Package index • tidyactuarial

Financial Mathematics and Interest Rates

Accumulation, discounting, equivalent rates, equations of value, cash-flow valuation, and internal rates of return.

accumulation_factor(): Accumulation factor under conventional or time-varying interest
discount_factor(): Discount factor under conventional or time-varying interest
standardize_interest(): Standardize an interest rate to the annual effective rate i
interest_equivalents(): Equivalent interest rates in FM actuarial notation
present_value(): Present value of a single payment
future_value(): Future value of a single payment
pv_flow(): Present value of a general cash flow
fv_flow(): Future value of a general cash flow
solve_value(): Solve a scalar equation of value
irr_flow(): Internal rate of return for a cash flow
irr_flow_multi(): Multiple internal rates of return for a cash flow
plot_cash_flow(): Plot a cash-flow diagram

Annuities and Loans

Level and varying annuities, amortization schedules, and loan repayment.

a_angle(): Level annuity factor a-angle-n
s_angle(): Level annuity accumulation factor s-angle-n
annuity_arith(): Arithmetic annuity factor
annuity_geom(): Geometric annuity factor
amort_schedule(): Amortization schedule with optional prepayment adjustment
amort_schedule_general(): General amortization schedule with variable rates and payments
sinking_fund_schedule(): Sinking fund amortization schedule for a loan

Bonds, Duration, Convexity, and Immunization

Bond valuation, yield, book value, callable bonds, duration, convexity, portfolio measures, and immunization.

bond_cash_flows(): Cash flow structure of a level coupon bond
accrued_interest(): Accrued coupon interest and clean/dirty bond prices
bond_price(): Price of a level coupon bond from its yield
bond_ytm(): Yield to maturity of a level coupon bond
bond_book_value(): Book value of a level coupon bond at a coupon date
bond_callable_price(): Price of a callable bond at a target minimum yield
duration_cash_flow(): Duration of a general cash-flow stream
convexity_cash_flow(): Convexity of a general cash-flow stream
bond_duration(): Macaulay and modified duration of a level coupon bond under a flat yield
bond_convexity(): Discrete convexity of a level coupon bond under a flat yield
portfolio_duration(): Compute portfolio duration as a market-value-weighted average
portfolio_convexity(): Compute portfolio convexity as a market-value-weighted average
immunize_duration(): Duration-based immunization with multiple assets
immunize_duration_convexity(): Duration and convexity immunization with multiple assets
plot_immunization_gap(): Plot immunization performance under interest-rate shifts

Term Structure of Interest Rates

Spot discount factors, yield curves, and forward rates.

discount_factor_spot(): Spot discount factor
yield_curve(): Validate a yield curve and compute discount factors
forward_rate(): Compute an implied forward rate from a discrete spot curve
bootstrap_spot_curve(): Bootstrap a spot yield curve from instrument prices
forward_curve(): Construct a forward-rate curve from spot rates
par_rate(): Par coupon rate implied by a spot yield curve

Life Tables and Survival

Life-table construction, mortality laws, Kaplan-Meier estimation, survival probabilities, life expectancy, and commutation functions.

lifetable(): Build an annual life table (tidy tibble) from lx, qx, px, or mx
mortality_law_table(): Generate a tidy life table from a theoretical mortality law
km_lifetable(): Kaplan–Meier survival curve and a lifetable-style life table
plot_km(): Plot a Kaplan–Meier survival curve
t_px(): t-year survival probability from a life table
t_qx(): t-year death probability from a life table
t_Ex(): Pure endowment (discounted survival): \({}_tE_x\)
e_x(): Expected future lifetime from an annual life table
commutation_table(): Build an annual commutation table (discrete ages)

Single-Life Contingencies

Life annuities, life insurance, premiums, reserves, and contract workflows for a single life.

life_contract(): Create a life-contingency contract specification
add_insurance(): Add an insurance benefit specification to a life contract
add_premium_schedule(): Add a contingent premium-payment schedule to a life contract
annuity_x(): Actuarial present value of a life annuity
insurance_x(): Actuarial present value of a life insurance
insurance_variable_k(): Actuarial present value of a life insurance with variable k-thly benefits
apv_life_flow(): Actuarial present value of a payment stream under mortality
plot_contingent_cash_flow(): Plot discrete life-contingent cash flows
premium_x(): Net premium for single-life insurance by the equivalence principle
premium_gross(): Gross premium under a simple expense-loaded equivalence principle
reserve_x(): Benefit reserves for single-life insurance

Multiple-Life Contingencies

Joint-life, last-survivor, and multi-life survival and contingent values.

t_pxy(): Two-life survival probability for independent lives
e_xy(): Expected future lifetime for two independent lives
annuity_xy(): Actuarial present value of a two-life annuity
insurance_xy(): Actuarial present value of a two-life insurance
premium_xy(): Net premium for two-life insurance by the equivalence principle
reserve_xy(): Benefit reserves for two-life insurance
annuity_multi(): Actuarial present value of a multi-life annuity (up to 3 independent lives)

Multiple Decrements

Multiple-decrement tables, total-decrement life tables, cause-specific probabilities, and cause-specific insurance values.

md_table(): Multiple decrement table (annual, discrete ages)
lt_tau(): Total-decrement lifetable from a multiple decrement table: lt_tau
t_qxj(): t-year probability of decrement by cause j: t_qxj
insurance_xj() A_xj(): Cause-specific term/whole-life insurance APV under multiple decrements

Simulation and Actuarial Risk

Lifetime simulation, Monte Carlo valuation, loss distributions, reserves, multi-life simulation, and simulation summaries.

simulate_lifetime(): Simulate future lifetimes from a life table
simulate_lifetimes(): Simulate future lifetimes for multiple lives
simulate_annuity_x(): Monte Carlo simulation of a life annuity
simulate_insurance_x(): Monte Carlo simulation of a life insurance
mc_annuity(): Compute simulated present values for life annuities
mc_insurance(): Compute simulated present values for life insurance benefits
mc_premium(): Compute Monte Carlo net premiums for life contingencies
mc_reserve(): Compute Monte Carlo prospective reserves for life contingencies
mc_loss(): Compute Monte Carlo loss random variables for life contingencies
mc_multilife_status(): Compute multiple-life simulated status variables
summary_mc(): Summarise Monte Carlo simulation output

Collective Risk, Coverage, and Tail Measures

Frequency and severity models, insurance payments, aggregate losses, simulation, and risk measures.

frequency_spec(): Specify a claim frequency distribution
severity_spec(): Specify an individual claim severity distribution
empirical_frequency(): Specify an empirical claim frequency distribution
empirical_severity(): Specify an empirical claim severity distribution
distribution_moments(): Calculate moments of a frequency or severity distribution
collective_risk_spec(): Specify a collective risk model
coverage_spec(): Specify an insurance coverage contract
apply_coverage(): Apply an insurance contract to a loss severity specification
to_payment_basis(): Specify a change from per-loss to per-payment basis
discretize_severity(): Discretize a continuous claim severity distribution
distribution_convolution(): Specify a convolution of probability distributions
aggregate_moments(): Calculate moments of a collective aggregate loss
aggregate_distribution(): Compute the aggregate loss distribution
simulate_frequency(): Simulate claim counts from a frequency model
simulate_severity(): Simulate individual claim severities
simulate_aggregate(): Simulate a collective risk model
value_at_risk(): Value at Risk for actuarial losses
tail_value_at_risk(): Tail Value at Risk (Expected Shortfall)
stop_loss_premium(): Net stop-loss premium
print(<tidyact_aggregate_distribution>): Print an aggregate loss distribution
print(<tidyact_collective_risk_spec>): Print a collective risk model specification
print(<tidyact_convolution_spec>): Print a convolution specification
print(<tidyact_frequency_spec>): Print a frequency distribution specification
print(<tidyact_payment_spec>): Print a payment severity specification
print(<tidyact_severity_spec>): Print a severity distribution specification

Datasets

Reproducible datasets for financial and actuarial examples.

bonds_sample: Sample bond contracts for fixed-income examples
cash_flows_sample: Sample cash flows for interest theory examples
loans_sample: Sample loan contracts for amortization examples
mortality_colombia_tables: Colombian mortality tables
mortality_world_sample_2015_2023: World mortality sample panel, 2015–2023
mortality_world_sample_2023: World mortality sample, 2023
multiple_decrement_sample: Sample multiple decrement probabilities
soa08lt: SOA Illustrative Life Table