tf_quant_finance.experimental.instruments.FloatingRateNote

Last updated: 2023-03-16.

tf_quant_finance.experimental.instruments.FloatingRateNote#

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Represents a batch of floating rate notes.

tf_quant_finance.experimental.instruments.FloatingRateNote(
    settlement_date, maturity_date, coupon_spec, start_date=None,
    first_coupon_date=None, penultimate_coupon_date=None, holiday_calendar=None,
    dtype=None, name=None
)

Floating rate notes are bond securities where the value of the coupon is not fixed at the time of issuance but is rather reset for every coupon period typically based on a benchmark index such as LIBOR rate [1].

For example, consider a floating rate note with settlement date T_0 and maturity date T_n and equally spaced coupon payment dates T_1, T_2, …, T_n such that

T_0 < T_1 < T_2 < … < T_n and dt_i = T_(i+1) - T_i (A)

The floating rate is fixed on T_0, T_1, …, T_(n-1) and the payments are typically made on T_1, T_2, …, T_n (payment dates) and the i-th coupon payment is given by:

c_i = N * tau_i * L[T_{i-1}, T_i] (B)

where N is the notional amount, tau_i is the daycount fraction for the period [T_{i-1}, T_i] and L[T_{i-1}, T_i] is the flotaing rate reset at T_{i-1}.

The FloatingRateNote class can be used to create and price multiple FRNs simultaneously. However all FRNs within a FloatingRateNote object must be priced using a common reference and discount curve.

Example:#

The following example illustrates the construction of an IRS instrument and calculating its price.

import numpy as np
import tensorflow as tf
import tf_quant_finance as tff
dates = tff.datetime
instruments = tff.experimental.instruments
rc = tff.experimental.instruments.rates_common

dtype = np.float64
settlement_date = dates.convert_to_date_tensor([(2021, 1, 15)])
maturity_date = dates.convert_to_date_tensor([(2022, 1, 15)])
valuation_date = dates.convert_to_date_tensor([(2021, 1, 15)])
period_3m = dates.periods.months(3)
flt_spec = instruments.FloatCouponSpecs(
    coupon_frequency=period_3m,
    reference_rate_term=period_3m,
    reset_frequency=period_3m,
    currency='usd',
    notional=100.,
    businessday_rule=dates.BusinessDayConvention.NONE,
    coupon_basis=0.,
    coupon_multiplier=1.,
    daycount_convention=instruments.DayCountConvention.ACTUAL_365)

frn = instruments.FloatingRateNote(settlement_date, maturity_date,
                                   [flt_spec],
                                   dtype=dtype)

curve_dates = valuation_date + dates.periods.months([0, 6, 12, 36])
reference_curve = instruments.RateCurve(
    curve_dates,
    np.array([0.0, 0.005, 0.007, 0.015], dtype=dtype),
    valuation_date=valuation_date,
    dtype=dtype)
market = instruments.InterestRateMarket(discount_curve=reference_curve,
                                        reference_curve=reference_curve)

price = frn.price(valuation_date, market)
# Expected result: 100.

References:#

[1]: Tomas Bjork. Arbitrage theory in continuous time, Second edition. Chapter 20. 2004.

Args:#

  • settlement_date: A rank 1 DateTensor specifying the settlement date of the FRNs.

  • maturity_date: A rank 1 DateTensor specifying the maturity dates of the FRNs. The shape of the input should be the same as that of settlement_date.

  • coupon_spec: A list of FloatCouponSpecs specifying the coupon payments. The length of the list should be the same as the number of FRNs being created.

  • start_date: An optional DateTensor specifying the dates when the interest starts to accrue for the coupons. The input can be used to specify a forward start date for the coupons. The shape of the input correspond to the numbercof instruments being created. Default value: None in which case the coupons start to accrue from the settlement_date.

  • first_coupon_date: An optional rank 1 DateTensor specifying the dates when first coupon will be paid for FRNs with irregular first coupon.

  • penultimate_coupon_date: An optional rank 1 DateTensor specifying the dates when the penultimate coupon (or last regular coupon) will be paid for FRNs with irregular last coupon.

  • holiday_calendar: An instance of dates.HolidayCalendar to specify weekends and holidays. Default value: None in which case a holiday calendar would be created with Saturday and Sunday being the holidays.

  • dtype: tf.Dtype. If supplied the dtype for the real variables or ops either supplied to the bond object or created by the bond 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 ‘floating_rate_note’.

Methods#

price

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price(
    valuation_date, market, model=None, name=None
)

Returns the price of the FRNs 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 FRNs.

  • model: Reserved for future use.

  • name: Python str. The name to give to the ops created by this function. Default value: None which maps to ‘price’.

Returns:#

A Rank 1 Tensor of real dtype containing the price of each FRN based on the input market data.

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