Actuarial present value engine. Discount expected cash flows with mortality, survival, and risk adjustment for insurance and benefit obligations, generalising IFRS 17 (fulfilment cash flows), IAS 19 (employee benefits), IFRS 2 (share-based payments), and IAS 37 (provisions). Use this for regulated IFRS/HKFRS obligations only; it does NOT do generic project or scenario probability weighting (use calculate_expected_value). Methods: ifrs17_gmm: cash_flows, discount_rate, risk_adjustment; ifrs17_paa: premiums, claims_cash, acquisition_cash_flows, coverage_periods; ifrs17_vfa: cash_flows, discount_rate, underlying_items_return, risk_adjustment; ias19_puc: projected_benefits, discount_rate, attribution_years; ias37_provision: outcomes, probabilities, discount_rate, periods. Supply exactly one method with its declared inputs (no defaults). An unknown method, a missing input, or an extra field returns an error envelope (code INVALID_ARGUMENT) instead of raising.

Convertible-bond engine. Value callable and puttable convertible or exchangeable bonds with credit risk using a Tsiveriotis-Fernandes lattice (equity discounted at the risk-free rate, debt at a credit spread), with conversion, issuer call, holder put, coupon schedule, and a straight-bond floor. Use this for convertible and exchangeable bonds; for a plain bond or rate curve use calculate_fixed_income, and for a standalone option or warrant use calculate_option. The lattice_tsf, lattice_intensity, finite_difference, lsmc and quantlib methods are alternative numerical schemes for the same valuation and take identical inputs (Tsiveriotis-Fernandes is the reference, lsmc is Monte Carlo, quantlib needs the optional engine); choose one. Methods: lattice_tsf/lattice_intensity/finite_difference/lsmc/quantlib: spot, face, coupon_rate, maturity, conversion_ratio, volatility, risk_free, credit_spread, call_schedule, put_schedule, rights_priority. Supply exactly one method with its declared inputs (no defaults). An unknown method, a missing input, or an extra field returns an error envelope (code INVALID_ARGUMENT) instead of raising.

Credit-risk engine (IFRS 9 / HKFRS 9). Compute 12-month, lifetime, and staged expected credit loss, PD/LGD/EAD, provision matrices, hazard rates, and CVA/DVA. Use this for impairment, fair-value credit adjustment, and loan-loss provisioning; for the credit component of a specific convertible bond use calculate_convertible_bond, and for liquidity, control or marketability discounts rather than credit loss use calculate_fair_value_adjustment. Methods: ecl_12m: ead, pd, lgd; ecl_lifetime: ead, pd_lifetime, lgd; ecl_staged: ead, pd_12m, pd_lifetime, lgd, stage; provision_matrix: receivables_ageing, loss_rates; pd_from_spread: credit_spread, recovery, tenor_years; cumulative_pd: annual_pd, years; hazard: hazard_rate, tenor_years; cva_dva: exposure_profile, pd, lgd, discount_rate. Supply exactly one method with its declared inputs (no defaults). An unknown method, a missing input, or an extra field returns an error envelope (code INVALID_ARGUMENT) instead of raising.

Discounted cash flow valuation engine. Choose a method and supply its exact inputs to value a business from projected free cash flows, dividends, residual income, or economic profit. Covers FCFF/FCFE DCF, NPV/IRR, terminal values, and multi-stage growth. Use this for going-concern cash-flow businesses; for asset-anchored or financial firms use calculate_residual, for peer-based pricing use calculate_market_multiple, and for pre-profit companies use calculate_loss_making_company. Methods: dcf/npv: cash_flows, discount_rate; annuity: payment, discount_rate, periods; growing_annuity: payment, discount_rate, growth_rate, periods; perpetuity: payment, discount_rate; terminal_gordon: final_cash_flow, discount_rate, perpetual_growth; terminal_multiple: final_cash_flow, exit_multiple; viu_pre_tax: cash_flows, pre_tax_discount_rate; rnpv: cash_flows, discount_rate, probabilities; lease_pv: lease_payments, incremental_borrowing_rate. Supply exactly one method with its declared inputs (no defaults). An unknown method, a missing input, or an extra field returns an error envelope (code INVALID_ARGUMENT) instead of raising.

Cost-of-capital engine. Compute WACC, cost of equity (CAPM), cost of debt, unlevered/relevered beta, and country or size premiums from an explicit capital structure and market inputs. Use this to derive the discount rate an income-approach valuation needs; it returns a rate, not a valuation, so feed the result to calculate_dcf, or to calculate_residual for IFRS-basis measurement. Methods: wacc: equity_weight, debt_weight, cost_equity, cost_debt, tax_rate; capm: risk_free, beta, market_return; startup_capm: risk_free, beta, market_risk_premium, size_premium, illiquidity_premium; build_up: risk_free, equity_risk_premium, size_premium, industry_premium, specific_premium; currency_adjusted: base_rate, currency_risk_premium, country_risk_premium; country_risk: sovereign_yield, us_risk_free; esg: base_rate, esg_risk_premium, esg_opportunity_discount; portfolio_beta: weights, betas; ibr: risk_free, credit_spread, tenor_years. Supply exactly one method with its declared inputs (no defaults). An unknown method, a missing input, or an extra field returns an error envelope (code INVALID_ARGUMENT) instead of raising.

Expected-value engine. Compute expected values over discrete, continuous, simulated, or tree-structured uncertainty, plus football-field ranges. Use this for generic probability weighting of scenarios, Monte-Carlo and decision trees; it does NOT perform IFRS/HKFRS measurement of provisions, insurance or employee-benefit obligations (use calculate_actuarial_pv), and it does not price path-dependent payoffs (use calculate_structured_product). Methods: discrete: outcomes, probabilities; continuous: distribution, mean, std, lower, upper; scenario: scenarios; monte_carlo: iterations, distributions, base_params, seed; decision_tree: tree; football_field: estimates. Supply exactly one method with its declared inputs (no defaults). An unknown method, a missing input, or an extra field returns an error envelope (code INVALID_ARGUMENT) instead of raising.

Fair-value-adjustment engine (IFRS 13). Compute exit-price adjustments including credit, liquidity, control and marketability discounts, blockage, and the fair-value hierarchy level. Use this to move from an indicated value to the fair value recognised in the accounts; for liquidity/marketability inputs of a listed instrument prefer calculate_market_multiple, and for expected credit loss use calculate_credit_loss. Methods: dlom: base_value, restricted_period, volatility, risk_free; dloc: base_value, transaction_cost_pct; control_premium: base_value, control_premium_pct; minority_discount: base_value, minority_discount_pct; highest_best_use: base_value, alternative_use_values; hierarchy_level: inputs. Supply exactly one method with its declared inputs (no defaults). An unknown method, a missing input, or an extra field returns an error envelope (code INVALID_ARGUMENT) instead of raising.

Fixed-income engine. Price plain coupon bonds, solve for yield to maturity, measure interest-rate sensitivity via Macaulay and modified duration and convexity, and build a HIBOR/HKD-style term structure: bootstrap a zero curve from par rates, infer forward rates, and discount cash flows on the curve. Use this for vanilla bonds, rate risk and discount curves; for convertibles use calculate_convertible_bond and for structured payoffs use calculate_structured_product. Methods: bond_price/duration/convexity: face, coupon_rate, years, ytm, frequency; bond_yield: face, coupon_rate, years, price, frequency; matrix_pricing: target_tenor, benchmark_tenors, benchmark_yields; discount_factor: rate, years, frequency; zero_curve: par_rates, tenors, frequency; forward_rate: zero_rates, tenors, t1, t2; pv_curve: cash_flows, times, zero_rates, tenors. Supply exactly one method with its declared inputs (no defaults). An unknown method, a missing input, or an extra field returns an error envelope (code INVALID_ARGUMENT) instead of raising.

Loss-making-company engine. Value currently unprofitable companies with margin-ramp DCF, revenue multiples, Merton structural equity, the VC method, distressed waterfalls, bank residual income, and SPAC deals; every method returns a central value plus a dispersion (sigma, percentiles, long-tail). Use this when earnings-based multiples break down; for standalone probability weighting of arbitrary scenarios use calculate_expected_value, and for a single going-concern DCF use calculate_dcf. Methods: margin_ramp_dcf: revenue, growth_rate, start_margin, target_margin, ramp_years, discount_rate, years, shares_outstanding, net_debt, range_method; revenue_multiple: revenue, ev_revenue_multiple, net_debt, shares_outstanding, range_method; merton_equity: firm_value, firm_volatility, debt, risk_free, maturity, range_method; vc_method: terminal_value, target_return, investment, shares_outstanding, range_method; distressed_waterfall: enterprise_value, claims, range_method; bank_residual_income: book_value, net_income, cost_equity, growth_rate, range_method; spac_deal: trust_cash, shares_outstanding, redemption_price, range_method. Supply exactly one method with its declared inputs (no defaults). An unknown method, a missing input, or an extra field returns an error envelope (code INVALID_ARGUMENT) instead of raising.

Market-multiple engine. Apply peer multiples (P/E, P/B, EV/EBITDA, EV/Sales, PEG and more) or derive implied multiples to price a company on a comparable basis. Use this for market-approach pricing where peers exist; it does peer multiples only — for intrinsic cash-flow value use calculate_dcf, and for residual-income or IFRS-basis measurement use calculate_residual. Methods: ev_revenue: revenue, ev_revenue_multiple; ev_ebitda: ebitda, ev_ebitda_multiple; ev_arr: arr, ev_arr_multiple; ev_gmv: gmv, ev_gmv_multiple; pe: eps, pe_multiple; pb: book_value_per_share, pb_multiple; ps: sales_per_share, ps_multiple; cap_rate: net_operating_income, cap_rate; regression: intercept, growth_rate, growth_coefficient, market_maturity, maturity_coefficient; royalty_cap: revenue, royalty_rate, discount_rate; ddm: dividend_per_share, cost_equity, growth_rate. Supply exactly one method with its declared inputs (no defaults). An unknown method, a missing input, or an extra field returns an error envelope (code INVALID_ARGUMENT) instead of raising.

Option-pricing engine. Price European and American options and warrants (Black-Scholes, Black-76, CRR binomial, Garman-Kohlhagen FX, digital, range, share-based) and their greeks. Use this for a single contingent claim or warrant on one underlying; it does NOT price listed structured payoffs such as CBBCs, inline/derivative warrants or autocallables (use calculate_structured_product). Methods: black_scholes: spot, strike, maturity, risk_free, volatility, option_type; black76: forward, strike, maturity, risk_free, volatility, option_type; binomial_american: spot, strike, maturity, risk_free, volatility, option_type, steps; garman_kohlhagen: spot, strike, maturity, domestic_rate, foreign_rate, volatility, option_type; barrier_first_passage: spot, strike, maturity, risk_free, volatility, option_type, barrier, barrier_type; asian_average: spot, strike, maturity, risk_free, volatility, option_type, average_type; digital: spot, strike, maturity, risk_free, volatility, cash_payout; range: spot, lower_strike, upper_strike, maturity, risk_free, volatility, payout; share_based: share_price, exercise_price, expected_life, volatility, risk_free, dividend_yield. Supply exactly one method with its declared inputs (no defaults). An unknown method, a missing input, or an extra field returns an error envelope (code INVALID_ARGUMENT) instead of raising.

IFRS/HKFRS measurement engine. Compute goodwill and purchase-price allocation, impairment (IAS 36), inventory net realisable value, held-for-sale, debt waterfalls, cap tables, sum-of-the-parts and SPAC redemption; residual income and justified price-to-book; and non-financial asset fair value: investment property (IAS 40 / HKAS 40), PP&E revaluation via depreciated replacement cost (IAS 16) and biological assets at fair value less costs to sell (IAS 41). Use this for accounting-basis measurement of assets and equity; for going-concern cash flow use calculate_dcf and for peer multiples use calculate_market_multiple. Methods: goodwill: purchase_price, fair_value_net_identifiable_assets; ppa: purchase_price, tangible_assets_fv, identified_intangibles_fv; impairment_fvlcd: carrying_value, fair_value_less_costs_to_dispose; impairment_viu: carrying_value, value_in_use; inventory_nrv: carrying_value, net_realisable_value; held_for_sale: carrying_value, fair_value_less_costs_to_sell; debt_waterfall/cap_table: enterprise_value, claims; sotp: segments, net_debt, holding_discount; spac_redemption: trust_cash, shares_outstanding, redemption_price; investment_property: noi, cap_rate; ppe_revaluation: replacement_cost, accumulated_depreciation; biological_asset: expected_price, quantity, costs_to_sell; residual_income: book_value, net_income, cost_equity; justified_pb: roe, cost_equity, growth_rate; relief_from_royalty: revenue, royalty_rate, discount_rate, periods; mpeem: cash_flows, contributory_charges, discount_rate; with_without: with_cash_flows, without_cash_flows, discount_rate; recoverable_amount: fair_value_less_costs_to_dispose, value_in_use; liability_fulfilment: fulfilment_costs, mark_up, discount_rate; inventory_residual: selling_price, costs_to_complete, profit_allowance; development_residual: gross_development_value, development_costs, developer_profit. Supply exactly one method with its declared inputs (no defaults). An unknown method, a missing input, or an extra field returns an error envelope (code INVALID_ARGUMENT) instead of raising.

Sector-metric engine. Compute the metrics that anchor valuation in specific industries: SaaS (ARR, NRR, magic number, Rule of 40), marketplaces (take rate, GMV multiple), lending (LTV/CAC), and crypto (NVT, Metcalfe). It returns operating metrics, not a valuation; use them as inputs to calculate_market_multiple or calculate_dcf. Methods: ltv: arpu, gross_margin, churn_rate; cac: sales_marketing_expense, new_customers; arr: subscription_values; nrr: starting_revenue, ending_revenue, expansion_revenue; magic_number: net_new_arr, sales_marketing_expense_prior; rule_of_40: growth_rate, profit_margin; take_rate: revenue, gmv; gmv_multiple: gmv, ev_gmv_multiple; retention: retained_customers, starting_customers; trl: market_size, market_share, margin, exit_multiple, trl_discount; break_even: fixed_costs, asp, variable_cost; gross_margin: asp, variable_cost; token: transaction_volume, price_per_tx, velocity, supply; nvt: market_cap, transaction_volume; metcalfe: n, coefficient. Supply exactly one method with its declared inputs (no defaults). An unknown method, a missing input, or an extra field returns an error envelope (code INVALID_ARGUMENT) instead of raising.

Structured-product engine. Value HKEX-listed and OTC structures: CBBCs, derivative and inline warrants, equity-linked notes and investments, autocallables, accumulators and decumulators, credit-linked notes, TRS, and CFDs. Use this for equity-linked and credit-linked payoff structures; for a plain option or warrant use calculate_option, for a convertible or exchangeable bond use calculate_convertible_bond, and for a vanilla bond or term structure use calculate_fixed_income. Methods: cbbc: notional, spot, strike, barrier, barrier_type, maturity, risk_free, volatility, option_type; cbbc_residual: notional, spot, call_price, entitlement, barrier, barrier_type, maturity, risk_free, volatility, option_type; derivative_warrant: notional, spot, strike, maturity, risk_free, volatility, average_type, option_type; inline_warrant: notional, spot, lower_strike, upper_strike, maturity, risk_free, volatility, payout; inline_warrant_avg: notional, spot, lower_strike, upper_strike, maturity, risk_free, volatility, payout, fixing_days; eli/eln: notional, spot, strike, maturity, risk_free, volatility, coupon_rate; autocallable: notional, spot, knock_out_level, observation_dates, coupon_rate_structured, maturity, risk_free, volatility; credit_linked_note: notional, credit_spread, recovery, maturity, risk_free, coupon_rate_structured; accumulator/decumulator: notional, spot, strike, knock_out_level, observation_dates, risk_free, volatility; trs: notional, spot, maturity, risk_free, dividend_yield; cfd: notional, spot, strike, maturity, risk_free. Supply exactly one method with its declared inputs (no defaults). An unknown method, a missing input, or an extra field returns an error envelope (code INVALID_ARGUMENT) instead of raising.