Financial Algorithms Cookbook | Engineering

Algorithm: Forward Exchange Rate Calculations

f = currentSpot*[1+i_Q*(DAYS/BASIS_Q)]/[1+i_B*(DAYS/BASIS_B)]

def forwardRate(currentSpot, quoted_i, base_i, DAYS, quotedBASIS, baseBASIS):
   quoted = 1+ quoted_i*DAYS/quotedBASIS
   base = 1 + base_i*DAYS/baseBASIS
   forwardRate = currentSpot*quoted/base
   return forwardRate

Example

An foreign exchange dealer in Zurich is asked by a US client to quote a rate for Euro against the dollar for delivery in one year after spot. The client wants to buy 1980k Euro:

1. What is the price of these Euro in USD.
2. What is the far exchange rate for USD-Euro one year forward.

• currentSpot 1USD = 1.8 Euro
• US interest for one year = 6%
• Euro = 10%
• The bank needs to lend 1.8M Euro now @10% to get in one year 1980K Euro.
• This means the bank has to buy 1.8M Euro at spot rate, i.e. 1M USD.
• 1M USD is borrowed @ 6% costing over the year 1060K USD.

  >>> 
  >>> currentSpot=1.8
  >>> quoted_i=10
  >>> base_i=.06
  >>> quoted_i=.10
  >>> DAYS=360
  >>> quotedBASIS=360
  >>> baseBASIS=360
  >>> forwardRate(currentSpot, quoted_i, base_i, DAYS, quotedBASIS, baseBASIS)
  1.8679245283018868
  >>> 
  

Algorithm: FRA - Forward rate Agreement

FRA's are forward-forward loans granted at a fixed interest rate, but are without an actual lending commitment. They are used as an agreement between two parties that want to either hedge against or speculate on a movement in future interest rates. The seller of a FRA nominally agrees to lend a sum of money to the buyer. The buyer agrees to nominally borrow this sum. The sum (Contracyt Amount) is specified in a currency (Contract Currency) at a fixed rate of interest for a specified period starting on a fixed date in the future. here is the time line. An example should illustrate things better:

1x4 FRa in 1m USD @ 6.25%

Dealing Date	Typically 2 days	Spot Date	Deferment Period	Fixing Date	Typically 2 days	Settlement Date	Contract Period	Maturity Date
Mon. 12th April 03	2 days	Wed. 14th April 03	1 month	Fri. 14th May	2 days	94 days	Mon. 16th August
			Reference Rate (LIBOR) 7%

FRA - Settlement Sum

effectiveInterestCost= [(referenceRate -contractRate)*contractAmount]*(BASIS/DAYS)
discount=  1+[referenceRate* (BASIS/DAYS)]
fraSettlementSum = effectiveInterestCost/discount

def fraSettlementSum(referenceRate, contractRate, contractAmount, DAYS, BASIS):
   return ((referenceRate - contractRate)*contractAmount)/(BASIS/DAYS+referenceRate)

Example

An foreign exchange dealer in Zurich is asked by a US client to quote a rate for Euro against the dollar for delivery in one year after spot. The client wants to buy 1980k Euro:

1. What is the price of these Euro in USD.
2. What is the far exchange rate for USD-Euro one year forward.

• currentSpot 1USD = 1.8 Euro
• US interest for one year = 6%
• Euro = 10%
• The bank needs to lend 1.8M Euro now @10% to get in one year 1980K Euro.
• This means the bank has to buy 1.8M Euro at spot rate, i.e. 1M USD.
• 1M USD is borrowed @ 6% costing over the year 1060K USD.

  >>> 
  >>> currentSpot=1.8
  >>> quoted_i=10
  >>> base_i=.06
  >>> quoted_i=.10
  >>> DAYS=360
  >>> quotedBASIS=360
  >>> baseBASIS=360
  >>> forwardRate(currentSpot, quoted_i, base_i, DAYS, quotedBASIS, baseBASIS)
  1.8679245283018868
  >>> 
  

FRA - Price

fraRate = (imDm-isDs)/Df(1+isDs/B)


where:
  is - is the cash market interest rate to settlement date.
  im  is the cash market interest rate to maturity date.
  Ds - is the number of days from spot date  to settlement date.
  Dm - is the number of days from spot date  to maturity date.
  Df - days in contract period.
  B - is the day count convenstion (i.e: 360 or 365)

def fraRate (rate2Settlement, rate2Maturity, days2Settlement, days2Maturity,  contractDays, BASIS):
   num = rate2Maturity*days2Maturity- rate2Settlement*days2Settlement)
   dem = contractDays*(1+ rate2Settlement*days2Settlement/BASIS)
   return num/dem

Example

>>> days2Settlement = 30
>>> days2Maturity = 124
>>> contarctDays = 94
>>> B = 360
>>> rate2Settlement = 8.125/100.0
>>> rate2Maturity = 6.25/100.0
>>> fraRate (rate2Settlement , rate2Maturity , days2Settlement , contractDays , BASIS)
0.062580
>>> 0.062580 * 100
6.26