code: def cap_floor_price(
      *,
      strikes: types.RealTensor,
      expiries: types.RealTensor,
      maturities: types.RealTensor,
      daycount_fractions: types.RealTensor,
      reference_rate_fn: Callable[..., types.RealTensor],
      dim: int,
      mean_reversion: types.RealTensor,
      volatility: Union[
          types.RealTensor, Callable[..., types.RealTensor]
      ],
      corr_matrix: types.RealTensor = None,
      notional: types.RealTensor = 1.0,
      is_cap: types.BoolTensor = True,
      num_samples: types.IntTensor = 1,
      random_type: random.RandomType = None,
      seed: types.IntTensor = None,
      skip: types.IntTensor = 0,
      time_step: types.RealTensor = None,
      dtype: tf.DType = None,
      name: str = None,
  ) -> types.RealTensor:
      """Calculates the prices of interest rate Caps/Floors using the HJM model.
  
      An interest Cap (or Floor) is a portfolio of call (or put) options where the
      underlying for the individual options are successive forward rates. The
      individual options comprising a Cap are called Caplets and the corresponding
      options comprising a Floor are called Floorlets. For example, a
      caplet on forward rate `F(T_i, T_{i+1})` has the following payoff at time
      `T_{i_1}`:
  
      ```None
  
       caplet payoff = tau_i * max[F(T_i, T_{i+1}) - X, 0]
  
      ```
      where where `X` is the strake rate and `tau_i` is the daycount fraction. The
      caplet payoff (at `T_{i+1}`) can be expressed as the following at `T_i`:
  
      ```None
  
      caplet_payoff = (1.0 + tau_i * X) *
                      max[1.0 / (1 + tau_i * X) - P(T_i, T_{t+1}), 0]
  
      ```
  
      where `P(T_i, T_{i+1})` is the price at `T_i` of a zero coupon bond with
      maturity `T_{i+1}. Thus, a caplet can be priced as a put option on zero
      coupon bond [1].
  
      #### References
        [1]: D. Brigo, F. Mercurio. Interest Rate Models-Theory and Practice.
        Second Edition. 2007.
  
      #### Example
      The example shows how value a batch containing spot starting 1-year and
      2-year Caps and with quarterly frequency.
  
      ````python
      import numpy as np
      import tensorflow.compat.v2 as tf
      import tf_quant_finance as tff
  
      dtype = tf.float64
  
      reference_rate_fn = lambda x: 0.01 * tf.ones_like(x, dtype=dtype)
      expiries = np.array([[0.0, 0.25, 0.5, 0.75, 1.0, 1.0, 1.0, 1.0],
                           [0.0, 0.25, 0.5, 0.75, 1.0, 1.25, 1.5, 1.75]])
      maturities = np.array([[0.25, 0.5, 0.75, 1.0, 1.0, 1.0, 1.0, 1.0],
                           [0.25, 0.5, 0.75, 1.0, 1.25, 1.5, 1.75, 2.0]])
      strikes = 0.01 * np.ones_like(expiries)
      daycount_fractions = np.array([[0.25, 0.25, 0.25, 0.25, 0.0, 0.0, 0.0, 0.0],
                           [0.0, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25]])
      price = tff.models.hjm.cap_floor_price(
          strikes=strikes,
          expiries=expiries,
          maturities=maturities,
          daycount_fractions=daycount_fractions,
          notional=1.0e6,
          dim=1,
          mean_reversion=[0.03],
          volatility=[0.02],
          reference_rate_fn=reference_rate_fn,
          num_samples=500000,
          time_step=0.025,
          random_type=tff.math.random.RandomType.STATELESS_ANTITHETIC,
          seed=[1, 2],
          dtype=dtype)
      # Expected value: [[4071.821182], [15518.53244292]]
      ````
  
      Args:
        strikes: A real `Tensor` of any shape and dtype. The strike rate of the
          caplets or floorlets. The shape of this input determines the number (and
          shape) of the options to be priced and the shape of the output. For an
          N-dimensional input `Tensor`, the first N-1 dimensions correspond to the
          batch dimension, i.e., the distinct caps and floors and the last dimension
          correspond to the caplets or floorlets contained with an instrument.
        expiries: A real `Tensor` of the same dtype and compatible shape as
          `strikes`.  The reset time of each caplet (or floorlet).
        maturities: A real `Tensor` of the same dtype and compatible shape as
          `strikes`.  The maturity time of each caplet (or floorlet) and also the
          time at which payment is made.
        daycount_fractions: A real `Tensor` of the same dtype and compatible shape
          as `strikes`. The daycount fractions associated with the underlying
          forward rates.
        reference_rate_fn: A Python callable that accepts expiry time as a real
          `Tensor` and returns a `Tensor` of shape `input_shape`. Returns the
          continuously compounded zero rate at the present time for the input expiry
          time.
        dim: A Python scalar which corresponds to the number of factors within a
          single HJM model.
        mean_reversion: A real positive `Tensor` of shape `[dim]`. Corresponds to
          the mean reversion rate of each factor.
        volatility: A real positive `Tensor` of the same `dtype` and shape as
          `mean_reversion` or a callable with the following properties: (a)  The
            callable should accept a scalar `Tensor` `t` and a 1-D `Tensor` `r(t)`
            of shape `[num_samples]` and returns a 2-D `Tensor` of shape
            `[num_samples, dim]`. The variable `t`  stands for time and `r(t)` is
            the short rate at time `t`.  The function returns instantaneous
            volatility `sigma(t) = sigma(t, r(t))`. When `volatility` is specified
            is a real `Tensor`, each factor is assumed to have a constant
            instantaneous volatility  and the  model is effectively a Gaussian HJM
            model. Corresponds to the instantaneous volatility of each factor.
        corr_matrix: A `Tensor` of shape `[dim, dim]` and the same `dtype` as
          `mean_reversion`. Corresponds to the correlation matrix `Rho`.
          Default value: None, meaning the factors are uncorrelated.
        notional: An optional `Tensor` of same dtype and compatible shape as
          `strikes`specifying the notional amount for the cap (or floor).
           Default value: None in which case the notional is set to 1.
        is_cap: A boolean `Tensor` of a shape compatible with `strikes`. Indicates
          whether the option is a Cap (if True) or a Floor (if False). If not
          supplied, Caps are assumed.
        num_samples: Positive scalar `int32` `Tensor`. The number of simulation
          paths during Monte-Carlo valuation.
          Default value: The default value is 1.
        random_type: Enum value of `RandomType`. The type of (quasi)-random number
          generator to use to generate the simulation paths.
          Default value: `None` which maps to the standard pseudo-random numbers.
        seed: Seed for the random number generator. The seed is only relevant if
          `random_type` is one of `[STATELESS, PSEUDO, HALTON_RANDOMIZED,
          PSEUDO_ANTITHETIC, STATELESS_ANTITHETIC]`. For `PSEUDO`,
          `PSEUDO_ANTITHETIC` and `HALTON_RANDOMIZED` the seed should be an Python
          integer. For `STATELESS` and  `STATELESS_ANTITHETIC `must be supplied as
          an integer `Tensor` of shape `[2]`.
          Default value: `None` which means no seed is set.
        skip: `int32` 0-d `Tensor`. The number of initial points of the Sobol or
          Halton sequence to skip. Used only when `random_type` is 'SOBOL',
          'HALTON', or 'HALTON_RANDOMIZED', otherwise ignored.
          Default value: `0`.
        time_step: Scalar real `Tensor`. Maximal distance between time grid points
          in Euler scheme. Relevant when Euler scheme is used for simulation.
          Default value: `None`.
        dtype: The default dtype to use when converting values to `Tensor`s.
          Default value: `None` which means that default dtypes inferred by
            TensorFlow are used.
        name: Python string. The name to give to the ops created by this class.
          Default value: `None` which maps to the default name
            `hjm_cap_floor_price`.
  
      Returns:
        A `Tensor` of real dtype and shape  strikes.shape[:-1] containing
        the computed option prices. For caplets that have reset in the past
        (expiries<0), the function sets the corresponding caplet prices to 0.0.
      """
      name = name or "hjm_cap_floor_price"
      with tf.name_scope(name):
          strikes = tf.convert_to_tensor(
              strikes, dtype=dtype, name="strikes"
          )
          dtype = dtype or strikes.dtype
          expiries = tf.convert_to_tensor(
              expiries, dtype=dtype, name="expiries"
          )
          maturities = tf.convert_to_tensor(
              maturities, dtype=dtype, name="maturities"
          )
          daycount_fractions = tf.convert_to_tensor(
              daycount_fractions, dtype=dtype, name="daycount_fractions"
          )
          notional = tf.convert_to_tensor(
              notional, dtype=dtype, name="notional"
          )
          is_cap = tf.convert_to_tensor(
              is_cap, dtype=tf.bool, name="is_cap"
          )
          is_call_options = ~is_cap
          bond_option_strikes = 1.0 / (
              1.0 + daycount_fractions * strikes
          )
  
          # The dimension of `caplet_prices` is going to be strikes.shape
          caplet_prices = zcb.bond_option_price(
              strikes=bond_option_strikes,
              expiries=expiries,
              maturities=maturities,
              discount_rate_fn=reference_rate_fn,
              dim=dim,
              mean_reversion=mean_reversion,
              volatility=volatility,
              corr_matrix=corr_matrix,
              is_call_options=is_call_options,
              num_samples=num_samples,
              random_type=random_type,
              seed=seed,
              skip=skip,
              time_step=time_step,
              dtype=dtype,
              name=name + "_bond_option",
          )
  
          caplet_prices = tf.where(
              expiries < 0.0, tf.zeros_like(expiries), caplet_prices
          )
  
          cap_prices = tf.math.reduce_sum(
              notional
              * (1.0 + daycount_fractions * strikes)
              * caplet_prices,
              axis=-1,
          )
          return cap_prices
  
imports: from typing import Callable, Union
  import tensorflow.compat.v2
  from tf_quant_finance import types
  from tf_quant_finance.math import random
  from tf_quant_finance.models.hjm import zero_coupon_bond_option
label_desc: Use image node_id 1 for calling a global function with example usage: cap_floor_price() and returns: cap_prices