Support Getting Clean and Dirty Price from CDS

ProjectX.AnalyticsLib.Tests/CreditDefaultSwapFunctionsTest.cs

@@ -51,8 +51,7 @@ public void WhenValuingCdsPVWithMultipleSpreadPointsItShouldReturnValidPVAndProb
         var recoveryRate = 0.4;
         var couponInBps = 100;
         var notional = 10_000;
-        Protection.Side protectionSide = Protection.Side.Buyer;
-        var interestRate = 0.07;
+        Protection.Side protectionSide = Protection.Side.Buyer;        
         var actual = CreditDefaultSwapFunctions.PV(
             evalDate,
             effectiveDate,
@@ -63,11 +62,42 @@ public void WhenValuingCdsPVWithMultipleSpreadPointsItShouldReturnValidPVAndProb
             couponInBps,
             notional,
             protectionSide,
-            interestRate);
+            0.07);
         Assert.That(actual.SurvivalProbabilityPercentage, Is.EqualTo(96.3).Within(1));
         Assert.That(actual.DefaultProbabilityPercentage, Is.EqualTo(3.6).Within(1));
         Assert.That(actual.HazardRatePercentage, Is.EqualTo(1.8).Within(1));
         Assert.That(actual.PV, Is.EqualTo(-137).Within(1), "PV must be equal to expected value within tolerance");
         Assert.That(actual.FairSpread, Is.EqualTo(51.3).Within(1), "Fair spread must be equal to expected value within tolerance");
     }
+
+    [Test]
+    public void WhenCdsPriceShouldReturnCleanAndDirtyPrice()
+    {
+        var evalDate = new DateTime(2015, 5, 15);
+        var effectiveDate = new DateTime(2015, 3, 20);
+        var maturityDate = new DateTime(2018, 6, 20);
+        var spreadsInBps = new double[] { 34.93, 53.6, 72.02, 106.39, 129.39, 139.46 };
+        var tenors = new string[] { "1Y", "2Y", "3Y", "5Y", "7Y", "10Y" };
+        var recoveryRate = 0.4;
+        var couponInBps = 100;
+        var couponFrequency = Frequency.Annual;
+        Protection.Side protectionSide = Protection.Side.Buyer;        
+
+        var actual = CreditDefaultSwapFunctions.Price(
+           evalDate,
+           effectiveDate,
+           maturityDate,
+           spreadsInBps,
+           tenors,
+           recoveryRate,
+           couponInBps,
+           couponFrequency,
+           protectionSide, 
+           0.07);
+
+        Assert.That(actual.cleanPrice, Is.EqualTo(100.43).Within(1));
+        Assert.That(actual.dirtyPrice, Is.EqualTo(100.67).Within(1));
+        Assert.That(actual.dirtyPrice, Is.GreaterThan(actual.cleanPrice));
+        Assert.That(actual.riskyAnnuity, Is.EqualTo(-0.04).Within(1));
+    }
 }

ProjectX.AnalyticsLib/CreditDefaultSwapFunctions.cs

@@ -6,11 +6,54 @@
 using QLNet;
 
 namespace ProjectX.AnalyticsLib;
-
+/// <summary>
+/// For CDS buyers or sellers the present value of a CDS contract is all what they care about.
+/// For quants, we want to calculate accrual amount, risk annuity (DV01), dirty price, clean price @ $100
+/// </summary>
 public class CreditDefaultSwapFunctions
 {
+    public static CreditDefaultSwapPriceResult Price(
+        DateTime evalDate,
+        DateTime effectiveDate,
+        DateTime maturityDate,
+        double[] spreadsInBps,
+        string[] tenors,
+        double recoveryRate,
+        double couponInBps,
+        Frequency couponFrequency,
+        Protection.Side protectionSide, 
+        double flatInterestRate)
+    {
+        // we want to know the dirty price and clean price for a notional of $100, just like a bond with a face value of $100
+        var cds = PV(evalDate, effectiveDate, maturityDate, spreadsInBps, tenors, recoveryRate, couponInBps, 100, protectionSide, flatInterestRate);
+        double upfront = cds.PV;
+        double dirtyPrice = protectionSide switch
+        {
+            Protection.Side.Buyer => 100 - upfront,
+            Protection.Side.Seller => 100 + upfront,
+            _ => throw new NotImplementedException(),
+        };           
+        int numDays = effectiveDate.Subtract(evalDate).Days + 1;
+        double accrual = couponInBps * numDays / 360.0 / 100.0;
+        double cleanPrice = protectionSide switch
+        {
+            Protection.Side.Buyer => dirtyPrice + accrual,
+            Protection.Side.Seller => dirtyPrice - accrual,
+            _ => throw new NotImplementedException(),
+        };
+
+        // compute risky annuity (dv01)
+        // the risky duration (dv01) relates to a trade and is the change in mark-to-market of a CDS trade for a 1 basis point parallel shift in spreads.        
+
+        // for a par trade Sinitial = SCurrent risky duration is equal to the risky annuity.  
+        double cds2coupon = cds.FairSpread + 1;
+        var cds2 = PV(evalDate, effectiveDate, maturityDate, spreadsInBps, tenors, recoveryRate, cds2coupon, 100, protectionSide, flatInterestRate);
+        double riskyAnnuity = cds2.PV;
+        return (cleanPrice, dirtyPrice, riskyAnnuity);
+    }
+
     /// <summary>
-    /// Uses Flat Interest Rate Curve - instead of PiecewiseLogCubic ISDA rate curves
+    /// Uses Flat Interest Rate Curve. Other possible implementations include market ISDA rate curve (PiecewiseLogCubic)
     /// </summary>    
     public static CreditDefaultSwapPVResult PV(
         DateTime evaluationDate, 
@@ -19,7 +62,7 @@ public class CreditDefaultSwapFunctions
         double[] spreadsInBps, 
         string[] tenors, 
         double recoveryRate, 
-        int couponInBps, 
+        double couponInBps, 
         int notional, 
         Protection.Side protectionSide, 
         double flatInterestRate)
@@ -96,3 +139,16 @@ public static implicit operator (double pv, double fairSpread, double survivalPr
         return new CreditDefaultSwapPVResult(value.pv, value.fairSpread, value.survivalProbabilityPercentage, value.hazardRatePercenatge, value.defaultProbabilityPercentage);
     }
 }
+
+public record struct CreditDefaultSwapPriceResult(double cleanPrice, double dirtyPrice, double riskyAnnuity)
+{
+    public static implicit operator (double cleanPrice, double dirtyPrice, double riskyAnnuity)(CreditDefaultSwapPriceResult value)
+    {
+        return (value.cleanPrice, value.dirtyPrice, value.riskyAnnuity);
+    }
+
+    public static implicit operator CreditDefaultSwapPriceResult((double cleanPrice, double dirtyPrice, double riskyAnnuity) value)
+    {
+        return new CreditDefaultSwapPriceResult(value.cleanPrice, value.dirtyPrice, value.riskyAnnuity);
+    }
+}