*Last updated: 2023-03-16.*
# tf_quant_finance.experimental.instruments.ForwardRateAgreement
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Represents a batch of Forward Rate Agreements (FRA).
```python
tf_quant_finance.experimental.instruments.ForwardRateAgreement(
settlement_date, fixing_date, fixed_rate, notional=1.0,
daycount_convention=None, rate_term=None, maturity_date=None, dtype=None,
name=None
)
```
An FRA is a contract for the period [T, T+tau] where the holder exchanges a
fixed rate (agreed at the start of the contract) against a floating payment
determined at time T based on the spot Libor rate for term `tau`. The
cashflows are exchanged at the settlement time T_s, which is either equal to T
or close to T. The FRA are structured so that the payments are made in T+tau
dollars (ref [1]).
The ForwardRateAgreement class can be used to create and price multiple FRAs
simultaneously. However all FRAs within a FRA object must be priced using
a common reference and discount curve.
#### Example:
The following example illustrates the construction of a FRA instrument and
calculating its price.
```python
import numpy as np
import tensorflow as tf
import tf_quant_finance as tff
dates = tff.datetime
dtype = np.float64
notional = 1.
settlement_date = dates.convert_to_date_tensor([(2021, 2, 8)])
fixing_date = dates.convert_to_date_tensor([(2021, 2, 8)])
valuation_date = dates.convert_to_date_tensor([(2020, 2, 8)])
fixed_rate = 0.02
rate_term = rate_term = dates.periods.months(3)
fra = tff.experimental.instruments.ForwardRateAgreement(
notional, settlement_date, fixing_date, fixed_rate,
rate_term=rate_term, dtype=dtype)
curve_dates = valuation_date + dates.periods.months([1, 2, 3, 12, 24, 60])
reference_curve = tff.experimental.instruments.RateCurve(
curve_dates,
np.array([0.02, 0.025, 0.0275, 0.03, 0.035, 0.0325], dtype=dtype),
dtype=dtype)
market = tff.experimental.instruments.InterestRateMarket(
reference_curve=reference_curve, discount_curve=reference_curve)
price = fra.price(valuation_date, market)
# Expected result: 0.00378275
```
#### References:
[1]: Leif B.G. Andersen and Vladimir V. Piterbarg. Interest Rate Modeling,
Volume I: Foundations and Vanilla Models. Chapter 5. 2010.
#### Args:
* `settlement_date`: A rank 1 `DateTensor` specifying the dates on which
cashflows are settled. The shape of the input correspond to the number
of instruments being created.
* `fixing_date`: A rank 1 `DateTensor` specifying the dates on which forward
rate will be fixed. The shape of the inout should be the same as that of
`settlement_date`.
* `fixed_rate`: A rank 1 `Tensor` of real dtype specifying the fixed rate
payment agreed at the initiation of the individual contracts. The shape
should be the same as that of `settlement_date`.
* `notional`: A scalar or a rank 1 `Tensor` of real dtype specifying the
notional amount for each contract. When the notional is specified as a
scalar, it is assumed that all contracts have the same notional. If the
notional is in the form of a `Tensor`, then the shape must be the same
as `settlement_date`.
Default value: 1.0
* `daycount_convention`: An optional `DayCountConvention` to determine
how cashflows are accrued for each contract. Daycount is assumed to be
the same for all contracts in a given batch.
Default value: None in which case the daycount convention will default
to DayCountConvention.ACTUAL_360 for all contracts.
* `rate_term`: An optional rank 1 `PeriodTensor` specifying the term (or the
tenor) of the Libor rate that determines the floating cashflow. The
shape of the input should be the same as `settlement_date`.
Default value: `None` in which case the the forward rate is determined
for the period [settlement_date, maturity_date].
* `maturity_date`: An optional rank 1 `DateTensor` specifying the maturity of
the underlying forward rate for each contract. This input is only used
if the input `rate_term` is `None`.
Default value: `None`
* `dtype`: `tf.Dtype`. If supplied the dtype for the real variables or ops
either supplied to the FRA object or created by the FRA object.
Default value: None which maps to the default dtype inferred by
TensorFlow.
* `name`: Python str. The name to give to the ops created by this class.
Default value: `None` which maps to 'forward_rate_agreement'.
#### Raises:
* `ValueError`: If both `maturity_date` and `rate_term` are unspecified.
## Methods
price
View source
```python
price(
valuation_date, market, model=None
)
```
Returns the present value of the instrument on the valuation date.
#### Args:
* `valuation_date`: A scalar `DateTensor` specifying the date on which
valuation is being desired.
* `market`: A namedtuple of type `InterestRateMarket` which contains the
necessary information for pricing the FRA instrument.
* `model`: Reserved for future use.
#### Returns:
A Rank 1 `Tensor` of real type containing the modeled price of each FRA
contract based on the input market data.