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Bond Clean Price between Coupon Payments with a Short First Coupon

The clean price of a bond is the value of a bond, excluding accrued interest since issue or the most recent coupon payment.

The clean price of a bond depends on the remaining time on the current coupon, the number of coupons remaining, the rate and frequency of coupons, the face value of the bond, its redemption value and the annual yield, as well as days in the initial short coupon period.

Formula

QuantityVariable[Subscript["P", "c"], "Money"] == -(((QuantityVariable["DCS", "Time"] - QuantityVariable["DIS", "Time"])*QuantityVariable["i", "Unitless"]*QuantityVariable["par", "Money"])/(QuantityVariable["DICQ", "Time"]*QuantityVariable["f", "Time"])) + ((-1 + QuantityVariable["DFC", "Time"]/QuantityVariable["DICQ", "Time"])*QuantityVariable["i", "Unitless"]*QuantityVariable["par", "Money"]*(1 + QuantityVariable["y", "Unitless"]/QuantityVariable["f", "Time"])^(-1 + QuantityVariable["DCS", "Time"]/QuantityVariable["DICQ", "Time"]))/QuantityVariable["f", "Time"] + (((QuantityVariable["f", "Time"] + QuantityVariable["y", "Unitless"])/QuantityVariable["f", "Time"])^(QuantityVariable["DCS", "Time"]/QuantityVariable["DICQ", "Time"] - QuantityVariable["n", "Unitless"])*(QuantityVariable["red", "Money"]*QuantityVariable["y", "Unitless"] + QuantityVariable["i", "Unitless"]*QuantityVariable["par", "Money"]*(-1 + ((QuantityVariable["f", "Time"] + QuantityVariable["y", "Unitless"])/QuantityVariable["f", "Time"])^QuantityVariable["n", "Unitless"])))/QuantityVariable["y", "Unitless"]

symbol description physical quantity
Pc price "Money"
DICQ days in quasi­coupon period containing settlement "Time"
DCS days from last quasi­coupon (possibly occurring before issue date) to settlement "Time"
DIS days from issue to settlement "Time"
f coupon frequency "Time"
i coupon rate "Unitless"
par face value "Money"
DFC actual days in short first coupon period "Time"
y annual yield "Unitless"
n remaining coupons payable to maturity "Unitless"
red redemption value "Money"

Forms

Examples

Get the resource:

In[1]:=
ResourceObject["Bond Clean Price between Coupon Payments with a Short \ First Coupon"]
Out[1]=

Get the formula:

In[2]:=
FormulaData[ ResourceObject[ "Bond Clean Price between Coupon Payments with a Short First \ Coupon"]]
Out[2]=

Use some values:

In[3]:=
FormulaData[ ResourceObject[ "Bond Clean Price between Coupon Payments with a Short First \ Coupon"], {QuantityVariable["DCS","Time"] -> Quantity[1, "Days"], QuantityVariable["red","Money"] -> Quantity[1000, "USDollars"], QuantityVariable["i","Unitless"] -> Quantity[7, "Percent"], QuantityVariable[ \!\(\*SubscriptBox[\("P"\), \("c"\)]\),"Money"] -> Quantity[998, "USDollars"], QuantityVariable["y","Unitless"] -> Quantity[10, "Percent"], QuantityVariable["n","Unitless"] -> 6, QuantityVariable["DICQ","Time"] -> Quantity[10, "Days"], QuantityVariable["DFC","Time"] -> Quantity[8, "Days"]}]
Out[3]=

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