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YieldCurve Related Functions

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YieldCurve Related Functions

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Visit the Mathema Option Pricing System for foreign exchange options and structured product valuation!

YieldCurve Construction Functions

Excel: =McpYieldCurve2(args1, args2, args3, args4, args5, fmt="VP|HD")

Python: McpYieldCurve2(*args)

  • Function: Constructs a bilateral yield curve.
  • Parameters:
    • args1~args5 or *args: Parameter groups, supporting the following three input methods:
      1. Interest Rate Data Construction:
        • ReferenceDate: Trade date or valuation date.
        • Tenors: Array of tenors.
        • BidZeroRates: Array of bid-side zero rates.
        • AskZeroRates: Array of ask-side zero rates.
        • Frequency: Period (default is NoFrequency).
        • Variable: Interest rate type (default is SIMPLERATES).
        • Method: Interpolation method (default is LINEARINTERPOLATION).
        • Calendar: Holiday calendar object (default is empty).
        • DayCounter: Day count convention (default is Act360).
        • ValueDate: Value date.
      2. Bid/Ask Yield Curve Construction:
        • BidYieldCurve: Bid-side yield curve object.
        • AskYieldCurve: Ask-side yield curve object.
      3. Forward Curve Construction:
        • FxForwardPointsCurve2: Forward curve object.
        • YieldCurve2: Yield curve object.
        • CalculatedTarget: Calculation target (enumeration value).
        • Calendar: Holiday calendar object.
    • fmt: Parameter format (default is VP|HD),Excel-specific parameters.
  • Returns: Bilateral yield curve object.

Excel: =McpYieldCurve(args1, args2, args3, args4, args5, fmt="VP|HD")

Python: McpYieldCurve(*args)

  • Function: Constructs a unilateral yield curve.
  • Parameters:
    • args1~args5 or *args: Parameter groups, supporting the following two input methods:
      1. Date Parameters:
        • ReferenceDate: Trade date or valuation date.
        • Dates: Array of dates.
        • ZeroRates: Array of zero rates.
        • Frequency: Period (default is NoFrequency).
        • Variable: Interest rate type (default is SIMPLERATES).
        • Method: Interpolation method (default is LINEARINTERPOLATION).
      2. Tenor Parameters:
        • ReferenceDate: Trade date or valuation date.
        • Tenors: Array of tenors.
        • ZeroRates: Array of zero rates.
        • Method: Interpolation method (default is LINEARINTERPOLATION).
        • Calendar: Holiday calendar object (default is empty).
        • DayCounter: Day count convention (default is ActActISDA).
        • ValueDate: Value date.
    • fmt: Parameter format (default is VP|HD),Excel-specific parameters.
  • Returns: Unilateral yield curve object.

YieldCurve Usage Functions

Excel: =YieldCurve2ZeroRate(Curve, Date, BidMidAsk)

Python: ZeroRate(*args)

  • Function: Retrieves the zero rate for a specified date from a bilateral yield curve.
  • Parameters:
    • Curve: Bilateral yield curve object.
    • Date: Target date.
    • BidMidAsk: Specifies the direction (bid, mid, or ask).
    • *args：is a dictionary, does not require the Curve parameter, other parameters are the same as those in Excel.
  • Returns: Zero rate for the specified direction.
  • Example:
    =YieldCurve2ZeroRate(McpYieldCurve2(...), "2023-12-31", "mid")
    Returns 0.025 (assuming the mid rate is 2.5%).

Excel: =YieldCurveZeroRate(Curve, Date)

Python: ZeroRate(endDate)

  • Function: Retrieves the zero rate for a specified date from a unilateral yield curve.
  • Parameters:
    • Curve: Unilateral yield curve object,Python API does not require this parameter.
    • Date: Target date.
  • Returns: Zero rate.

Excel: =YieldCurve2DiscountFactor(Curve, Date, BidMidAsk)

Python: DiscountFactor(*args)

  • Function: Retrieves the discount factor for a specified date from a bilateral yield curve.
  • Parameters:
    • Curve: Bilateral yield curve object.
    • Date: Target date.
    • BidMidAsk: Specifies the direction (bid, mid, or ask).
    • *args：is a dictionary, does not require the Curve parameter, other parameters are the same as those in Excel.
  • Returns: Discount factor for the specified direction.

Excel: =YieldCurveDiscountFactor(Curve, Date)

Python: DiscountFactor(*args)

  • Function: Retrieves the discount factor for a specified date from a unilateral yield curve.
  • Parameters:
    • Curve: Unilateral yield curve object.
    • Date: Target date.
    • *args：is a dictionary, does not require the Curve parameter, other parameters are the same as those in Excel.
  • Returns: Discount factor.

SwapCurve Construction Functions

Excel: =McpVanillaSwapCurveData(args1, args2, args3, args4, args5, Fmt)

Python: McpVanillaSwapCurveData(*args)

  • Function: Constructs a unilateral SwapCurve.
  • Parameters:
    • args1, args2, args3, args4, args5 or *args: Parameter group, supporting the following three input methods:
      1. First Parameter Set:
        • ReferenceDate: Trade date or valuation date.
        • StartDate: Start date.
        • MaturityDates: Array of maturity dates.
        • Frequencies: Array of frequencies.
        • Coupons: Array of coupon rates.
        • FixedDayCounter: Fixed leg day count convention (default is Act365Fixed).
        • FloatDayCounter: Floating leg day count convention (default is Act365Fixed).
        • BumpAmounts: Array of rate bumps (e.g., 0.01 adds 0.01 to all rates).
        • BUses: Whether to use the row data (Y or N).
        • Calendar: Array of holiday calendars.
        • AdjustRule: Adjustment rule (default is ModifiedFollowing).
        • UseIndexEstimation: Whether to use floating rate index estimation (default is TRUE).
        • SwapStartLag: Value date adjustment (default is 2).
        • CompoundingFrequency: Compounding frequency (default is 0).
        • FixInAdvance: Fixed in advance flag (default is true).
        • FixDaysBackward: Floating rate fixing days backward (default is 1).
        • EndStub: Default is false.
      2. Second Parameter Set:
        • Similar to the first set but omits some parameters.
      3. Third Parameter Set:
        • Similar to the first set but adds FixingIndex, FixingRateMethod, etc.
    • fmt: Parameter format VP|HD, specifically for Excel.
  • Returns: VanillaSwapCurve object.

Excel: =McpSwapCurve(args1, args2, args3, args4, args5, fmt="VP")

Python: McpSwapCurve(*args)

  • Function: Constructs a unilateral SwapCurve object.
  • Parameters:
    • args1~args5 or *args: Parameter groups, supporting the following two input methods:
      1. First Parameter Set:
        • SettlementDate: Trade date.
        • CalibrationSet: Portfolio of instruments (e.g., VanillaSwaps or Deposits) used to build the curve.
        • InterpolatedVariable: Interest rate type (enumeration value).
        • InterpolationMethod: Interpolation method (enumeration value).
        • DayCounter: Day count convention (default is Act365Fixed).
        • UseGlobalSolver: Whether to use a global solver (default is True).
        • PillarEndDate: Default is 0.
      2. Second Parameter Set:
        • ReferenceDate: Trade date.
        • InterpolatedVariable: Interest rate type (enumeration value).
        • InterpolationMethod: Interpolation method (enumeration value).
        • FixedDayCounter: Fixed leg day count convention (default is Act365Fixed).
        • FloatDayCounter: Floating leg day count convention (default is Act365Fixed).
        • DayCounter: Day count convention (default is Act365Fixed).
        • Calendar: Holiday calendar object.
        • AdjustRule: Adjustment rule (enumeration value).
        • SettlementDates: Array of settlement dates.
        • MaturityDates: Array of maturity dates.
        • Coupons: Array of coupon rates.
        • FixedFrequencies: Array of fixed leg frequencies.
        • FloatingFrequencies: Array of floating leg frequencies.
        • BumpAmounts: Array of rate bumps.
        • BUses: Whether to use the row data (Y or N).
    • fmt: Parameter format (default is VP),Excel-specific parameters.
  • Returns: Unilateral SwapCurve object.

Excel: =McpSwapCurve2(args1, args2, args3, args4, args5, fmt="VP")

  • Function: Constructs a bilateral SwapCurve object.
  • Parameters: Similar to McpSwapCurve, supporting two input methods.
  • Returns: Bilateral SwapCurve object.

SwapCurve Usage Functions

Excel: =SwapCurveZeroRate(curve, date)

Python: ZeroRate(endDate)

  • Function: Retrieves the zero rate for a specified date from a SwapCurve.
  • Parameters:
    • curve: Swap curve object,Python API does not require this parameter.
    • date: Target date.
  • Returns: Zero rate.

Excel: =SwapCurveZeroRates(curve, dates, fmt='V')

  • Function: Retrieves zero rates for multiple dates from a SwapCurve.
  • Parameters:
    • curve: Swap curve object.
    • dates: Array of dates.
    • fmt: Return format (default is V).
  • Returns: Array of zero rates.

Excel: =SwapCurveDiscountFactor(curve, date)

Python: DiscountFactor(endDate)

  • Function: Retrieves the discount factor for a specified date from a SwapCurve.
  • Parameters:
    • curve: Swap curve object,Python API does not require this parameter.
    • date: Target date.
  • Returns: Discount factor.

Excel: =SwapCurveDiscountFactors(curve, dates, fmt='V')

  • Function: Retrieves discount factors for multiple dates from a SwapCurve.
  • Parameters:
    • curve: Swap curve object.
    • dates: Array of dates.
    • fmt: Return format (default is V).
  • Returns: Array of discount factors.

Excel: =YieldCurveForwardRate(curve, startDate, endDate, dayCounter=DayCounter.Act365Fixed, compounding=False, frequency=Frequency.NoFrequency)

Python: ForwardRate(startDate, endDate, dayCounter, compounding, frequency)

  • Function: Retrieves the forward rate from a SwapCurve.
  • Parameters:
    • curve: Swap curve object,Python API does not require this parameter.
    • startDate: Start date.
    • endDate: End date.
    • dayCounter: Day count convention (default is Act365Fixed).
    • compounding: Whether to use compounding (default is false).
    • frequency: Compounding frequency (default is NoFrequency).
  • Returns: Forward rate.

Excel: =SwapCurveParSwapRate(curve, start, end)

  • Function: Calculates the par swap rate for a given interest rate curve.
  • Parameters:
    • curve: The interest rate curve object.
    • start: The start tenor of the interest rate swap.
    • end: The end tenor of the interest rate swap.
  • Returns: The calculated par swap rate value.

Excel: =SwapCurveCarry(curve, horizon, maturityPeriod)

  • Function: Calculates the carry (holding收益) for a given interest rate curve.
  • Parameters:
    • curve: The interest rate curve object.
    • horizon: The start tenor of the holding period.
    • maturityPeriod: The end tenor of the holding period (or the instrument's maturity period).
  • Returns: The calculated carry value.

Excel: =SwapCurveRoll(curve, horizon, maturityPeriod)

  • Function: Calculates the roll (rolling收益) for a given interest rate curve.
  • Parameters:
    • curve: The interest rate curve object.
    • horizon: The start tenor of the roll period.
    • maturityPeriod: The end tenor of the roll period (or the instrument's maturity period).
  • Returns: The calculated roll value.

Notes

  1. Parameter Format: The fmt parameter specifies the format of the parameters, with a default value of VP|HD or VP.
  2. Enumeration Values: Some parameters (e.g., Frequency, Variable, Method) are enumeration values. Refer to specific definitions for details.
  3. Default Values: Parameters not explicitly stated usually have default values, which can be adjusted as needed.
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