Fwd Clean Price
Function Fwd Clean Price within Bond with keys Bond Fwd Clean Price keysreturns the forward clean price of the referenced bond at a given future horizon date Tʰ for a given clean price recorded as of some earlier settlement date Tˢ and a given repo rate r applying for the time period from Tˢ to Tʰ
Several values may be also returned here in the form of a 1D-array
By default, Tˢ is the bond's settlement date, but this function allows it to be any future date, as long as Tˢ < Tʰ
If the settlement date Tˢ is not explicitly given, it will be set to the bond's settlement date as implied by a trade transaction assumed to occur on the trade dateT₀ (typically today).
The forward price is calculated according to the Bloomberg methodology, as follows:
Download the workbook bond-carryroll.xlsx that demonstrates the method described here.
Step 1: The initial settlement invoice amount Sˢ is calculated as of Tˢ from the given clean price Pᶜ using the function Settle Value
Step 2: The corresponding terminal invoice amount Sʰ is calculated as Sʰ = Sˢ(1+rΔ) - CPN, where Δ = Tʰ - Tˢ in annual units according to the daycount convention of the repo rate r and CPN is the cummulative value (as of Tʰ) of any coupons paid between Tˢ and Tʰ as described by the entry Coupon Interest
Step 3: The corresponding dirty price Pᵈ at horizon Tʰ is given by the expression Pᵈ = Sʰ100/N, where N is the notional as of Tʰ
Step 4: The final clean price is given by the expression Pᵈ - I100/N, where I is the interest amount that has been accrued until Tʰ during the coupon accrual period containing Tʰ