` is indeed ordered. When
          `False` invalid inputs may silently render incorrect outputs, yet runtime
          performance may be improved.
          Default value: False.
        dtype: `tf.Dtype`. If supplied the dtype for the input and output `Tensor`s.
          Default value: None leading to use of `ordered_strikes.dtype`.
        name: Python str. The name to give to the ops created by this function.
          Default value: `None` which maps to 'variance_replicating_weights'.
  
      Returns:
        A `Tensor` of shape `batch_shape + [num_strikes - 1]` representing the
        weight which should be given to each strike in the replicating portfolio,
        save for the final strike which is not represented.
      """
      with tf.name_scope(name or "replicating_weights"):
          # Input conversion.
          ordered_strikes = tf.convert_to_tensor(
              ordered_strikes, dtype=dtype, name="ordered_strikes"
          )
          dtype = dtype or ordered_strikes.dtype
          reference_strikes = tf.expand_dims(
              tf.convert_to_tensor(
                  reference_strikes,
                  dtype=dtype,
                  name="reference_strikes",
              ),
              -1,
          )
          expiries = tf.expand_dims(
              tf.convert_to_tensor(
                  expiries, dtype=dtype, name="expiries"
              ),
              -1,
          )
          # Descending is required for the formulae regardless of use as control dep.
          strike_diff = diff_ops.diff(
              ordered_strikes, order=1, exclusive=True
          )
          strikes_descending = tf.math.reduce_all(strike_diff < 0)
          control_dependencies = []
          if validate_args:
              strikes_ascending = tf.math.reduce_all(strike_diff > 0)
              control_dependencies.append(
                  tf.compat.v1.debugging.Assert(
                      tf.math.logical_or(
                          strikes_descending, strikes_ascending
                      ),
                      [strike_diff],
                  )
              )
          with tf.control_dependencies(control_dependencies):
              # Weights calculation
              term_lin = (
                  ordered_strikes - reference_strikes
              ) / reference_strikes
              term_log = tf.math.log(ordered_strikes) - tf.math.log(
                  reference_strikes
              )
              payoff = (2.0 / expiries) * (term_lin - term_log)
              payoff_diff = diff_ops.diff(
                  payoff, order=1, exclusive=True
              )
              r_vals = tf.math.divide_no_nan(payoff_diff, strike_diff)
              zero = tf.zeros(
                  r_vals.shape[:-1] + [1], dtype=r_vals.dtype
              )
              r_vals_diff = diff_ops.diff(
                  tf.concat([zero, r_vals], axis=-1),
                  order=1,
                  exclusive=True,
              )
              # If the strikes were for puts we need to flip the sign before returning.
              return tf.where(
                  strikes_descending, -r_vals_diff, r_vals_diff
              )
  
imports: import tensorflow.compat.v2
  from tf_quant_finance.black_scholes import vanilla_prices
  from tf_quant_finance.math import diff_ops
label_desc: Use image node_id 1 for calling a global function with example usage: replicating_weights(ordered_strikes, reference_strikes, expiries, validate_args, dtype, name) and returns: tf