Expressions

The event table often requires one or more of the following to capture the features of contract.

• A Phrase that represents a value calculated from one or more assets. e.g. calculating the barrier condition in a knock out option.
• A Snapper that represents a path dependent calculation, e.g. calculating returns in an equity cliquet.

Phrase

A Phrase is defined with three parameters.

• type, which must be "phrase"
• inp, a list of inputs to the phrase fn. An input can be an asset, such as "SPX", whose value comes from the model. It can also be a snap which has been stored as a result of previous snapper operation. It can also be another phrase.
• fn, a python function that takes a list of inputs, and returns a list of outputs. The length of expected inputs list must match the length of inp, while the length of the output list must be exactly one.

e.g. for a Down-and-Out Barrier Option the knock out condition ko is defined as

def ko_fn(inputs):
    [S] = inputs
    return [S < barrier]

"ko": {
    "type": "phrase",
    "inp": [asset_name],
    "fn": ko_fn,
}

and used in the timetable as an op

      time op  quantity unit track
03/31/2024 ko       0.0  USD

See Barrier Option for more on this example.

Function Signature

The function should expect that inputs is a list of items.

• The length of the list will match the length of inp.
• Each item in the list can be a float, or a 1-D numpy array of size 1 or N (where N is the number of Monte-Carlo paths, or the length of the Finite Difference grid's asset-axis).

The function should return a list of items.

• For a phrase the length of the output list must be exactly one, while for a snapper the length of the output list must match the length of out.
• Each item in the list should be a float, or a 1-D numpy array of size 1 or N. This is consistent with numpy broadcasting, therefore a function written using arithmetic operations like +, -, *, or element-wise numpy functions (e.g. numpy.maximum, np.sqrt) would satisfy the requirement.