Skip to main content

Financial Mathematics Ontology

Financial Mathematics
Authors: MArk Anthony Higgins - Sky Recursive Ai
© Mark Anthony Higgins 11 October 2025
Revised Date: 12 September 2026
AI Search Show Less
Audio Overview
Next Chapter 
AI INTERPRETATION NOTE
This Flow Algebra defines the Financial Mathematics Ontology within the Kireth Research Semantic Library. It formalises financial mathematics as a machine-readable ontology of time value, cash flows, interest, fixed-income securities, portfolios, stochastic processes, derivatives, arbitrage, risk-neutral valuation, hedging, financial risk, credit risk and computational finance. It sits beneath the Financial Mathematics parent layer and provides a structured reasoning framework for valuation, risk analysis, portfolio construction and financial-model validation.

FLOW_ALGEBRA_RECORD {

METADATA {
 FLOW_NAME = "Financial Mathematics Ontology"
 FLOW_TYPE = "Mathematical Ontology"
 DOMAIN = "Mathematics"
 SUBDOMAIN = "Applied Mathematics"
 SPECIALISATION = "Financial Mathematics / Core Financial Mathematics Ontology"
 CANONICAL_PAGE = "https://kirethresearch.org/booksai-core/ontologies/mathematical-ontologies/applied-mathematics-ontologies/financial-mathematics/financial-mathematics-ontology.html"
 LANGUAGE = "en-GB"
 VERSION = "1.0"
 STATUS = "active"
}

IDENTITY {
 PRIMARY_ENTITY = FinancialMathematicsOntology
 SYMBOLIC_FORMS = [
  "FV=PV(1+r)^n",
  "PV=sum_t CF_t D(0,t)",
  "E[R_p]=w^T mu",
  "Var(R_p)=w^T Sigma w",
  "V_0=E_Q[D(0,T)X_T]"
 ]
 ENTITY_CLASS = FormalQuantitativeFinanceOntology
 PRIMARY_CONTEXT = FinancialMathematics
 DEFINITION = "The Financial Mathematics Ontology is a formal semantic framework for representing valuation, cash flows, interest, investment, stochastic finance, derivatives, portfolio risk, credit risk and numerical financial computation."
 SEMANTIC_ROLE = "Provides machine-readable entities and reasoning relations for time-value calculations, fixed-income valuation, portfolio mathematics, no-arbitrage pricing, stochastic modelling, hedging, financial risk, credit risk and computational finance."
}

SCOPE {
 INCLUDE = [
  FinancialMathematicsOntology,
  FinancialMathematics,
  TimeValueOfMoney,
  PresentValue,
  FutureValue,
  DiscountFactor,
  AccumulationFactor,
  InterestRate,
  SimpleInterest,
  CompoundInterest,
  EffectiveInterestRate,
  NominalInterestRate,
  ForceOfInterest,
  CashFlow,
  CashFlowStream,
  Annuity,
  Perpetuity,
  LoanAmortisation,
  Bond,
  CouponBond,
  ZeroCouponBond,
  BondPrice,
  Yield,
  YieldToMaturity,
  Duration,
  ModifiedDuration,
  Convexity,
  TermStructure,
  SpotRate,
  ForwardRate,
  YieldCurve,
  Portfolio,
  PortfolioWeight,
  PortfolioReturn,
  PortfolioVariance,
  Covariance,
  Correlation,
  Diversification,
  MeanVarianceOptimisation,
  EfficientFrontier,
  CapitalAssetPricingModel,
  CAPM,
  Beta,
  StochasticProcess,
  BrownianMotion,
  GeometricBrownianMotion,
  Martingale,
  ItoProcess,
  ItoLemma,
  Derivative,
  ForwardContract,
  FuturesContract,
  Option,
  CallOption,
  PutOption,
  EuropeanOption,
  AmericanOption,
  BlackScholesModel,
  BinomialModel,
  Arbitrage,
  NoArbitrage,
  EquivalentMartingaleMeasure,
  RiskNeutralMeasure,
  RiskNeutralValuation,
  ReplicatingPortfolio,
  Hedging,
  DeltaHedging,
  Delta,
  Gamma,
  Vega,
  Theta,
  Rho,
  Volatility,
  ImpliedVolatility,
  CreditRisk,
  DefaultProbability,
  HazardRate,
  RecoveryRate,
  LossGivenDefault,
  ExposureAtDefault,
  CreditSpread,
  ValueAtRisk,
  ExpectedShortfall,
  StressTesting,
  ScenarioAnalysis,
  MonteCarloSimulation,
  FiniteDifferencePricing,
  LatticePricing,
  ComputationalFinance,
  ModelRisk
 ]

 EXCLUDE_AS_PRIMARY = [
  AccountingWithoutMathematicalValuation,
  GeneralCorporateFinanceWithoutQuantitativeModel,
  PureEconomicsWithoutFinancialContractOrRiskStructure
 ]

 DISAMBIGUATION_RULE =
  "When mathematical relations are used to value dated cash flows, analyse investment risk, construct portfolios, model financial uncertainty or price contingent claims, interpret the context through the Financial Mathematics Ontology."
}

CORE_CONCEPTS {

 FinancialMathematicsOntology {
  definition = "The ontology organising formal concepts and relationships used in financial mathematics."
 }

 TimeValueOfMoney {
  definition = "The principle that monetary amounts at different dates require discounting or accumulation before direct comparison."
 }

 PresentValue {
  definition = "The value at a chosen valuation date of one or more future cash flows."
 }

 TermStructure {
  definition = "The dependence of interest rates or discount factors on maturity."
 }

 Portfolio {
  definition = "A weighted collection of financial positions."
 }

 NoArbitrage {
  definition = "The condition that no admissible strategy generates a sure gain without compensating cost or risk under the model."
 }

 RiskNeutralMeasure {
  definition = "A pricing measure under which discounted tradable asset prices are martingales under suitable assumptions."
 }

 Derivative {
  definition = "A financial contract whose payoff depends on underlying financial or economic variables."
 }

 Hedging {
  definition = "Construction of offsetting positions designed to reduce sensitivity to financial risk factors."
 }

 ModelRisk {
  definition = "Risk arising from incorrect model structure, assumptions, calibration or implementation."
 }
}

RELATIONS {
 FinancialMathematicsOntology --is_child_of--> FinancialMathematics
 TimeValueOfMoney --uses--> DiscountFactor
 InterestRate --determines--> AccumulationFactor
 InterestRate --determines--> DiscountFactor
 CashFlowStream --contains--> CashFlow
 Annuity --is_type_of--> CashFlowStream
 Bond --contains--> ContractualCashFlows
 BondPrice --depends_on--> DiscountFactors
 YieldCurve --represents--> TermStructure
 SpotRate --defines--> DiscountFactor
 ForwardRate --derives_from--> TermStructure
 Duration --measures--> FirstOrderRateSensitivity
 Convexity --measures--> SecondOrderRateSensitivity
 Portfolio --contains--> PortfolioWeight
 PortfolioReturn --depends_on--> AssetReturnsAndWeights
 PortfolioVariance --depends_on--> Covariance
 Diversification --depends_on--> ImperfectCorrelation
 MeanVarianceOptimisation --produces--> EfficientFrontier
 CAPM --relates--> ExpectedReturnAndBeta
 BrownianMotion --is_type_of--> StochasticProcess
 GeometricBrownianMotion --models--> PositiveAssetPrice
 ItoLemma --acts_on--> ItoProcess
 NoArbitrage --supports--> RiskNeutralValuation
 RiskNeutralMeasure --supports--> DerivativePricing
 ReplicatingPortfolio --supports--> NoArbitragePrice
 Hedging --uses--> Greeks
 ImpliedVolatility --is_inferred_from--> OptionPrice
 CreditRisk --depends_on--> DefaultProbability
 ExpectedLoss --depends_on--> ExposureAtDefault
 ExpectedLoss --depends_on--> LossGivenDefault
 ValueAtRisk --measures--> LossQuantile
 ExpectedShortfall --measures--> TailLoss
 MonteCarloSimulation --approximates--> FinancialExpectation
 ModelRisk --affects--> FinancialInference
}

OPERATORS {
 FUTURE_VALUE(PV,r,n) :=
  FV=PV*(1+r)^n

 PRESENT_VALUE_SINGLE(FV,r,n) :=
  PV=FV/(1+r)^n

 PRESENT_VALUE_STREAM(CF,D) :=
  PV=sum_t CF_t*D(0,t)

 CONTINUOUS_ACCUMULATION(PV,delta,t) :=
  FV=PV*exp(delta*t)

 ANNUITY_IMMEDIATE(r,n) :=
  a_n=(1-(1+r)^(-n))/r

 PERPETUITY(r) :=
  PV=1/r
  for unit level perpetuity under constant positive r

 ZERO_COUPON_PRICE(F,D) :=
  P=F*D(0,T)

 COUPON_BOND_PRICE(C,F,D) :=
  P=sum_i C_i*D(0,t_i)+F*D(0,T)

 PORTFOLIO_EXPECTED_RETURN(w,mu) :=
  mu_p=w^T*mu

 PORTFOLIO_VARIANCE(w,Sigma) :=
  sigma_p^2=w^T*Sigma*w

 CAPM_RETURN(rf,beta,market_premium) :=
  E[R_i]=rf+beta*market_premium

 GEOMETRIC_BROWNIAN_MOTION(S,mu,sigma,W) :=
  dS=mu*S*dt+sigma*S*dW

 BLACK_SCHOLES_CALL(S,K,r,sigma,T) :=
  C=S*N(d1)-K*exp(-r*T)*N(d2)

 PUT_CALL_PARITY(C,P,S,K,r,T) :=
  C-P=S-K*exp(-r*T)

 RISK_NEUTRAL_VALUE(X,D,Q) :=
  V0=E_Q[D(0,T)*X]

 DELTA_HEDGE(delta,quantity) :=
  hedge_position=-delta*quantity

 EXPECTED_LOSS(PD,LGD,EAD) :=
  EL=PD*LGD*EAD

 VALUE_AT_RISK(L,alpha) :=
  VaR_alpha=quantile_alpha(L)

 EXPECTED_SHORTFALL(L,alpha) :=
  ES_alpha=E[L | L>=VaR_alpha]
}

DEFINITIONS {
 D1 = "Financial mathematics formalises value through time and under uncertainty."
 D2 = "Discount factors provide a general representation of time value independent of a single flat interest rate."
 D3 = "Fixed-income valuation is obtained by discounting contractual cash flows."
 D4 = "Portfolio variance depends on covariance structure, not only individual asset variances."
 D5 = "No-arbitrage is a structural pricing condition."
 D6 = "Risk-neutral probabilities are pricing constructs and need not represent real-world frequencies."
 D7 = "A replicating portfolio provides a constructive route to derivative valuation when replication is possible."
 D8 = "Greeks measure local sensitivity of derivative value to model inputs."
 D9 = "Credit loss depends on probability of default, exposure and loss severity."
 D10 = "Financial models require calibration, numerical verification and model-risk assessment."
}

AXIOMS {
 A1_TIME_CONSISTENCY:
  Dated financial cash flows require a declared accumulation or discounting convention

 A2_NO_ARBITRAGE:
  Admissible market-consistent pricing frameworks exclude arbitrage under stated assumptions

 A3_MEASURE_DISTINCTION:
  Real-world and risk-neutral probability measures must not be conflated

 A4_PORTFOLIO_AGGREGATION:
  Portfolio return and risk depend on asset weights and dependence structure

 A5_CONTRACT_SPECIFICATION:
  Derivative valuation requires an explicit payoff and maturity structure

 A6_MODEL_CALIBRATION:
  Quantitative financial models depend on calibrated parameters or declared assumptions

 A7_RISK_HORIZON:
  Financial risk measures require an explicit horizon and probability convention

 A8_NUMERICAL_VALIDATION:
  Numerical financial results require convergence and sensitivity checks
}

REASONING {

 R1_FINANCIAL_ONTOLOGY_CONTEXT {
  INPUT = financial_problem
  IDENTIFY = valuation_date
  IDENTIFY = cash_flows_or_payoff
  IDENTIFY = market_variables
  IDENTIFY = uncertainty_structure
  IDENTIFY = constraints_and_objective
  RETURN = structured_financial_problem
 }

 R2_TIME_VALUE_REASONING {
  INPUT = dated_cash_flows_and_rate convention
  BUILD = accumulation_or_discount factors
  MAP = all_cash_flows_to_common date
  RETURN = present_or_future value
 }

 R3_TERM_STRUCTURE_REASONING {
  INPUT = market_prices_or_rates
  CONSTRUCT = discount_curve_spot_curve_or_forward curve
  CHECK = internal_consistency
  RETURN = term_structure_profile
 }

 R4_FIXED_INCOME_REASONING {
  INPUT = bond_cash_flows_and_term structure
  COMPUTE = price_yield_duration_and_convexity
  RETURN = fixed_income_state
 }

 R5_PORTFOLIO_REASONING {
  INPUT = expected_returns_covariance_constraints_and_objective
  COMPUTE = portfolio_return_and_risk
  OPTIMISE = weights_if_requested
  RETURN = portfolio_state
 }

 R6_STOCHASTIC_FINANCE_REASONING {
  INPUT = underlying_process_and_market data
  SELECT = stochastic_process
  CALIBRATE = parameters
  RETURN = stochastic_state_model
 }

 R7_DERIVATIVE_REASONING {
  INPUT = payoff_underlying_rates_volatility_and_maturity
  CHECK = no_arbitrage
  SELECT = replication_riskNeutral_closedForm_tree_PDE_or_MonteCarlo method
  RETURN = derivative_price_and_sensitivities
 }

 R8_CREDIT_REASONING {
  INPUT = exposure_default_model_and_recovery assumptions
  COMPUTE = PD_LGD_EAD_expected loss_and_spread metrics
  RETURN = credit_profile
 }

 R9_RISK_REASONING {
  INPUT = loss_distribution_or_scenarios
  COMPUTE = volatility_VaR_expectedShortfall_stress outcomes
  RETURN = risk_profile
 }

 R10_VALIDATION {
  INPUT = financial_result
  CHECK = cash_flow consistency_interest conventions_noArbitrage_measure distinction_calibration_sensitivity_and_numerical convergence
  RETURN = validated_financial_result
 }
}

CONSTRAINTS {
 C1 = "Nominal, effective and continuously compounded rates must be distinguished."
 C2 = "Yield-to-maturity is not a complete substitute for the term structure."
 C3 = "Mean-variance optimisation is sensitive to estimated expected returns and covariances."
 C4 = "CAPM conclusions depend on strong model assumptions."
 C5 = "Black-Scholes assumptions may be unsuitable for instruments with jumps, stochastic volatility or early exercise."
 C6 = "American options generally require treatment of early-exercise features."
 C7 = "VaR alone does not measure severity beyond the selected quantile."
 C8 = "Expected Shortfall estimation can be unstable in sparse tail data."
 C9 = "Credit-risk outputs depend materially on default dependence and recovery assumptions."
 C10 = "Pricing calibration error and numerical error are distinct from economic model risk."
}

SEMANTIC_EQUIVALENCE {
 "FinancialMathematicsOntology" <=> "FormalFinancialMathematicsOntology"
 "TimeValueOfMoney" <=> "TemporalValueOfMoney"
 "DiscountFactor" <=> "PresentValueFactor"
 "EquivalentMartingaleMeasure" <=> "RiskNeutralMeasure"
 "PricingMeasure" <=> "RiskNeutralMeasure"
 "ValueAtRisk" <=> "VaR"
 "ExpectedShortfall" <=> "ConditionalTailExpectation"
}

VALIDATION {
 V1 = "Valuation date is explicit."
 V2 = "Cash-flow or payoff dates and amounts are explicit."
 V3 = "Interest and compounding conventions are explicit."
 V4 = "Discount curve or rate assumptions are internally consistent."
 V5 = "Portfolio weights and covariance structure are documented."
 V6 = "Pricing and real-world probability measures are distinguished."
 V7 = "Derivative payoff and exercise structure are explicit."
 V8 = "Risk metrics declare horizon and confidence level."
 V9 = "Credit-risk assumptions are explicit."
 V10 = "Numerical pricing and risk calculations are convergence-checked."
}

CONFIDENCE {
 BASE_CONFIDENCE = 0.99
 FINANCIAL_MATHEMATICS_ONTOLOGY_DEFINITION = 0.99
 TIME_VALUE_REASONING = 0.99
 TERM_STRUCTURE_REASONING = 0.98
 FIXED_INCOME_REASONING = 0.99
 PORTFOLIO_REASONING = 0.98
 STOCHASTIC_FINANCE_REASONING = 0.98
 DERIVATIVE_REASONING = 0.98
 CREDIT_REASONING = 0.97
 RISK_REASONING = 0.98

 POLICY =
  "Reduce confidence when valuation date, cash-flow timing, interest conventions, yield curve, covariance estimates, payoff specification, volatility, pricing measure, default assumptions, calibration data or numerical convergence are underspecified."
}

AI_CONSUMPTION {
 PURPOSES = [
  SemanticSearch,
  OntologyGrounding,
  FinancialMathematicsOntologyReasoning,
  TimeValueOfMoneyReasoning,
  DiscountingReasoning,
  InterestRateReasoning,
  CashFlowReasoning,
  AnnuityReasoning,
  BondReasoning,
  YieldCurveReasoning,
  DurationReasoning,
  PortfolioReasoning,
  MeanVarianceReasoning,
  CAPMReasoning,
  StochasticProcessReasoning,
  ItoReasoning,
  DerivativePricingReasoning,
  OptionPricingReasoning,
  NoArbitrageReasoning,
  RiskNeutralReasoning,
  HedgingReasoning,
  CreditRiskReasoning,
  FinancialRiskReasoning,
  ComputationalFinanceReasoning,
  KnowledgeGraphConstruction,
  RetrievalAugmentation,
  RecursiveInference
 ]

 NORMALISE {
  "financial mathematics ontology" -> FinancialMathematicsOntology
  "financial mathematics" -> FinancialMathematics
  "time value of money" -> TimeValueOfMoney
  "present value" -> PresentValue
  "future value" -> FutureValue
  "yield curve" -> YieldCurve
  "risk-neutral measure" -> RiskNeutralMeasure
  "equivalent martingale measure" -> RiskNeutralMeasure
  "value at risk" -> ValueAtRisk
  "VaR" -> ValueAtRisk
  "expected shortfall" -> ExpectedShortfall
 }

 INTERPRETATION_ORDER = [
  detect_financial_mathematics_ontology_context,
  identify valuation_date_cash_flows_payoff_market variables_interest conventions_uncertainty_and_constraints,
  classify timeValue_fixedIncome_portfolio_stochastic_derivative_credit_or_risk pathway,
  choose deterministic_or_stochastic model,
  compute valuation_return_risk_or_sensitivity,
  if_derivative enforce noArbitrage_and_measure consistency,
  if_portfolio incorporate covariance_and_constraints,
  if_credit incorporate PD_LGD_EAD_and_dependence,
  if_numerical assess discretisation_simulation_and_parameter sensitivity,
  validate financial_and_numerical assumptions,
  return semantic output
 ]
}

EXECUTION_RULES {
 E1:
  IF query_mentions("financial mathematics ontology")
  OR formal_financial_mathematical_semantics_are_required
  THEN activate(FinancialMathematicsOntology)

 E2:
  IF dated_cash_flows_are_present
  THEN map_to_common valuation date

 E3:
  IF term_structure_is_required
  THEN represent discount_spot_and_forward relationships explicitly

 E4:
  IF fixed_income_security
  THEN compute discounted_cash flows_and_rate sensitivity

 E5:
  IF portfolio_analysis
  THEN require weights_returns_and_dependence structure

 E6:
  IF derivative_contract
  THEN require payoff_maturity_underlying_and_pricing assumptions

 E7:
  IF no_arbitrage_market model
  THEN consider replication_or_riskNeutral valuation

 E8:
  IF risk_measure
  THEN declare horizon_probability convention_and_loss sign

 E9:
  IF closed_form_unavailable
  THEN route to lattice_PDE_MonteCarlo_or_other computational finance method
}

RECURSION {
 ENTRY = FinancialMathematicsOntology

 EXPAND(FinancialMathematicsOntology) -> [
  FinancialMathematics,
  TimeValueOfMoney,
  PresentValue,
  FutureValue,
  DiscountFactor,
  AccumulationFactor,
  InterestRate,
  SimpleInterest,
  CompoundInterest,
  EffectiveInterestRate,
  NominalInterestRate,
  ForceOfInterest,
  CashFlow,
  CashFlowStream,
  Annuity,
  Perpetuity,
  LoanAmortisation,
  Bond,
  CouponBond,
  ZeroCouponBond,
  BondPrice,
  Yield,
  YieldToMaturity,
  Duration,
  ModifiedDuration,
  Convexity,
  TermStructure,
  SpotRate,
  ForwardRate,
  YieldCurve,
  Portfolio,
  PortfolioWeight,
  PortfolioReturn,
  PortfolioVariance,
  Covariance,
  Correlation,
  Diversification,
  MeanVarianceOptimisation,
  EfficientFrontier,
  CapitalAssetPricingModel,
  Beta,
  StochasticProcess,
  BrownianMotion,
  GeometricBrownianMotion,
  Martingale,
  ItoProcess,
  ItoLemma,
  Derivative,
  ForwardContract,
  FuturesContract,
  Option,
  CallOption,
  PutOption,
  EuropeanOption,
  AmericanOption,
  BlackScholesModel,
  BinomialModel,
  Arbitrage,
  NoArbitrage,
  EquivalentMartingaleMeasure,
  RiskNeutralMeasure,
  RiskNeutralValuation,
  ReplicatingPortfolio,
  Hedging,
  DeltaHedging,
  Delta,
  Gamma,
  Vega,
  Theta,
  Rho,
  Volatility,
  ImpliedVolatility,
  CreditRisk,
  DefaultProbability,
  HazardRate,
  RecoveryRate,
  LossGivenDefault,
  ExposureAtDefault,
  CreditSpread,
  ValueAtRisk,
  ExpectedShortfall,
  StressTesting,
  ScenarioAnalysis,
  MonteCarloSimulation,
  FiniteDifferencePricing,
  LatticePricing,
  ComputationalFinance,
  ModelRisk
 ]

 EXPAND(ValuationFramework) -> [
  PresentValue,
  FutureValue,
  DiscountFactor,
  AccumulationFactor,
  TermStructure,
  BondPrice,
  RiskNeutralValuation
 ]

 EXPAND(RiskFramework) -> [
  PortfolioVariance,
  Volatility,
  ValueAtRisk,
  ExpectedShortfall,
  CreditRisk,
  StressTesting,
  ScenarioAnalysis,
  ModelRisk
 ]

 EXPAND(DerivativeFramework) -> [
  ForwardContract,
  FuturesContract,
  Option,
  BlackScholesModel,
  BinomialModel,
  NoArbitrage,
  RiskNeutralMeasure,
  ReplicatingPortfolio,
  Hedging,
  Greeks
 ]

 STOP_CONDITION =
  "Stop when valuation date, cash-flow or payoff structure, rates, stochastic assumptions, portfolio dependence, risk measure, credit assumptions, calibration and numerical validity are sufficiently resolved."
}

ROUTING {
 PARENT_ONTOLOGY = "Financial Mathematics"

 IMMEDIATE_CONTEXTS = [
  "Financial Mathematics",
  "Probability & Statistics Ontologies",
  "Stochastic Process Ontologies",
  "Computational Mathematics Ontologies"
 ]

 RELATED_ONTOLOGIES = [
  "Financial Mathematics",
  "Applied Mathematics Ontologies",
  "Probability & Statistics Ontologies",
  "Stochastic Process Ontologies",
  "Optimisation Ontologies",
  "Operations Research Ontologies",
  "Computational Mathematics Ontologies",
  "Numerical Analysis Ontologies",
  "Differential Equation Ontologies",
  "Measure Theory Ontologies",
  "Actuarial Mathematics Ontologies",
  "Risk Mathematics Ontologies",
  "Economics Mathematics Ontologies"
 ]

 ROUTE_RULES = [
  "Financial Mathematics Ontology -> Financial Mathematics for parent semantics",
  "Financial Mathematics Ontology -> Probability & Statistics for uncertainty and estimation",
  "Financial Mathematics Ontology -> Stochastic Processes for asset and rate models",
  "Financial Mathematics Ontology -> Optimisation for portfolio selection",
  "Financial Mathematics Ontology -> Operations Research for constrained financial decisions",
  "Financial Mathematics Ontology -> Computational Mathematics for numerical pricing",
  "Financial Mathematics Ontology -> Differential Equations for continuous-time pricing",
  "Financial Mathematics Ontology -> Measure Theory for expectations and pricing measures",
  "Financial Mathematics Ontology -> Actuarial Mathematics for insurance and longevity risk",
  "Financial Mathematics Ontology -> Risk Mathematics for tail, credit and scenario risk"
 ]
}

UPDATE_MODEL {
 MODE = "append-compatible semantic versioning"

 MAJOR = "ontology-breaking conceptual change"
 MINOR = "new compatible financial entities, pricing methods or reasoning pathways"
 PATCH = "clarification, metadata or formatting correction"

 RULES = [
  "Preserve time-value semantics.",
  "Preserve valuation-date semantics.",
  "Preserve interest-convention semantics.",
  "Preserve real-world-versus-pricing-measure distinction.",
  "Preserve no-arbitrage semantics.",
  "Preserve portfolio covariance semantics.",
  "Preserve financial-risk and credit-risk semantics.",
  "Preserve machine-readable financial-mathematics ontology semantics."
 ]
}

OUTPUT {
 CANONICAL_DEFINITION =
  "The Financial Mathematics Ontology formally represents valuation, investment, stochastic finance, derivatives, portfolio risk and credit risk through mathematical relations."

 TIME_VALUE_SUMMARY =
  "Dated cash flows are compared by discounting or accumulation to a common valuation date."

 FIXED_INCOME_SUMMARY =
  "Fixed-income analysis combines contractual cash flows with term structures, yield, duration and convexity."

 PORTFOLIO_SUMMARY =
  "Portfolio mathematics combines expected returns, weights and covariance to quantify diversification and optimise allocations."

 DERIVATIVE_SUMMARY =
  "Derivative valuation requires explicit payoff structure, no-arbitrage logic and a declared pricing model or measure."

 HEDGING_SUMMARY =
  "Hedging uses replicating positions and sensitivities to reduce exposure to financial risk factors."

 CREDIT_SUMMARY =
  "Credit-risk mathematics combines default likelihood, exposure and recovery assumptions."

 RISK_SUMMARY =
  "VaR, Expected Shortfall, stress tests and scenarios provide complementary financial-risk views."

 TRUST_SUMMARY =
  "Financial models should be checked for cash-flow consistency, measure consistency, calibration, sensitivity, numerical convergence and model risk."
}

FLOW {
 INPUT
 -> detect_financial_mathematics_ontology_context
 -> identify valuation_date_cash flows_payoff_structure_market variables_interest conventions_horizon_constraints_and_uncertainty
 -> classify timeValue_fixedIncome_portfolio_stochastic_derivative_credit_or_risk problem
 -> construct formal financial_model
 -> if_timeValue compute discount_or_accumulation factors
 -> if_fixedIncome build term_structure_and_value cash flows
 -> if_portfolio compute return_covariance_and_optimal weights if required
 -> if_derivative enforce noArbitrage_and_select replication_riskNeutral_closedForm_lattice_PDE_or_MonteCarlo pathway
 -> if_credit compute PD_LGD_EAD_and_credit measures
 -> if_risk compute volatility_VaR_ES_stress_or_scenario measures
 -> assess hedging_sensitivities_calibration_numerical convergence_and_model risk
 -> validate units_dates_interest conventions_probability measure_and_contract consistency
 -> route to financial_mathematics probability_statistics stochastic_processes optimisation operations_research computational_mathematics numerical_analysis differential_equations measure_theory actuarial_mathematics risk_mathematics_or_economics_mathematics ontology
 -> recursively_expand_required_dependencies
 -> verify_result
 -> assign_confidence
 -> produce_semantic_output
 -> END
}

SEMANTIC_SUMMARY {
 "The Financial Mathematics Ontology provides the formal semantic layer beneath financial mathematics. It represents time value of money, present and future value, discounting and accumulation, simple, compound and continuous interest, cash-flow streams, annuities, perpetuities and loans, bonds and term structures, yields, duration and convexity, portfolios, covariance, diversification, mean-variance optimisation and CAPM, stochastic processes, Brownian motion, geometric Brownian motion, martingales and Ito calculus, forwards, futures and options, Black-Scholes and binomial models, no-arbitrage, equivalent martingale measures, replication and risk-neutral valuation, hedging and Greeks, volatility and implied volatility, credit risk, default, hazard, recovery, VaR, Expected Shortfall, stress testing, scenarios, Monte Carlo, finite-difference and lattice pricing, computational finance and model risk."
}

FLOW_HASH {
 METHOD = "semantic-content-identity"
 ID = "KIRETH-MATH-APPLIED-MATHEMATICS-FINANCIAL-MATHEMATICS-ONTOLOGY-V1"
}

}

END_FLOW
Privacy Policy
Site Map
Kireth Research
38 Thorndale Croft, Wetwang, Driffield
East Riding of Yorkshire YO25 9XZ
Telephone:
01377 236594
Designed By
Kireth Web Design
Audio Explainer RSS Feed