tf_quant_finance.rates.analytics.swap.equity_leg_cashflows

Last updated: 2023-03-16.

tf_quant_finance.rates.analytics.swap.equity_leg_cashflows#

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Computes cashflows for a batch of equity legs.

tf_quant_finance.rates.analytics.swap.equity_leg_cashflows(
    forward_prices, spots, notional, dividends=None, dtype=None, name=None
)

Equity cashflows are defined as a total equity return between pay dates, say, T_1, ..., T_n. Let S_i represent the value of the equity at time T_i and d_i be a discrete dividend paid at this time. Then the the payment at time T_i is defined as (S_i - S_{i - 1}) / S_{i-1} + d_i. The value of the cashflow is then the discounted sum of the paments. See, e.g., [1] for the reference.

Example#

notional = 10000
forward_prices = [[110, 120, 140], [210, 220, 240]]
spots = [100, 200]
dividends = [[1, 1, 1], [2, 2, 2]]
equity_leg_cashflows(forward_prices, spots, notional, dividends,
                     dtype=tf.float64)
# Expected:
#  [[1000.01, 909.1, 1666.675],
#   [ 500.01, 476.2, 909.1]]

Args:#

  • forward_prices: A real Tensor of shape batch_shape + [num_cashflows], where num_cashflows is the number of cashflows for each batch element. Equity forward prices at leg reset times.

  • spots: A Tensor of the same dtype as forward_prices and of shape compatible with batch_shape. Spot prices for each batch element

  • notional: A Tensor of the same dtype as forward_prices and of compatible shape. Notional amount for each cashflow.

  • dividends: A Tensor of the same dtype as forward_prices and of compatible shape. Discrete dividends paid at the leg reset times. Default value: None which maps to zero dividend.

  • dtype: tf.Dtype. If supplied the dtype for the input and output Tensors. Default value: None which maps to the default dtype inferred from forward_prices.

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

Returns:#

A Tensor of the same dtype as forward_prices and of shape batch_shape + [num_cashflows].

References#

[1] Don M. Chance and Don R Rich, The Pricing of Equity Swaps and Swaptions, 1998 https://jod.pm-research.com/content/5/4/19

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