ch04-bond-present-value-supplemental

arbitrage.jl

function maturityYield(presVal, couponRate, time)
  f(y) = 1 / y ^ time + sigma(1:time, t -> couponRate / y ^ t) - presVal
  fzero(f, 0.5, 2.5)
end

bond-present-value.jl

function sigma(range, fn)
  output = 0
  for i = range
    output += fn(i)
  end
  output
end

function presentValue(marketYield, couponRate, time)
  1 / (1 + marketYield) ^ time + sigma(1:time, t -> couponRate / ( 1 + marketYield ) ^ t)  
end

spot-rate.jl

function spotRate(pvPercent, nYear)
  1 / pvPercent ^ ( 1 / nYear) - 1
end

function forwardRate(currRateSp, prevRateSp, n)
  ((1 + currRateSp) ^ n) / ((1 + prevRateSp) ^ (n-1) ) - 1
end

As a sanity check, consider the following:

Notice that when:

• the couponRate is equal to the marketYield, then the bond sells at face value
• the couponRate is much lower than the market yield, the bond is worthless
• the coupon rate is much lower than the market yield, the bond's value scales up indefinitely with the time