Fwd Clean Price
Function Fwd Clean Price within with keys returns the forward of the referenced bond(s) at a given future horizon date Tʰ for a given clean price (or prices) recorded as of some earlier settlement date Tˢ and a given repo rate (or rates) r applying for the time period from Tˢ to Tʰ
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 T₀ (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
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
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