Manual and help for add-in Calculus - Calcs for financial markets

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A bond indexed for a foreign currency - or corrected by the money exchange of this currency - pays a interest rate know as BMF FRC contract.
However, BMF FRC contract it's the interest rate received in an investment done in a external currency. in example, US dollars.

Exist many ways to negotiate a BMF FRC contract, be for exchange bonds, future interest contracts and currency or derivatives of BMF FRC contract. All this ways, however, must be equivalent, that is, arbitrated.

By the currency exchange correction (indexing). the BMF FRC contract it reflects the oscilations of the spot foreign currency and lean to be so volatile. This is the "dirty" BMF FRC contract. If the spot currency volatileness is removed in any way from the coupon calc, having the "clean" BMF FRC contract.

The calc of BMF FRC contract its directly relationed to the future trajectory of foreign currency and with local interest rates.

Access:

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Description: Return the linear interest rate ACT/360 of the clean exchange cambial contract or FRC according to the yield curve and the future dollar. Must be informed the values for the short side and for the long side used to reply the FRC.

For the future dollar with long side, must be informed a rolling value for the next settlement (30 days betweem settlements) or a rate of anual depreciation (linear ACT/360) for all future dollars curve. In case of points roll, this value is converted in the anual rate of depreciation by the standard 30/360.

Call: CC.CUPOM_FRA (Short Yield, Short Workdays, Short Settlement, Long Yield, Long Workdays, Long Settlement, Roll Over, Short Dollar)

The result for FRC of BMF FRC contract:

• FRC: interest rate of the contract of exchaneg coupon relative to the settlements (long and short side) indicated. Considering P_longa (long side) and P_curta (short side) equal to the interest rates for the long and short setttlement respectively, D_longa(long workdays) and D_curta(short workdays) equal to the workdays until this settlements, Vcto_longa(long settlement) and Vcto_curta (short) the dates of this settlements and R the roll over in points or ^r the depreciation rate, being Dol_curta(short dollar) the value for the future contract of the short side:
• FRC:
  
  
  Where:
  • 
    
    
  • Period's interest rate:
    
    
    
  • 
    
    
  • Depreciation rate(ACT/360):
    
    
    

Example of clean BMF FRC contract (FRC) with roll over indicted in points:

• side rate 18.75% e.y. (base 252) – first's value (shorter) DI1 contract
• Workdays on the short side 18
• Settlement on the short side 01/08/02 (august 2002)
• Rate on the short side 19.55% e.y. (base 252)
• Workdays on long side 40
• Settlement on long side 02/09/02 (september 2002)
• Roll over in points 18
• Quotation on the first (shorter) future dollar contract 2,892.00

Results:

The interest rate calculated for the contract of clean BMF FRC contract – FRC – based in the yield curve and in dollar's future market, considering a roll over of 18 points for the first dollar future contract (30 days for next settlement), is 10.53% (linear ACT/360). If the contract's value of FRA of a negotiated BMF FRC contract its different, lesser in example, mean that value of roll over implicit in the contract FRC is bigger.

Example of clean BMF FRC contract (FRC) with roll over indicated in rate:

• Rate on curve's side 18.75% e.y. (base 252) – first's value (shorter) DI1 contract
• Workdays on short side 18
• Settlement on the short side 08/01/02 (august 2002)
• Rate on long side 19.55% e.y. (base 252)
• Workdays on long side 40
• Settlement on long side 09/02/02 (september 2002)
• Interest rates on roll over ACT/360 de 7.471%

Results:

The interest rate arbitrated for the contract FRC its 10.53%. If the value of the contract FRC negotiated its different, lesser in example, mean that depreciation implcit in the contract of FRC negotiated is bigger.

Note that this result is the same from previous example, that is, a roll over of 18 points between the first future dollar settlement and the second (converted in a interest rate by the standard 30/360), it's equivalent to an anual depreciation (linear ACT/360) de 7.471%.

Access:

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Description: Returns the number of contracts to be registered in the BM&F on the short side of a contracr FRC considering one client only.

Call: CC.CUPOM_FRACURTA ( FRC Yield, Contracts, Long Settlement, Short Settlement)

The result for the amount of contracts is:

• N° short: total amount of rounded contracts (for the nearest unit) for the short side of a FRC, being C the number of contracts of the long side, P_FRC the interest rate linear ACT/360 of FRC and Vcto_longa (long settlement) and Vcto_curta (short) the dates of the settlements on the sides long and short, respectively:
• Contracts on short side:
  
  
  Where:
  • 
    
    

Usage example:

• FRC rate 11.20% (ACT/360)
• Contracts 100
• Settlement for long side 03/01/02 (march 2002)
• Settlement for short side 03/01/01 (march 2001)

Results:

For opertaion of 100 contracts of FRA of BMF FRC contract, will be registrated 100 contracts on the long side and 90 on the short side for one client only.

Access:

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Description: Returns the roll over in points for future dollar implicit in the quotation of FRA of BMF FRC contract (clean coupon).

The returned value represents the points of exchange variation for the first roll over (30 days for the next settlement) of future dollar, obtained by determinating a continuous and successive depreciating percentual from the rate of exchange depreciation implicit in the FRC for the period.

Call: CC.CUPOM_ROLIMP ( FRC Yield, Long Settlement, Long Workdays, Short Yield, Workdays Short, Short Dollar, Short Settlement, Long Yield)

The result for the implict roll over is:

• Roll over: value in points for the first roll over off future dollar, P_FRC the FRC rate, P_longa (long side) and P_curta (short side) equal to the interest rate for the long and short settlement respectively, D_longa (long workdays) and D_curta (short workdays) equals to the workdays to this settlement, Vcto_longa (long settlement) and Vcto_curta (short) the date sof this settlement and Dol_curta (short dolar) the valu of the future dollar contract on the short side:
• Roll over:
  
  
  Where:
  • 
    
    
  • 
    
    
  • Period's interest rate:
    
    
    
  • 
    
    

Usage example:

This is the most commom case, where the midday interval it is considered a negotiations interruption . The actual volume makes reference to the negotiated volume in stock exchange until the time now.

• Rate FRC 11,20% (ACT/360)
• Settlement in the long side 09/02/02 (september 2002)
• Workdays in long side 40
• Rate in the short side 18.75% e.y. (base 252) – first's value (shorter) DI1 contract
• Workdays in short side 18
• First's quotation (shorter) of the future dollar contract 2,892.00
• Settlement in short side 08/01/02 (august 2002)
• Rate in long side 19.45% e.y. (base 252)

Results:

The BMF FRC contract FRA contract negotiated on 11.20% indicates an implicit roll over for future dollar of 16.40 points on the first roll over (30 days between settlements).

For following roll overs, the depreciation percentual its continuous and equal to 0.567% (16.40 / 2,892.00) for each month.

Access:

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Description: Returns the anual devaluation rate (ACT/360) for the future dollar accounted in BMF FRC contract.

Call: CC.CUPOM_DEVIMP ( FRC Yield, Long Settlement, Workdays Long, Short Yield, Workdays Short, Short Settlement, Long Yield)

The result for implicit devaluation is:

• Devaluation: anual devaluation rate ACT/360. Considering P_FRC the FRC's rate, P_longa (long side) and P_curta (short) equal to the interest rates for the long and short settlement respectively, D_longa (workdays long) and D_curta (short) equal to the workdays until this settlements and Vcto_longa (long settlement) and Vcto_curta (short settlement) the dates of this settlements:
• Implicit devaluation:
  
  
  Where:
  • 
    
    
  • Period's interest rate:
    
    
    
  • 
    
    

Usage example:

Will be used the same data in roll over example:

• Rate FRC 11,20% (ACT/360)
• Settlement in the long side 09/02/02 (september 2002)
• Workdays in long side 40
• Rate in the short side 18.75% e.y. (base 252) – first's value (shorter) DI1 contract
• Workdays in short side 18
• First's quotation (shorter) of the future dollar contract 2,892.00
• Settlement in short side 08/01/02 (august 2002)
• Rate in long side 19.45% e.y. (base 252)

Results:

The anual interest rate (ACT/360) implicit in the BMF FRC contract for dollar devaluation in roll overs is 6.804% or 0.567% by month.

The result is the same obtained in the function CC.CUPOM_ROLIMP, when the devaluation percentual for the first month was calculated.

Accesso:

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Description: Returns annual yield (ACT/360) of dirty BMF FRC contract according yield curve, R$/U$ roll over and PTAX.

Call: CC.CUPOM_SUJO ( PTAX Yesterday, Dollar 2, Dollar 2 Settlement, Today, Long Yield, Workdays Long, Long Settlement, Roll Over, Type)

For obtaining the future dollar of the long side, must be informed a roll over value for 30 days from the settlement of the Dollar 2 or an anual devaluation rate (ACT/360) for whole future dolla curve. In case of points roll over, this value its converted in the anual devaluation rate by the 30/360 standard.

Result for dirty BMF FRC contract:

• Dirty BMF FRC contract: interest rate of the dirty BMF FRC contract for present date until the long side informed. Considering P_longa (long side) equal to the interest rate for the long settlement, D_longa (workdays long) equal to the workdays until the long settlement, Vcto_longa (settlement long) and Vcto₂ (settlement 2), respectively today's date, of the long settlement and of the second dollar used (sttlement date of the future dollar or today's date for PTAX) and R the roll over in points or T_R the devaluation rate, being Dol₂ thge short dollar value used (PTAX or future contract) and PTAX the PTAX for yesterday:
• Dirty:
  
  
  Where:
  • 
    
    
  • 
    
    
  • Period's interest rate:
    
    
    
    
  • 
    
    
  • 
    
    
  • 
    
    

Example of dirty BMF FRC contract with roll over in points:

This example uses today's PTAX for calculatig the dirty BMF FRC contract.

• PTAX yesterday 2.870 R$/US$
• PTAX today 2.892 R$/US$
• Today 08/01/02 (august 2002)
• Rate in long side 21.00% e.y. (base 252)
• Workdays in long side 44
• Settlement in long side 11/01/02 (november 2002)
• Roll over in points 20

Results:

The dirty BMF FRC contract is 1.91% (ACT/360), considering a roll over (30 days) of 18 points by the PTAX now informed.

Example of dirty BMF FRC contract with roll over in rate :

• PTAX yesterday 2,870 R$/US$
• PTAX today 2,892 R$/US$
• Today 08/01/02 (august 2002)
• Rate in long side 21.00% e.y. (base 252)
• Workdays on long side 44
• Settlement on the long side 11/01/02 (september 2002)
• Interest rate roll over ACT/360 8,299%
• Type 1

Results:

The dirty BMF FRC contract it's 1.917% (ACT/360), considering a devaluation rate of 8.299% by year - linear ACT/360 for all roll overs.

Once more, this result its the same to the previous example, that is, a roll over (30 days) of 20 points over actual PTAX (converted in interest rate by the standard 30/360), equivalent to an anual devaluation (ACT/360) 8.229%.

Example of BMF FRC contract with roll over rate and future dollar usage:

• PTAX yesterday 2,870 R$/US$
• Future dollar 2.912,00 R$/1.000 US$
• Settlement for future dollar 08/31/02 (august 2002)
• Today 08/01/02 (agosto de 2002)
• Rate in long side 21.00% e.y. (base 252)
• Workdays in long side 44
• Settlement in long side 11/01/02 (novembro de 2002)
• Roll over rate ACT/360 de 8,299%
• Type 1

Resultados:

The dirty BMF FRC contract is 1.917% (ACT/360), considering a devaluation rate of 8.299% by year - ACT/360 for all roll overs. this contract uses future dollar as settlement in october to compose the dirty BMF FRC contract.

This result its equivalent to the previous examples, cause the future dollar used have a differential of 20 pointsfor the today's PTAX (2.892 R$/US$), which its equivalent to a devaluation of 8.299% for all roll overs.

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