## Fwd Clean Price

Function

**within Bond with keys Bond Fwd Clean Price keys returns the forward clean price(s) of the referenced bond(s) at a given future horizon date**

*Fwd Clean Price***for a given clean price (or prices) recorded as of some earlier settlement date**

*Tʰ***and a given repo rate (or rates)**

*Tˢ***applying for the time period from**

*r***to**

*Tˢ*

*Tʰ*By default,

**is the bond's settlement date, but this function allows it to be any future date, as long as**

*Tˢ*

*Tˢ < Tʰ*If the settlement date

**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 date**

*Tˢ***(typically today).**

*T₀*The forward price is calculated according to the Bloomberg methodology, as follows:

Download the workbook bond-carryroll.xlsx that demonstrates the method described here.

**The initial**

*Step 1:*

*settlement invoice amount***is calculated as of**

*Sˢ***from the given clean price**

*Tˢ***using the function Settle Value**

*Pᶜ***The corresponding**

*Step 2:*

*terminal invoice amount***is calculated as**

*Sʰ***, where**

*Sʰ = Sˢ(1+rΔ) - CPN***in annual units according to the daycount convention of the repo rate**

*Δ = Tʰ - Tˢ***and**

*r***is the cummulative value (as of**

*CPN***) of any coupons paid between**

*Tʰ***and**

*Tˢ***as described by the entry Coupon Interest**

*Tʰ***The corresponding dirty price**

*Step 3:***at horizon**

*Pᵈ***is given by the expression**

*Tʰ***, where**

*Pᵈ = Sʰ100/N***is the notional as of**

*N*

*Tʰ***The final clean price is given by the expression**

*Step 4:***, where**

*Pᵈ - I100/N***is the interest amount that has been accrued until**

*I***during the coupon accrual period containing**

*Tʰ*

*Tʰ*