Asian Option Related Functions

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

Construction Functions

Excel: =McpAsianOption(args1, args2, args3, args4, args5, fmt='VP')

Python: McpAsianOption(*args)

• Function: Constructs an Asian option object.
• Parameters:
  • args1~args5 or *args: Parameter groups, supporting the following two input methods:
    1. First Parameter Set:
       • CallPut: Option type (enumeration value, e.g., Call or Put).
       • ReferenceDate: Trade date or valuation date.
       • SpotPx: Spot price.
       • AveRate: Initial average rate.
       • FirstAverageDate: Start date for averaging.
       • ExpiryDate: Expiry date.
       • SettlementDate: Settlement date.
       • StrikePx: Strike price.
       • ForwardPx: Forward price.
       • DomesticRate: Interest rate for currency 2.
       • ForeignRate: Interest rate for currency 1.
       • BuySell: Buy/sell direction (enumeration value, e.g., Buy or Sell).
       • Volatility: Volatility.
       • PremiumDate: Premium payment date.
       • FixingFrequency: Fixing frequency (default is Monthly).
       • LastAverageDate: End date for averaging.
       • CalculatedTarget: Calculation target (default is CCY1).
       • AverageMethod: Averaging method (default is Arithmetic).
       • StrikeType: Strike type (default is Fixed).
       • PricingMethod: Pricing method (default is BINOMIAL).
       • FaceAmount: Notional amount (default is 1).
       • NumSimulation: Number of simulations (Monte Carlo, default is 10000).
       • FixingDateAdjuster: Fixing date adjustment rule (default is ModifiedFollowing).
       • KeepEndOfMonth: End-of-month rule (default is True).
       • FixingLongStub: Long stub for averaging (default is False).
       • FixingEndStub: Short stub for averaging (default is True).
       • Calendar: Holiday calendar object.
       • DayCounter: Day count convention (default is Act365Fixed).
       • TimeStep: Time step (default is 10).
       • PipsUnit: Pips unit (default is 10000).
    2. Second Parameter Set:
       • CallPut: Option type (enumeration value).
       • ReferenceDate: Trade date or valuation date.
       • SpotPx: Spot price.
       • AveRate: Initial average rate.
       • FirstAverageDate: Start date for averaging.
       • ExpiryDate: Expiry date.
       • SettlementDate: Settlement date.
       • StrikePx: Strike price.
       • DomesticRate: Interest rate for currency 2.
       • ForeignRate: Interest rate for currency 1.
       • BuySell: Buy/sell direction (enumeration value).
       • Volatility: Volatility.
       • PremiumDate: Premium payment date.
       • NumFixings: Number of fixings.
       • Calendar: Holiday calendar object.
       • DayCounter: Day count convention (default is Act365Fixed).
       • AverageMethod: Averaging method (default is Arithmetic).
       • StrikeType: Strike type (default is Fixed).
       • PricingMethod: Pricing method (default is BINOMIAL).
       • FaceAmount: Notional amount (default is 1).
       • TimeStep: Time step (default is 10).
       • NumSimulation: Number of simulations (Monte Carlo, default is 10000).
       • PipsUnit: Pips unit (default is 10000).
  • fmt: Parameter format (default is 'VP'),Excel-specific parameters.
• Returns: Asian option object.

---

Usage Functions

Excel: =McpPrice(Obj, isAmount)

Python: Price(*args)

• Function: Calculates the option premium.
• Parameters:
  • Obj: Asian option object.
  • isAmount: Whether to return the amount (default is True, returns the premium in currency 2; False returns the premium in currency 1).
  • *args：is a dictionary, does not require the Obj parameter, other parameters are the same as those in Excel.
• Returns: Option premium.

Excel: =McpDelta(obj, isCcy2=False, isAmount=True, pricingMethod=1, isClosedFormMethod=True)

Python: Delta(isCCY2=False, isAmount=True, npricingMethod=1)

• Function: Calculates the Delta value of the option.
• Parameters:
  • obj: Asian option object.
  • isCcy2: Whether it is for currency 2 (True for currency 2, False otherwise).
  • isAmount: Whether to calculate the amount (default is True).
  • pricingMethod: Pricing method (default is 1).
  • isClosedFormMethod: Whether to use the closed-form method for Greeks calculation (default is True). If True, Greeks are calculated using the Black-Scholes model regardless of the selected pricing model; otherwise, the selected model is used.
• Returns: Delta.

Excel: =McpForwardDelta(obj, isCcy2=False, isAmount=True, pricingMethod=1, isClosedFormMethod=True)

Python: ForwardDelta(isCCY2=False, isAmount=True, npricingMethod=1)

• Function: Calculates the Forward Delta value of the option.
• Parameters:
  • obj: Asian option object.
  • isCcy2: Whether it is for currency 2 (True for currency 2, False otherwise).
  • isAmount: Whether to calculate the amount (default is True).
  • pricingMethod: Pricing method (default is 1).
  • isClosedFormMethod: Whether to use the closed-form method for Greeks calculation (default is True).
• Returns: Forward Delta.

Excel: =McpVega(obj, isCcy2=False, isAmount=True, pricingMethod=1, isClosedFormMethod=True)

Python: Vega(isCCY2=False, isAmount=True, npricingMethod=1)

• Function: Calculates the Vega value of the option.
• Parameters:
  • obj: Asian option object.
  • isCcy2: Whether it is for currency 2 (True for currency 2, False otherwise).
  • isAmount: Whether to calculate the amount (default is True).
  • pricingMethod: Pricing method (default is 1).
  • isClosedFormMethod: Whether to use the closed-form method for Greeks calculation (default is True).
• Returns: Vega.

Excel: =McpGamma(obj, isCcy2=False, isAmount=True, pricingMethod=1, isClosedFormMethod=True)

Python: Gamma(isCCY2=False, isAmount=True, npricingMethod=1)

• Function: Calculates the Gamma value of the option.
• Parameters:
  • obj: Asian option object.
  • isCcy2: Whether it is for currency 2 (True for currency 2, False otherwise).
  • isAmount: Whether to calculate the amount (default is True).
  • pricingMethod: Pricing method (default is 1).
  • isClosedFormMethod: Whether to use the closed-form method for Greeks calculation (default is True).
• Returns: Gamma.

Excel: =McpTheta(obj, isCcy2=False, isAmount=True, pricingMethod=1, isClosedFormMethod=True)

Python: Theta(isCCY2=False, isAmount=True, npricingMethod=1)

• Function: Calculates the Theta value of the option.
• Parameters:
  • obj: Asian option object.
  • isCcy2: Whether it is for currency 2 (True for currency 2, False otherwise).
  • isAmount: Whether to calculate the amount (default is True).
  • pricingMethod: Pricing method (default is 1).
  • isClosedFormMethod: Whether to use the closed-form method for Greeks calculation (default is True).
• Returns: Theta.

Excel: =McpVanna(obj, isCcy2=False, isAmount=True, pricingMethod=1, isClosedFormMethod=True)

Python: Vanna(isCCY2=False, isAmount=True, npricingMethod=1)

• Function: Calculates the Vanna value of the option.
• Parameters:
  • obj: Asian option object.
  • isCcy2: Whether it is for currency 2 (True for currency 2, False otherwise).
  • isAmount: Whether to calculate the amount (default is True).
  • pricingMethod: Pricing method (default is 1).
  • isClosedFormMethod: Whether to use the closed-form method for Greeks calculation (default is True).
• Returns: Vanna.

Excel: =McpVolga(obj, isCcy2=False, isAmount=True, pricingMethod=1, isClosedFormMethod=True)

Python: Volga(isCCY2=False, isAmount=True, npricingMethod=1)

• Function: Calculates the Volga value of the option.
• Parameters:
  • obj: Asian option object.
  • isCcy2: Whether it is for currency 2 (True for currency 2, False otherwise).
  • isAmount: Whether to calculate the amount (default is True).
  • pricingMethod: Pricing method (default is 1).
  • isClosedFormMethod: Whether to use the closed-form method for Greeks calculation (default is True).
• Returns: Volga.

Excel: =McpRho(obj, isCcy2=False, isAmount=True, pricingMethod=1, isClosedFormMethod=True)

Python: Rho(isCCY2=False, isAmount=True, npricingMethod=1)

• Function: Calculates the Rho value of the option.
• Parameters:
  • obj: Asian option object.
  • isCcy2: Whether it is for currency 2 (True for currency 2, False otherwise).
  • isAmount: Whether to calculate the amount (default is True).
  • pricingMethod: Pricing method (default is 1).
  • isClosedFormMethod: Whether to use the closed-form method for Greeks calculation (default is True).
• Returns: Rho.

Excel: =AOFixingSchedule(obj, fmt='V')

• Function: Retrieves the fixing schedule for averaging.
• Parameters:
  • obj: McpAsianOption object.
  • fmt: Parameter format (default is 'V').
• Returns: Fixing schedule for averaging.

---