robustfpm.finance.derivatives module

This submodule implements IOption interface class, European, American, and Bermudan styled option classes. Also provides option-generating method make_option() for seamless construction of different options.

class robustfpm.finance.derivatives.IOption(expiry, payoff_fcn)

Bases: abc.ABC

An abstract interface for Options

abstract payoff(prices, t=None)

Get the value of payoff function for prices and time t

Parameters

prices (array_like, size = (m,n) or (n,)) – Asset prices (or a set of prices), each price — a point in \(\mathbb{R}^{n}\)
t (int) – Current time

Return type

np.ndarray

abstract property expiry: Expiration date

class robustfpm.finance.derivatives.EuropeanOption(expiry: int, payoff_fcn: Callable)

Bases: robustfpm.finance.derivatives.IOption

Generic european-style option class

Parameters

expiry (int) – An expiration date
payoff_fcn (Callable) – Payoff function for given price(s)

payoff(prices, t=None)

Get the value of payoff function for prices and time t

Parameters

prices (array_like, size = (m,n) or (n,)) – Asset prices (or a set of prices), each price — a point in \(\mathbb{R}^{n}\)
t (int) – Current time

Return type

np.ndarray

property expiry: Expiration date

class robustfpm.finance.derivatives.AmericanOption(payoff_fcn: Callable, expiry=None)

Bases: robustfpm.finance.derivatives.IOption

Generic american-style option class

Parameters

payoff_fcn (Callable) – Payoff function for given price(s)
expiry (int, optional) – Expiration date

payoff(prices, t=None)

Get the value of payoff function for prices and time t

Parameters

prices (array_like, size = (m,n) or (n,)) – Asset prices (or a set of prices), each price — a point in \(\mathbb{R}^{n}\)
t (int) – Current time

Return type

np.ndarray

property expiry: Expiration date

class robustfpm.finance.derivatives.BermudanOption(payoff_dates, payoff_fcn: Callable)

Bases: robustfpm.finance.derivatives.IOption

Bermudan and Canary-styled option class

Parameters

payoff_dates (array_like) – Payoff dates (as integers)
payoff_fcn (Callable) – Payoff function for given price(s)

Notes

Bermudan and Canary options are very much alike, so we put both styles in the same class.

payoff(prices, t=None)

Get the value of payoff function for prices and time t

Parameters

prices (array_like, size = (m,n) or (n,)) – Asset prices (or a set of prices), each price — a point in \(\mathbb{R}^{n}\)
t (int) – Current time

Return type

np.ndarray

property expiry: Expiration date

robustfpm.finance.derivatives.make_option(option_type=None, strike=None, payoff_fcn=None, payoff_dates=None)

Create a new option

You must either give a specific type and strike or provide an option payoff_fcn.

If type and strike are given, payoff_fcn is ignored.

If type is given, but strike is omitted, strike defaults to zero.

If no type is given, but strike is provided, then payoff_fcn must be a wrapper, which accepts strike keyword argument and returns a payoff function (Callable) for a given strike.

If both type and strike are omitted, payoff_fcn must be a function that accepts 1 positional argument.

Parameters

option_type (str, optional) – A predefined type of option to be constructed.
strike (float, optional) – Strike price.
payoff_fcn (Callable, optional) – Payoff function of an option to be constructed.
payoff_dates (int or list or tuple or np.ndarray, optional) – Expiration date(s). If has only 1 element (or is int), the European option is constructed. If given an array of payoff times — Bermudan. If ommited — American.

Returns

The constructed option

Return type

IOption

Examples

Create a simple European call option with strike 10 and expiry 4 and evaluate its payoff at diffent points in time.

>>> from robustfpm.finance import *
>>> import numpy as np
>>> def call_10(x):
...     return np.array(np.maximum((x - 10), np.zeros_like(x)), float).squeeze()
>>> call = make_option(payoff_fcn = call_10, payoff_dates=4)
>>> isinstance(call, IOption)
True
>>> isinstance(call, EuropeanOption)
True
>>> isinstance(call, BermudanOption)
False
>>> call.payoff(9, 3)
array([-inf])
>>> call.payoff(11, 3)
array([-inf])
>>> call.payoff([[9],[11]], 4)
array([0., 1.])
>>> call.payoff([9, 11], 4)
array([0., 1.])

Do the same with wrapper-function

>>> from robustfpm.finance import *
>>> import numpy as np
>>> def call_payoff(strike):
...     def call_with_strike(x):
...         return np.array(np.maximum((x - strike), np.zeros_like(x)), float).squeeze()
...     return call_with_strike
>>> call = make_option(payoff_fcn = call_payoff, strike=10, payoff_dates=4)
>>> call.payoff([[9],[11]], 4)
array([0., 1.])
>>> call_5 = make_option(payoff_fcn = call_payoff, strike=5, payoff_dates=4)
>>> call_5.payoff([4,6,10], 4)
array([0., 1., 5.])

Alternatively, create the same option as call on max with 1 asset.

>>> from robustfpm.finance import *
>>> call = make_option(option_type='callonmax',strike=10, payoff_dates=4)
>>> isinstance(call, IOption)
True
>>> isinstance(call, EuropeanOption)
True
>>> call.payoff(11,4)
array([1.])
>>> call.payoff([[9],[11]], 4)
array([0., 1.])
>>> call.payoff([9, 11], 4)
array([1.]) #behaves differently since it's actually a call on max

In the same manner, create a Bermudan and American put2call1 option.

>>> from robustfpm.finance import *
>>> Option1 = make_option(option_type='put2call1',payoff_dates=[1,3,5])
>>> Option2 = make_option(option_type='put2call1')
>>> isinstance(Option1, BermudanOption)
True
>>> isinstance(Option2, AmericanOption)
True
>>> Option1.payoff([[1,2],[5,3], [3,5]], 3)
array([0., 2., 0.])
>>> Option2.payoff([[1,2],[5,3], [3,5]], 3)
array([0., 2., 0.])
>>> Option1.payoff([[1,2],[5,3], [3,5]], 4)
array([-inf, -inf, -inf])
>>> Option2.payoff([[1,2],[5,3], [3,5]], 4)
array([0., 2., 0.])