A Python library for generating discounted cashflows (dcf). Typical banking business methods are provided like interpolation, compounding, discounting and fx.

>>> from dcf import ZeroRateCurve

>>> time_grid = [0, 2] >>> rate_grid = [.03, .05]

>>> ZeroRateCurve(time_grid, rate_grid).get_zero_rate(0, 1) 0.04

>>> ZeroRateCurve(time_grid, rate_grid).get_discount_factor(0, 1) 0.9607894391523232

Or use datetime

>>> from datetime import date

>>> start = date(2013,1,1) >>> mid = date(2014,1,1) >>> end = date(2015,1,1)

>>> ZeroRateCurve([start, end], [.03, .05]).get_zero_rate(start, mid) 0.04

>>> ZeroRateCurve([start, end], [.03, .05]).get_discount_factor(start, mid) 0.9608157444936446

The framework works fine with native datetime but we recommend businessdate package for more convenient functionality to roll out date schedules.

>>> from businessdate import BusinessDate, BusinessSchedule

>>> today = BusinessDate(20201031) >>> schedule = BusinessSchedule(today, today + "8q", step="1q") >>> schedule [BusinessDate(20201031), BusinessDate(20210131), BusinessDate(20210430), BusinessDate(20210731), BusinessDate(20211031), BusinessDate(20220131), BusinessDate(20220430), BusinessDate(20220731), BusinessDate(20221031)]

To build payment plans for, e.g. annuity loans, pick a plan function and generate an redemption amount list for paying back the loan notional amount.

>>> from dcf.plans import annuity, outstanding

>>> number_of_payments = 8 >>> interest_rate = 0.02 >>> notional = 1000.

>>> plan = annuity(number_of_payments, amount=notional, fixed_rate=interest_rate) >>> plan [116.50979913376267, 118.83999511643792, 121.21679501876667, 123.64113091914203, 126.11395353752485, 128.63623260827535, 131.20895726044085, 133.83313640564967]

>>> sum(plan) 1000.0

>>> out = outstanding(plan, amount=notional) >>> out [1000.0, 883.4902008662373, 764.6502057497994, 643.4334107310327, 519.7922798118907, 393.6783262743659, 265.0420936660905, 133.83313640564967]

>>> compound = [o * interest_rate + p for o, p in zip(out, plan)] >>> compound [136.50979913376267, 136.50979913376267, 136.50979913376267, 136.50979913376267, 136.50979913376267, 136.50979913376267, 136.50979913376267, 136.50979913376267]

Putting all together and feeding the plan into a FixedCashFlowList and the list of outstanding into a RateCashflowList gives the legs of a loan.

>>> from businessdate import BusinessDate, BusinessSchedule >>> from dcf import FixedCashFlowList, RateCashFlowList >>> from dcf.plans import amortize, outstanding

Again, build a date schedule.

>>> today = BusinessDate(20201031) >>> schedule = BusinessSchedule(today, today + "8q", step="1q") >>> start_date, payment_dates = schedule[0], schedule[1:]

Fixing the properties of the product and rolling out the payment plan and list of notional outstanding.

>>> number_of_payments = 8 >>> interest_rate = 0.01 >>> notional = 1000.

>>> plan = amortize(number_of_payments, amount=notional) >>> out = outstanding(plan, amount=notional)

Finally, create for each leg a CashFlowList.

>>> principal = FixedCashFlowList([start_date], [-notional], origin=start_date) >>> print(principal) FixedCashFlowList([BusinessDate(20201031) ... BusinessDate(20201031)], [-1000.0 ... -1000.0], origin=BusinessDate(20201031))

>>> redemption = FixedCashFlowList(payment_dates, plan, origin=start_date) >>> print(redemption) FixedCashFlowList([BusinessDate(20210131) ... BusinessDate(20221031)], [125.0 ... 125.0], origin=BusinessDate(20201031))

>>> interest = RateCashFlowList(payment_dates, out, origin=start_date, fixed_rate=interest_rate) >>> print(interest) RateCashFlowList([BusinessDate(20210131) ... BusinessDate(20221031)], [1000.0 ... 125.0], origin=BusinessDate(20201031))

Add those legs to CashFlowLegList provides a smart container for valuation (get_present_value()).

>>> from dcf import CashFlowLegList, ZeroRateCurve, get_present_value

>>> loan = CashFlowLegList([principal, redemption, interest]) >>> curve = ZeroRateCurve([today, today + '2y'], [-.005, .01])

>>> get_present_value(cashflow_list=loan, discount_curve=curve, valuation_date=today) 4.935421637918839

Moreover, variable interest derived from float rates as given by a forward rate curve, e.g. a CashRateCurve, are possible, too.

>>> from dcf import CashRateCurve, RateCashFlowList >>> from tabulate import tabulate

>>> fwd = CashRateCurve([today, today + '2y'], [-.005, .007]) >>> spread = .001 >>> float_interest = RateCashFlowList(payment_dates, out, origin=start_date, fixed_rate=spread, forward_curve=fwd, pay_offset='2b', fixing_offset='2b')

>>> print(tabulate(float_interest.table, headers='firstrow'))

cashflow pay date notional start date end date year fraction fixed rate forward rate fixing date tenor

---------- ---------- ---------- ------------ ---------- --------------- ------------ -------------- ------------- ------- -0.996578 20210131 1000 20201029 20210128 0.249144 0.001 -0.005 20201027 3M

-0.554077 20210430 875 20210128 20210428 0.246407 0.001 -0.00356986 20210126 3M -0.205991 20210731 750 20210428 20210729 0.251882 0.001 -0.00209041 20210426 3M 0.065699 20211031 625 20210729 20211028 0.249144 0.001 -0.000578082 20210727 3M 0.238906 20220131 500 20211028 20220127 0.249144 0.001 0.000917808 20211026 3M 0.318939 20220430 375 20220127 20220428 0.249144 0.001 0.0024137 20220125 3M 0.305799 20220731 250 20220428 20220728 0.249144 0.001 0.00390959 20220426 3M 0.199486 20221031 125 20220728 20221027 0.249144 0.001 0.00540548 20220726 3M

>>> get_present_value(cashflow_list=float_interest, discount_curve=curve, valuation_date=today) -0.641528888054065

The latest stable version can always be installed or updated via pip:

$ pip install dcf

The latest development version can be installed directly from GitHub:

$ pip install --upgrade git+https://github.com/sonntagsgesicht/dcf.git

Issues and Pull Requests are always welcome.

Code and documentation are available according to the Apache Software License (see LICENSE).