Tutorial
To start with import the package.
Cashflow Objects and Valuation
Payment Plans
>>> 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]
CashFlowList Objects
Putting all together and feeding the plan into a CashFlowList and the list of outstanding into a `CashflowList gives the legs of a loan.
>>> from businessdate import BusinessDate, BusinessSchedule
>>> from dcf.plans import amortize, outstanding
>>> from dcf import CashFlowList
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 dcf.payoffs.CashFlowList.
>>> principal = CashFlowList.from_fixed_cashflows([start_date], [notional])
>>> print(principal)
pay date cashflow
---------- ----------
20201031 1_000.0
>>> redemption = CashFlowList.from_fixed_cashflows(payment_dates, plan)
>>> print(redemption)
pay date cashflow
---------- ----------
20210131 125.0
20210430 125.0
20210731 125.0
20211031 125.0
20220131 125.0
20220430 125.0
20220731 125.0
20221031 125.0
>>> interest = CashFlowList.from_rate_cashflows(payment_dates, out, fixed_rate=interest_rate)
>>> print(interest)
pay date cashflow notional is rec fixed rate start date end date year fraction
---------- ---------- ---------- -------- ------------ ------------ ---------- ---------------
20210131 2.518892 1_000.0 True 0.01 20201031 20210131 0.251889
20210430 2.13216 875.0 True 0.01 20210131 20210430 0.243675
20210731 1.889169 750.0 True 0.01 20210430 20210731 0.251889
20211031 1.574307 625.0 True 0.01 20210731 20211031 0.251889
20220131 1.259446 500.0 True 0.01 20211031 20220131 0.251889
20220430 0.913783 375.0 True 0.01 20220131 20220430 0.243675
20220731 0.629723 250.0 True 0.01 20220430 20220731 0.251889
20221031 0.314861 125.0 True 0.01 20220731 20221031 0.251889
Valuation
Add those legs to dcf.payoffs.CashFlowList provides a smart container for valuation.
>>> import dcf
>>> dcf.pricer.INCLUDE_VALUATION_DATE = True
>>> from yieldcurves import YieldCurve, DateCurve
>>> from dcf import pv
>>> loan = -principal + redemption + interest
>>> yield_curve = YieldCurve.from_interpolation([0.0, 5.0], [0.01, 0.005])
>>> curve = DateCurve(yield_curve, origin=today)
>>> pv(cashflow_list=loan, discount_curve=curve.df, valuation_date=today)
1.562873826...
>>> dcf.pricer.INCLUDE_VALUATION_DATE = False
>>> pv(cashflow_list=loan, discount_curve=curve.df, valuation_date=today)
1001.562873...
>>> print(loan)
pay date cashflow notional is rec fixed rate start date end date year fraction
---------- ------------- ---------- -------- ------------ ------------ ---------- ---------------
20201031 -1_000.0
20210131 125.0
20210430 125.0
20210731 125.0
20211031 125.0
20220131 125.0
20220430 125.0
20220731 125.0
20221031 125.0
20210131 2.518892 1_000.0 True 0.01 20201031 20210131 0.251889
20210430 2.13216 875.0 True 0.01 20210131 20210430 0.243675
20210731 1.889169 750.0 True 0.01 20210430 20210731 0.251889
20211031 1.574307 625.0 True 0.01 20210731 20211031 0.251889
20220131 1.259446 500.0 True 0.01 20211031 20220131 0.251889
20220430 0.913783 375.0 True 0.01 20220131 20220430 0.243675
20220731 0.629723 250.0 True 0.01 20220430 20220731 0.251889
20221031 0.314861 125.0 True 0.01 20220731 20221031 0.251889