public PiecewiseconstantHazardRate makeFromRT(List <double> t, double[] ht)
{
List <DateTime> jumpdate = jumpDates_;
PiecewiseconstantHazardRate curve = new PiecewiseconstantHazardRate(latestReference_, null, jumpDates_, t, ht.ToList());
return(curve);
}
public double ProtectionLegNPV_Exact(List <CashFlow> cf, double notional, PiecewiseconstantHazardRate hazard,
YieldTermStructure yt, DateTime tradedate, DateTime settlementDate, double recoveryrate, List <DateTime> Jumps, List <DateTime> creditCurveKnot)
{
DateTime Stepindate = tradedate.AddDays(1);
OMLib.Conventions.DayCount.Actual360 dc = new OMLib.Conventions.DayCount.Actual360();
if (cf.Count() == 0)
{
return(0.0);
}
DateTime t0 = tradedate;
DateTime T = cf.Last().CashFlowDate;
List <DateTime> JumpNodes = new List <DateTime>();
JumpNodes.Add(t0);
for (int j = 0; j < Jumps.Count; j++)
{
if ((DateTime.Compare(Jumps[j], T) < 0))
{
JumpNodes.Add(Jumps[j]);
}
}
JumpNodes.Add(T);
double ht0 = hazard.getRT(JumpNodes[0]);
double rt0 = yt.getRT(JumpNodes[0]);
double b0 = Math.Exp(-ht0 - rt0); // risky discount factor
double pv = 0.0;
double dPV = 0.0;
for (int i = 1; i < JumpNodes.Count; ++i)
{
double ht1 = hazard.getRT(JumpNodes[i]);
double rt1 = yt.getRT(JumpNodes[i]);
double b1 = Math.Exp(-ht1 - rt1);
double dht = ht1 - ht0;
double drt = rt1 - rt0;
double dhrt = dht + drt;
// The formula has been modified from ISDA (but is equivalent) to avoid log(exp(x)) and explicitly
// calculating the time step - it also handles the limit
if (Math.Abs(dhrt) < 1e-5)
{
dPV = dht * b0 * (Math.Exp(-dhrt) - 1) / (-dhrt);
}
else
{
dPV = (b0 - b1) * dht / dhrt;
}
pv += dPV;
ht0 = ht1;
rt0 = rt1;
b0 = b1;
}
return(pv * notional * (1 - recoveryrate) / yt.discount(settlementDate));
}
/**
* The normalised expected default settlement value paid on the exercise settlement
* date <b>when no defaults have yet occurred</b>.
* The actual default settlement is this multiplied by the (initial)
* index notional. This calculation assumes an homogeneous pool that can be described by a single index curve.
*
* @param timeToExpiry Time to expiry
* @param indexCurve Pseudo credit curve for the index.
* @param lgd The index Loss Given Default (LGD)
* @return The normalised expected default settlement value
*/
public double expectedDefaultSettlementValue(
double timeToExpiry,
PiecewiseconstantHazardRate indexCurve,
double lgd)
{
double q = Math.Exp(-indexCurve.getRT_(timeToExpiry));
double d = lgd * (1 - q);
return(d);
}
/**
* For a future expiry date, the default adjusted forward index value is the expected (full)
* value of the index plus the cash settlement of any defaults before
* the expiry date, valued on the (forward) cash settlement date (usually 3 working days after
* the expiry date - i.e. the expiry settlement date).
* This calculation assumes an homogeneous pool that can be described by a single index curve.
*
* @param fwdStartingCDS A forward starting CDS to represent cash flows in the index.
* The stepin date should be one day after the expiry and the cashSettlement
* date (usually) 3 working days after expiry. This must contain the index recovery rate.
* @param timeToExpiry the time in years between the trade date and expiry.
* This should use the same DCC as the curves (ACT365F unless manually changed).
* @param yieldCurve The yield curve
* @param indexCoupon The coupon of the index
* @param indexCurve Pseudo credit curve for the index.
* @return the default adjusted forward index value
*/
public double defaultAdjustedForwardIndexValue(
CDS fwdStartingCDS,
double timeToExpiry,
YieldTermStructure yieldCurve,
double indexCoupon,
PiecewiseconstantHazardRate indexCurve)
{
double defSet = expectedDefaultSettlementValue(timeToExpiry, indexCurve, fwdStartingCDS.getLGD());
return(defSet + _pricer.pv(fwdStartingCDS, yieldCurve, indexCurve, indexCoupon));
}
private PiecewiseconstantHazardRate[] adjustCurves(PiecewiseconstantHazardRate[] creditCurve, double amount)
{
int nCurves = creditCurve.Length;
PiecewiseconstantHazardRate[] adjCurves = new PiecewiseconstantHazardRate[nCurves];
for (int jj = 0; jj < nCurves; jj++)
{
adjCurves[jj] = adjustCreditCurve(creditCurve[jj], amount);
}
return(adjCurves);
}
public static PiecewiseconstantHazardRate[] buildCreditCurves(DateTime tradeDate, double[,] parSpreads, double[] recoveryRates, int[] tenors,
YieldTermStructure yieldCurve)
{
CdsAnalyticFactory factory = new CdsAnalyticFactory(0.0);
CDS[] pillarCDS = factory.makeImmCds(tradeDate, CDX_HY_TENORS);
int indexSize = parSpreads.GetLength(0);
PiecewiseconstantHazardRate[] creditCurves = new PiecewiseconstantHazardRate[indexSize];
//this section of code is hugely wasteful. If we do this for real (i.e. not just in a test), must improve
for (int i = 0; i < indexSize; i++)
{
int m = parSpreads.GetLength(1);
double[] spreads = new double[m];
for (int j = 0; j < m; j++)
{
spreads[j] = parSpreads[i, j];
}
int nPillars = spreads.Length;
CDS[] tempCDS = new CDS[nPillars];
double[] tempSpreads = new double[nPillars];
int count = 0;
for (int j = 0; j < nPillars; j++)
{
if (!double.IsNaN(parSpreads[i, j]))
{
tempCDS[count] = pillarCDS[j].withRecoveryRate(recoveryRates[i]);
tempSpreads[count] = spreads[j];
count++;
}
}
CDS[] calCDS = null;
double[] calSpreads = null;
if (count == nPillars)
{
calCDS = tempCDS;
calSpreads = tempSpreads;
}
else
{
calCDS = new CDS[count];
calSpreads = new double[count];
Array.Copy(tempCDS, 0, calCDS, 0, count);
Array.Copy(tempSpreads, 0, calSpreads, 0, count);
}
CreditCurveCalibrator calibrator = new CreditCurveCalibrator(calCDS, yieldCurve);
creditCurves[i] = calibrator.calibrate(calSpreads);
}
return(creditCurves);
}
/**
* The (default adjusted) intrinsic forward spread of an index <b>when no defaults have yet occurred</b>.
* This is defined as the ratio of expected value of the
* protection leg and default settlement to the expected value of the annuity at expiry.
* This calculation assumes an homogeneous pool that can be described by a single index curve.
*
* @param fwdStartingCDS forward starting CDS to represent cash flows in the index.
* The stepin date should be one day after the expiry and the cashSettlement
* date (usually) 3 working days after expiry
* @param timeToExpiry the time in years between the trade date and expiry.
* This should use the same DCC as the curves (ACT365F unless manually changed).
* @param yieldCurve The yield curve
* @param indexCurve Pseudo credit curve for the index.
* @return The normalised expected default settlement value
*/
public double defaultAdjustedForwardSpread(
CDS fwdStartingCDS,
double timeToExpiry,
YieldTermStructure yieldCurve,
PiecewiseconstantHazardRate indexCurve)
{
double defSettle = expectedDefaultSettlementValue(timeToExpiry, indexCurve, fwdStartingCDS.getLGD());
double protLeg = _pricer.protectionLeg(fwdStartingCDS, yieldCurve, indexCurve);
double ann = _pricer.annuity(fwdStartingCDS, yieldCurve, indexCurve);
return((protLeg + defSettle) / ann);
}
public PiecewiseconstantHazardRate makeFromR(List <double> t, double[] h)
{
List <DateTime> jumpdate = jumpDates_;
List <double> rt_ = new List <double>();
for (int i = 0; i < t.Count; i++)
{
rt_.Add(h[i] * t[i]); // We make no check that rt is ascending (i.e. we allow negative forward rates)
}
PiecewiseconstantHazardRate curve = new PiecewiseconstantHazardRate(latestReference_, null, jumpDates_, t, rt_);
return(curve);
}
/**
* The normalised expected default settlement value paid on the exercise settlement date.
* The actual default settlement is this multiplied by the (initial)
* index notional. This calculation assumes an homogeneous pool that can be described by a single index curve.
* @param initialIndexSize Initial index size
* @param timeToExpiry Time to expiry
* @param indexCurve Pseudo credit curve for the index.
* @param lgd The index Loss Given Default (LGD)
* @param initialDefaultSettlement The (normalised) value of any defaults that have already occurred
* (e.g. if two defaults have occurred from an index with
* initially 100 entries, and the realised recovery rates are 0.2 and 0.35, the this value is (0.8 + 0.65)/100 )
* @param numDefaults The number of defaults that have already occurred
* @return The normalised expected default settlement value
*/
public double expectedDefaultSettlementValue(
int initialIndexSize,
double timeToExpiry,
PiecewiseconstantHazardRate indexCurve,
double lgd,
double initialDefaultSettlement,
int numDefaults)
{
double defFrac = numDefaults / ((double)initialIndexSize);
// this upper range is if all current defaults have zero recovery
double q = Math.Exp(-indexCurve.getRT_(timeToExpiry));
double d = (1 - defFrac) * lgd * (1 - q) + initialDefaultSettlement;
return(d);
}
public void Pricing(YieldTermStructure yt, PiecewiseconstantHazardRate hazard)
{
//Calculate PV for both legs
CashFlowCalculation engine = new CashFlowCalculation();
this.FixLeg = engine.Calculation(this.PremiumRate, this.Notional, this.Payment_Schedule, this.tradedate, yt, hazard, this.Cashsettlement, formerpaymentdate);
NPV_PricingEngine engine2 = new NPV_PricingEngine();
double pv_premium = engine2.PremiumLegNPV_Exact(this.FixLeg, this.piecewiseHazardRate, this.yieldcurve, this.tradedate, this.tradedate.AddDays(3), this.Notional, this.PremiumRate, yt.jumpDates_, formerpaymentdate);
double pv_protection = engine2.ProtectionLegNPV_Exact(this, this.Notional, this.piecewiseHazardRate, this.yieldcurve, this.tradedate, this.tradedate.AddDays(3), this.Recovery, yt.t, hazard.t);
this.pv = pv_protection - pv_premium;
this.marketvalue = this.pv + accruedamt;
}
public PiecewiseconstantHazardRate adjustCreditCurve(
PiecewiseconstantHazardRate creditCurve,
double amount,
int firstKnot,
int lastKnot)
{
double[] rt = creditCurve.rt.ToArray();
double[] rtAdj = rt;
for (int i = firstKnot; i < lastKnot; i++)
{
rtAdj[i] = rt[i] * amount;
}
PiecewiseconstantHazardRate hazard = new PiecewiseconstantHazardRate(creditCurve.latestReference_, null, null, null, null);
return(hazard.makeFromRT(creditCurve.t, rtAdj));
}
/**
* For a future expiry date, the default adjusted forward index value is the expected (full)
* value of the index plus the cash settlement of any defaults before
* the expiry date, valued on the (forward) cash settlement date (usually 3 working days after
* the expiry date - i.e. the expiry settlement date).
* This calculation assumes an homogeneous pool that can be described by a single index curve.
*
* @param fwdStartingCDS A forward starting CDS to represent cash flows in the index.
* The stepin date should be one day after the expiry and the cashSettlement
* date (usually) 3 working days after expiry. This must contain the index recovery rate.
* @param timeToExpiry the time in years between the trade date and expiry.
* This should use the same DCC as the curves (ACT365F unless manually changed).
* @param initialIndexSize The initial number of names in the index
* @param yieldCurve The yield curve
* @param indexCoupon The coupon of the index
* @param indexCurve Pseudo credit curve for the index.
* @param initialDefaultSettlement The (normalised) value of any defaults that have already
* occurred (e.g. if two defaults have occurred from an index with
* initially 100 entries, and the realised recovery rates are 0.2 and 0.35, the this value is (0.8 + 0.65)/100 )
* @param numDefaults The number of defaults that have already occurred
* @return the default adjusted forward index value
*/
public double defaultAdjustedForwardIndexValue(
CDS fwdStartingCDS,
double timeToExpiry,
int initialIndexSize,
YieldTermStructure yieldCurve,
double indexCoupon,
PiecewiseconstantHazardRate indexCurve,
double initialDefaultSettlement,
int numDefaults)
{
double f = (initialIndexSize - numDefaults) / ((double)initialIndexSize);
double defSet = expectedDefaultSettlementValue(initialIndexSize, timeToExpiry, indexCurve, fwdStartingCDS.getLGD(),
initialDefaultSettlement, numDefaults);
return(defSet + f * _pricer.pv(fwdStartingCDS, yieldCurve, indexCurve, indexCoupon));
}
/**
* The (default adjusted) intrinsic forward spread of an index.
* This is defined as the ratio of expected value of the protection leg and default settlement to
* the expected value of the annuity at expiry. This calculation assumes an homogeneous pool that
* can be described by a single index curve.
*
* @param fwdStartingCDS forward starting CDS to represent cash flows in the index.
* The stepin date should be one day after the expiry and the cashSettlement
* date (usually) 3 working days after expiry
* @param timeToExpiry the time in years between the trade date and expiry.
* This should use the same DCC as the curves (ACT365F unless manually changed).
* @param initialIndexSize The initial number of names in the index
* @param yieldCurve The yield curve
* @param indexCurve Pseudo credit curve for the index.
* @param initialDefaultSettlement The (normalised) value of any defaults that have
* already occurred (e.g. if two defaults have occurred from an index with
* initially 100 entries, and the realised recovery rates are 0.2 and 0.35, the this value is (0.8 + 0.65)/100 )
* @param numDefaults The number of defaults that have already occurred
* @return The normalised expected default settlement value
*/
public double defaultAdjustedForwardSpread(
CDS fwdStartingCDS,
double timeToExpiry,
int initialIndexSize,
YieldTermStructure yieldCurve,
PiecewiseconstantHazardRate indexCurve,
double initialDefaultSettlement,
int numDefaults)
{
double f = (initialIndexSize - numDefaults) / ((double)initialIndexSize);
double defSettle = expectedDefaultSettlementValue(initialIndexSize, timeToExpiry, indexCurve, fwdStartingCDS.getLGD(),
initialDefaultSettlement, numDefaults);
double protLeg = f * _pricer.protectionLeg(fwdStartingCDS, yieldCurve, indexCurve);
double ann = f * _pricer.annuity(fwdStartingCDS, yieldCurve, indexCurve);
return((protLeg + defSettle) / ann);
}
public PiecewiseconstantHazardRate adjustCreditCurve(PiecewiseconstantHazardRate creditCurve, double amount)
{
if (creditCurve == null)
{
return(creditCurve);
}
int nKnots = creditCurve.t.Count;
double[] rt = creditCurve.rt.ToArray();
double[] rtAdj = new double[nKnots];
for (int i = 0; i < nKnots; i++)
{
rtAdj[i] = rt[i] * amount;
}
PiecewiseconstantHazardRate hazard = new PiecewiseconstantHazardRate(creditCurve.latestReference_, null, null, null, null);
return(hazard.makeFromRT(creditCurve.t, rtAdj));
}
public void curve_output(YieldTermStructure yt, PiecewiseconstantHazardRate ct)
{
double it = ct.SurvivalProb(new DateTime(2021, 06, 20));
List <double> yield = new List <double>();
for (int j = 1; j < 120; j++)
{
DateTime t = this.evalDate.AddMonths(j);
double t_ = (double)j / 12;
yield.Add(-Math.Log(yt.discount(t)) / t_);
}
this.yield_series = yield;
List <double> survival = new List <double>();
for (int j = 1; j < 120; j++)
{
DateTime t = this.tradedate.AddMonths(j);
survival.Add(ct.SurvivalProb(t));
}
this.survival_prob = survival;
}
public double PremiumLegNPV_Exact(CDS cds, PiecewiseconstantHazardRate hazard,
YieldTermStructure yt, DateTime tradedate, DateTime settlementDate, double notional, double coupon, List <double> Jumps, DateTime lastpayment)
{
double ita = (double)365 / 360;
double totalNPV = 0.0;
CdsCoupon[] cf = cds.getCoupons();
for (int i = 0; i < cf.Length; ++i)
{
totalNPV += cf[i].getYearFrac() * notional * Math.Exp(-hazard.getRT_(cf[i].getEffEnd()))
* Math.Exp(-yt.getRT_(cf[i].getEffEnd()));
}
double accrualpaidondefault = calculateSinglePeriodAccrualOnDefault(cf, coupon, tradedate, yt, hazard, lastpayment);
totalNPV += ita * coupon * accrualpaidondefault * notional / yt.discount(tradedate.AddDays(3));
OMLib.Conventions.DayCount.Actual360 dc = new OMLib.Conventions.DayCount.Actual360();
Calendar calendar = new UnitedStates();
return(totalNPV / Math.Exp(-yt.getRT_(cds.getCashSettleTime())));
}
public PiecewiseconstantHazardRate[] adjustCurves(
PiecewiseconstantHazardRate[] creditCurve,
double amount,
int[] firstKnots,
int[] lastknots)
{
int nCurves = creditCurve.Length;
PiecewiseconstantHazardRate[] adjCurves = new PiecewiseconstantHazardRate[nCurves];
for (int jj = 0; jj < nCurves; jj++)
{
if (creditCurve[jj] == null)
{
adjCurves[jj] = null;
}
else
{
adjCurves[jj] = adjustCreditCurve(creditCurve[jj], amount, firstKnots[jj], lastknots[jj]);
}
}
return(adjCurves);
}
public double PremiumLegNPV_Exact(List <CashFlow> cf, PiecewiseconstantHazardRate hazard,
YieldTermStructure yt, DateTime tradedate, DateTime settlementDate, double notional, double coupon, List <DateTime> Jumps, DateTime lastpayment)
{
if (cf.Count() == 0)
{
return(0.0);
}
double ita = (double)365 / 360;
double totalNPV = 0.0;
for (int i = 0; i < cf.Count; ++i)
{
totalNPV += cf[i].Amount * cf[i].DiscountFactor * cf[i].Survivalprobability;
}
double accrualpaidondefault = calculateSinglePeriodAccrualOnDefault(cf, coupon, tradedate, yt, hazard, Jumps, lastpayment);
totalNPV += ita * coupon * accrualpaidondefault * notional / yt.discount(tradedate.AddDays(3));
OMLib.Conventions.DayCount.Actual360 dc = new OMLib.Conventions.DayCount.Actual360();
Calendar calendar = new UnitedStates();
return(totalNPV / yt.discount(settlementDate));
}
public double PremiumLegNPV_Approx(List <CashFlow> cf, PiecewiseconstantHazardRate HazardTermStructure,
YieldTermStructure yt, DateTime tradedate, DateTime settlementDate)
{
if (cf.Count() == 0)
{
return(0.0);
}
double totalNPV = 0.0;
for (int i = 0; i < cf.Count; ++i)
{
if (i == 0)
{
totalNPV += cf[i].Amount * cf[i].DiscountFactor * 1 / 2 * (1 + cf[i].Survivalprobability);
}
else
{
totalNPV += cf[i].Amount * 1 / 2 * (cf[i].Survivalprobability
+ cf[i - 1].Survivalprobability) * cf[i].DiscountFactor;
}
}
return(totalNPV);
}
public IntrinsicIndexDataBundle adjustCurves(
double[] indexPUF,
CDS[] indexCDS,
double indexCoupon,
YieldTermStructure yieldCurve,
IntrinsicIndexDataBundle intrinsicData)
{
int nIndexTerms = indexCDS.Length;
if (nIndexTerms == 1)
{
return(adjustCurves(indexPUF[0], indexCDS[0], indexCoupon, yieldCurve, intrinsicData));
}
double[] indexKnots = new double[nIndexTerms];
for (int i = 0; i < nIndexTerms; i++)
{
indexKnots[i] = indexCDS[i].getProtectionEnd();
}
PiecewiseconstantHazardRate[] creditCurves = intrinsicData.getCreditCurves();
int nCurves = creditCurves.Length;
//we cannot assume that all the credit curves have knots at the same times or that the terms of the indices fall on these knots.
PiecewiseconstantHazardRate[] modCreditCurves = new PiecewiseconstantHazardRate[nCurves];
int[,] indexMap = new int[nCurves, nIndexTerms];
for (int i = 0; i < nCurves; i++)
{
if (creditCurves[i] == null)
{
modCreditCurves[i] = null; //null credit curves correspond to defaulted names, so are ignored
}
else
{
double[] ccKnots = creditCurves[i].t.ToArray();
double[] comKnots = DoublesScheduleGenerator.combineSets(ccKnots, indexKnots);
int nKnots = comKnots.Length;
if (nKnots == ccKnots.Length)
{
modCreditCurves[i] = creditCurves[i];
}
else
{
double[] rt = new double[nKnots];
for (int j = 0; j < nKnots; j++)
{
rt[j] = creditCurves[i].getRT_(comKnots[j]);
}
PiecewiseconstantHazardRate hazard = new PiecewiseconstantHazardRate(creditCurves[i].latestReference_, null, null, null, null);
modCreditCurves[i] = hazard.makeFromRT(comKnots.ToList(), rt);
}
for (int j = 0; j < nIndexTerms; j++)
{
int index = Array.BinarySearch(modCreditCurves[i].t.ToArray(), indexKnots[j]);
indexMap[i, j] = index;
}
}
}
int[] startKnots = new int[nCurves];
int[] endKnots = new int[nCurves];
double alpha = 1.0;
for (int i = 0; i < nIndexTerms; i++)
{
if (i == (nIndexTerms - 1))
{
for (int jj = 0; jj < nCurves; jj++)
{
if (modCreditCurves[jj] != null)
{
endKnots[jj] = modCreditCurves[jj].t.Count;
}
}
}
else
{
for (int jj = 0; jj < nCurves; jj++)
{
if (modCreditCurves[jj] != null)
{
endKnots[jj] = indexMap[jj, i] + 1;
}
}
}
IntrinsicIndexDataBundle modIntrinsicData = intrinsicData.withCreditCurves(modCreditCurves);
Func <double, double> func = getHazardRateAdjFunction(indexPUF[i], indexCDS[i], indexCoupon, yieldCurve,
modIntrinsicData, startKnots, endKnots);
alpha = ROOTFINDER.getRoot(func, alpha);
modCreditCurves = adjustCurves(modCreditCurves, alpha, startKnots, endKnots);
startKnots = endKnots;
}
return(intrinsicData.withCreditCurves(modCreditCurves));
}
public PiecewiseconstantHazardRate impliedHazardRate(double targetNPV, double Notional, DateTime tradedate, List <double> spreads, List <DateTime> tenor,
YieldTermStructure yt,
OMLib.Conventions.DayCount.DayCounter dayCounter, string frequency, DateTime firstpaymentdate, DateTime lastpaymentdate, List <DateTime> Jumps,
double recoveryRate = 0.4,
double accuracy = 1e-8)
{
OMLib.Calendars.Calendar cal = new OMLib.Calendars.Calendar();
PiecewiseconstantHazardRate probability = new PiecewiseconstantHazardRate(tradedate, null, tenor,
null, null);
double error = 2;
double pv_premium = 0;
double pv_protection = 0;
NPV_PricingEngine engine = new NPV_PricingEngine();
//Join the knots
List <DateTime> result = new List <DateTime>();
int index = 0, indexj = 0, lastIndex = 0;
while (index < Jumps.Count || indexj < tenor.Count)
{
if (lastIndex > 0)
{
if (index >= Jumps.Count)
{
if (!DateTime.Equals(result.Last(), tenor[indexj]))
{
result.Add(tenor[indexj]);
lastIndex++;
}
indexj++;
continue;
}
if (indexj >= tenor.Count)
{
if (!DateTime.Equals(result.Last(), Jumps[index]))
{
result.Add(Jumps[index]);
lastIndex++;
}
index++;
continue;
}
}
DateTime smallestVal = tenor.Last();
// Choose the smaller of a or b
if (DateTime.Compare(Jumps[index], tenor[indexj]) < 0)
{
smallestVal = Jumps[index++];
}
else
{
smallestVal = tenor[indexj++];
}
// Don't insert duplicates
if (lastIndex > 0)
{
if (!DateTime.Equals(result.Last(), smallestVal))
{
result.Add(smallestVal);
lastIndex++;
}
}
else
{
result.Add(smallestVal);
lastIndex++;
}
}
for (int i = 0; i < spreads.Count(); i++)
{
//Accrued Interest
double guess = spreads[i] / (1 - recoveryRate);
//spreads[i] / (1 - recoveryRate);
probability.addhazardrate(tenor[i], guess);
double target = targetNPV - (double)85 / 360 * spreads[i] * Notional;
error = 2;
double step = guess * 0.01;
int j = 0;
double error_0 = 1000;
while (Math.Abs(error) > accuracy)
{
CashFlowCalculation cf_calculation = new CashFlowCalculation();
//Schedule should be built here
List <DateTime> schedule = new List <DateTime>();
schedule = PremiumDates(tenor[i], firstpaymentdate, frequency);
List <CashFlow> FixLeg = cf_calculation.Calculation(spreads[i], Notional, schedule, tradedate, yt, probability, 3, lastpaymentdate);
//pv_premium = engine.PremiumLegNPV_Approx(FixLeg, probability, yt, tradedate.AddDays(1), tradedate.AddDays(3)/*,Notional,spreads[i]*/);
pv_premium = engine.PremiumLegNPV_Exact(FixLeg, probability, yt, tradedate, tradedate.AddDays(3), Notional, spreads[i], Jumps, lastpaymentdate);
pv_protection = engine.ProtectionLegNPV_Exact(FixLeg, Notional, probability, yt, tradedate, tradedate.AddDays(3), recoveryRate, result, tenor);
//pv_protection = engine.ProtectionLeg_Approx(FixLeg, Notional, probability, yt, tradedate, tradedate.AddDays(3), recoveryRate);
int k1 = dayCounter.DayCount(tradedate, FixLeg[1].CashFlowDate);
error = pv_protection - pv_premium - target;
if (j > 1)
{
double temp = guess;
guess = guess + step * error / (error_0 - error);
step = guess - temp;
}
else
{
guess = guess + step;
}
error_0 = error;
j = j + 1;
probability.update(guess);
}
}
// probability.update2();
return(probability);
}
public List <CashFlow> Calculation(double fixrate, double initialNotional, List <DateTime> fixedSchedule, DateTime tradedate,
YieldTermStructure yt, PiecewiseconstantHazardRate piecewiseFlatHazardRate, int settlement, DateTime lastpaymentdate)
{
List <CashFlow> result = new List <CashFlow>();
OMLib.Conventions.DayCount.Actual360 daycountconvention = new OMLib.Conventions.DayCount.Actual360();
for (int i = 0; i < fixedSchedule.Count; i++)
{
CashFlow cf = new CashFlow();
Calendar calendar = new UnitedStates();
//fixedSchedule[i] = calendar.adjust(fixedSchedule[i], BusinessDayConvention.Following);
cf.CashFlowDate = fixedSchedule[i];
if (i == 0)
{
//The protection buyer pays the next coupon in full on the coupon date,
//(even if this is the next day); in return the buyer receives (from the protection seller) the accrued
//interest[Geoff Chaplin. Credit Derivatives.], which is paid on the cash settlement date.
if (lastpaymentdate != null)
{
lastpaymentdate = calendar.adjust(lastpaymentdate, BusinessDayConvention.Following);
cf.Amount = (double)initialNotional * fixrate * (daycountconvention.DayCount(lastpaymentdate, fixedSchedule[i])) / 360;
}
else
{
cf.Amount = (double)initialNotional * fixrate * (daycountconvention.DayCount(tradedate, fixedSchedule[i])) / 360;
}
}
else
{
//Each coupon is equal to (annual coupon/360) (# of days in accrual period).
//The accrual period always stretches from (previous coupon payment date) through (this coupon
//payment date–1), inclusive; except a contract's last accrual period, which ends with (and
//includes) the unadjusted maturity date.
if (i == fixedSchedule.Count - 1)
{
cf.Amount = (double)initialNotional * fixrate * (daycountconvention.DayCount(fixedSchedule[i - 1], fixedSchedule[i].AddDays(1))) / 360;
}
else
{
cf.Amount = (double)initialNotional * fixrate * (daycountconvention.DayCount(fixedSchedule[i - 1], fixedSchedule[i])) / 360;
}
}
//Assume all cash flows are discounted to the cash settlement date
cf.DiscountFactor = yt.discount(fixedSchedule[i]);
if (i == fixedSchedule.Count - 1)
{
cf.Survivalprobability = piecewiseFlatHazardRate.SurvivalProb(fixedSchedule[i].AddDays(1));
}
else
{
cf.Survivalprobability = piecewiseFlatHazardRate.SurvivalProb(fixedSchedule[i]);
}
result.Add(cf);
}
return(result);
}
public void testMethod1()
{
for (int i = 0; i < PRICES.Length; i++)
{
PILLAR_PUF[i] = new PointsUpFront(INDEX_COUPON, 1 - PRICES[i]);
}
int pos = 1; // target CDX is 5Y
CDS targentCDX = CDX[pos];
int n = PILLAR_PUF.Length;
double[] indexPUF = new double[n];
for (int i = 0; i < n; i++)
{
indexPUF[i] = PILLAR_PUF[i].getPointsUpFront();
}
IntrinsicIndexDataBundle dataDefaulted = INTRINSIC_DATA;
int accrualDays = targentCDX.getAccuredDays();
double accruedPremium = targentCDX.getAccruedPremium(INDEX_COUPON) * NOTIONAL * dataDefaulted.getIndexFactor();
/*
* Using credit curves for constituent single name CDSs.
* The curves are adjusted by using only the target CDX.
*/
double cleanPV = INDEX_CAL.indexPV(targentCDX, INDEX_COUPON, YIELD_CURVE, dataDefaulted) * NOTIONAL;
double dirtyPV = INDEX_CAL.indexPV(targentCDX, INDEX_COUPON, YIELD_CURVE, dataDefaulted, CdsPriceType.DIRTY) * NOTIONAL; // should be consistent with 1 - PRICES[pos]
double expectedLoss = INDEX_CAL.expectedDefaultSettlementValue(targentCDX.getProtectionEnd(), dataDefaulted) * NOTIONAL;
double cleanRPV01 = INDEX_CAL.indexAnnuity(targentCDX, YIELD_CURVE, dataDefaulted);
double dirtyRPV01 = INDEX_CAL.indexAnnuity(targentCDX, YIELD_CURVE, dataDefaulted, CdsPriceType.DIRTY);
double durationWeightedAverageSpread = INDEX_CAL.intrinsicIndexSpread(targentCDX, YIELD_CURVE, dataDefaulted) *
TEN_THOUSAND;
double parallelIR01 = INDEX_CAL.parallelIR01(targentCDX, INDEX_COUPON, YIELD_CURVE, dataDefaulted) * NOTIONAL;
double[] jumpToDefault = INDEX_CAL.jumpToDefault(targentCDX, INDEX_COUPON, YIELD_CURVE, dataDefaulted);
for (int i = 0; i < jumpToDefault.Length; ++i)
{
jumpToDefault[i] *= NOTIONAL;
}
double[] recovery01 = INDEX_CAL.recovery01(targentCDX, INDEX_COUPON, YIELD_CURVE, dataDefaulted);
for (int i = 0; i < recovery01.Length; ++i)
{
recovery01[i] *= NOTIONAL;
}
IntrinsicIndexDataBundle adjCurvesAll = PSA.adjustCurves(indexPUF, CDX, INDEX_COUPON, YIELD_CURVE,
dataDefaulted);
double cleanPVAll = INDEX_CAL.indexPV(targentCDX, INDEX_COUPON, YIELD_CURVE, adjCurvesAll) * NOTIONAL;
double dirtyPVAll = INDEX_CAL.indexPV(targentCDX, INDEX_COUPON, YIELD_CURVE, adjCurvesAll, CdsPriceType.DIRTY) *
NOTIONAL; // should be consistent with 1 - PRICES[pos]
double expectedLossAll = INDEX_CAL.expectedDefaultSettlementValue(targentCDX.getProtectionEnd(), adjCurvesAll) *
NOTIONAL;
double cleanRPV01All = INDEX_CAL.indexAnnuity(targentCDX, YIELD_CURVE, adjCurvesAll);
double dirtyRPV01All = INDEX_CAL.indexAnnuity(targentCDX, YIELD_CURVE, adjCurvesAll, CdsPriceType.DIRTY);
double durationWeightedAverageSpreadAll = INDEX_CAL.intrinsicIndexSpread(targentCDX, YIELD_CURVE, adjCurvesAll) *
TEN_THOUSAND;
double parallelIR01All = INDEX_CAL.parallelIR01(targentCDX, INDEX_COUPON, YIELD_CURVE, adjCurvesAll) * NOTIONAL;
double[] jumpToDefaultAll = INDEX_CAL.jumpToDefault(targentCDX, INDEX_COUPON, YIELD_CURVE, adjCurvesAll);
for (int i = 0; i < jumpToDefaultAll.Length; ++i)
{
jumpToDefaultAll[i] *= NOTIONAL;
}
double[] recovery01All = INDEX_CAL.recovery01(targentCDX, INDEX_COUPON, YIELD_CURVE, adjCurvesAll);
for (int i = 0; i < recovery01All.Length; ++i)
{
recovery01All[i] *= NOTIONAL;
}
PiecewiseconstantHazardRate indexCurve = (new Commons.FastCreditCurveBuilder()).calibrateCreditCurve(targentCDX,
INDEX_COUPON, YIELD_CURVE, indexPUF[pos]); // single node index curve, indexFactors cancel out
double cleanPriceIndexCurve = PRICER_OG_FIX.pv(targentCDX, YIELD_CURVE, indexCurve, INDEX_COUPON) *
dataDefaulted.getIndexFactor() * NOTIONAL;
double dirtyPriceIndexCurve = PRICER_OG_FIX.pv(targentCDX, YIELD_CURVE, indexCurve, INDEX_COUPON,
CdsPriceType.DIRTY) * dataDefaulted.getIndexFactor() * NOTIONAL;
double cleanRPV01IndexCurve = PRICER_OG_FIX.annuity(targentCDX, YIELD_CURVE, indexCurve) *
dataDefaulted.getIndexFactor();
double dirtyRPV01IndexCurve = PRICER_OG_FIX.annuity(targentCDX, YIELD_CURVE, indexCurve, CdsPriceType.DIRTY) *
dataDefaulted.getIndexFactor();
double spreadIndexCurve = PRICER_OG_FIX.parSpread(targentCDX, YIELD_CURVE, indexCurve) * TEN_THOUSAND;
}
//public double ProtectionLeg_Approx(List<CashFlow> cf, double notional, PiecewiseconstantHazardRate HazardTermStructure,
// YieldTermStructure yt, DateTime tradedate, DateTime settlementDate, double recoveryrate)
//{
// if (cf.Count() == 0)
// {
// return 0.0;
// }
// double totalNPV = 0.0;
// for (int i = 0; i < cf.Count; ++i)
// {
// if (i == 0)
// {
// totalNPV += (1 - recoveryrate)*notional * cf[i].DiscountFactor * (1- cf[i].Survivalprobability);
// }
// else
// {
// totalNPV += notional * cf[i].DiscountFactor * (cf[i - 1].Survivalprobability
// - cf[i].Survivalprobability) * (1 - recoveryrate);
// }
// }
// return totalNPV/yt.discount(settlementDate);
//}
public double calculateSinglePeriodAccrualOnDefault(List <CashFlow> cf, double coupon,
DateTime tradedate,
YieldTermStructure yieldCurve,
PiecewiseconstantHazardRate creditCurve, List <DateTime> Jumps, DateTime lastpayment)
{
double Acc = 0;
DateTime effectiveStart = tradedate.AddDays(1);
for (int i = 0; i < cf.Count; ++i)
{
//Accured on default
DateTime t_0 = (i > 0) ? cf[i - 1].CashFlowDate.AddDays(-1) : tradedate;
DateTime T = cf[i].CashFlowDate;
if (i == cf.Count - 1)
{
T = cf[i].CashFlowDate;
}
else
{
T = cf[i].CashFlowDate.AddDays(-1);
}
List <DateTime> knots = new List <DateTime>();
knots.Add(t_0);
for (int j = 0; j < Jumps.Count; j++)
{
if ((DateTime.Compare(Jumps[j], T) < 0) && (DateTime.Compare(t_0, Jumps[j]) < 0))
{
knots.Add(Jumps[j]);
}
}
knots.Add(T);
DateTime t = knots[0];
double ht0 = creditCurve.getRT(t);
double rt0 = yieldCurve.getRT(t);
double b0 = Math.Exp(-rt0 - ht0); // this is the risky discount factor
OMLib.Conventions.DayCount.Actual365 dc = new OMLib.Conventions.DayCount.Actual365();
double t0;
if (i == 0)
{
t0 = (double)dc.DayCount(lastpayment.AddDays(1), knots[0]) / 365;
}
else
{
t0 = (double)dc.DayCount(cf[i].CashFlowDate.AddDays(1), knots[0]) / 365;
}
double pv = 0.0;
int nItems = knots.Count;
for (int j = 1; j < nItems; ++j)
{
t = knots[j];
double ht1 = creditCurve.getRT(t);
double rt1 = yieldCurve.getRT(t);
double b1 = Math.Exp(-rt1 - ht1);
double dt = (double)dc.DayCount(knots[j - 1], knots[j]) / 365;
double dht = ht1 - ht0;
double drt = rt1 - rt0;
double dhrt = dht + drt + 1e-50;
double tPV;
double t1;
if (i == 0)
{
t1 = (double)dc.DayCount(lastpayment.AddDays(1), knots[j]) / 365;
}
else
{
t1 = (double)dc.DayCount(cf[i].CashFlowDate.AddDays(1), knots[j]) / 365;
}
if (Math.Abs(dhrt) < 1e-5)
{
tPV = dht * b0 * (t0 * (Math.Exp(-dhrt) - 1) / (-dhrt) + dt * ((-dhrt - 1) * (Math.Exp(-dhrt) - 1) - dhrt) / (dhrt * dhrt));
}
else
{
tPV = dht * dt / dhrt * ((b0 - b1) / dhrt - b1);
}
t0 = t1;
pv += tPV;
ht0 = ht1;
rt0 = rt1;
b0 = b1;
}
Acc += pv;
}
return(Acc);
}
public double calculateSinglePeriodAccrualOnDefault(CdsCoupon[] cf, double coupon,
DateTime tradedate,
YieldTermStructure yieldCurve,
PiecewiseconstantHazardRate creditCurve, DateTime lastpayment)
{
double Acc = 0;
DateTime effectiveStart = tradedate.AddDays(1);
for (int i = 0; i < cf.Length; ++i)
{
//Accured on default
double t_0 = (i > 0) ? cf[i].getEffStart() : 0;
double T = cf[i].getEffEnd();
T = cf[i].getPaymentTime();
List <double> knots = new List <double>();
knots.Add(t_0);
for (int j = 0; j < yieldCurve.t.Count; j++)
{
if ((yieldCurve.t[j] < T) && (t_0 < yieldCurve.t[j]))
{
knots.Add(yieldCurve.t[j]);
}
}
knots.Add(T);
double t = knots[0];
double ht0 = creditCurve.getRT_(t);
double rt0 = yieldCurve.getRT_(t);
double b0 = Math.Exp(-rt0 - ht0); // this is the risky discount factor
OMLib.Conventions.DayCount.Actual365 dc = new OMLib.Conventions.DayCount.Actual365();
double t0;
if (i == 0)
{
t0 = knots[0] - cf[0].getEffStart();
}
else
{
t0 = knots[0] - cf[i].getEffStart();
}
double pv = 0.0;
int nItems = knots.Count;
for (int j = 1; j < nItems; ++j)
{
t = knots[j];
double ht1 = creditCurve.getRT_(t);
double rt1 = yieldCurve.getRT_(t);
double b1 = Math.Exp(-rt1 - ht1);
double dt = knots[j] - knots[j - 1];
double dht = ht1 - ht0;
double drt = rt1 - rt0;
double dhrt = dht + drt + 1e-50;
double tPV;
double t1;
if (i == 0)
{
t1 = knots[j] - cf[0].getEffStart();
}
else
{
t1 = knots[j] - cf[i].getEffStart();
}
if (Math.Abs(dhrt) < 1e-5)
{
tPV = dht * b0 * (t0 * (Math.Exp(-dhrt) - 1) / (-dhrt) + dt * ((-dhrt - 1) * (Math.Exp(-dhrt) - 1) - dhrt) / (dhrt * dhrt));
}
else
{
tPV = dht * dt / dhrt * ((b0 - b1) / dhrt - b1);
}
t0 = t1;
pv += tPV;
ht0 = ht1;
rt0 = rt1;
b0 = b1;
}
Acc += pv;
}
return(Acc);
}
public void hazardratecurve(YieldTermStructure yt, OMLib.Conventions.DayCount.Actual365 dayCounter, List <double> QuotedSpot, List <double> QuotedSpread, double FixRate, double Spread_traded, double Upfront, DateTime maturity,
DateTime firstpaymentdate, DateTime evalDate, DateTime formerpaymentdate, string frequency, double recovery)
{
List <DateTime> dates = new List <DateTime>();
List <DateTime> discountDates = new List <DateTime>();
int accrued = dayCounter.DayCount(formerpaymentdate, tradedate);
if (QuotedSpread == null)
{
if (Spread_traded > 0)
{
// Infer the constant hazard rate from the quoted spread
/*When the Spread is input: Consider a CDS with exactly the same specification as
* the Standard CDS except that its Coupon Rate is equal to the Spread. Assume that
* the Upfront of this CDS is zero. Solve for the Constant Hazard Rate that gives this
* CDS a MTM equal to minus its Accrued Premium (based on a Coupon Rate equal
* to Spread) discounted riskless to T
*/
impliedhazardrate ih = new impliedhazardrate();
List <double> spread = new List <double> {
Spread_traded
};
List <DateTime> mat = new List <DateTime> {
maturity
};
PiecewiseconstantHazardRate flatrate = ih.impliedHazardRate(-this.Notional * Spread_traded * accrued / 360, this.Notional,
this.tradedate, spread, mat, yt, dayCounter, frequency, firstpaymentdate, this.formerpaymentdate, this.Jump_Nodes, recovery);
this.piecewiseHazardRate = flatrate;
}
else if (Upfront > 0)
{
// Infer the constant hazard rate from the quoted upfront
/*When the Upfront is input: Solve for the Constant Hazard Rate that gives the
* Standard CDS a MTM equal to Notional * Upfront – AccruedPremium discounted riskless to T*/
impliedhazardrate ih = new impliedhazardrate();
List <double> spread = new List <double> {
Spread_traded
};
List <DateTime> mat = new List <DateTime> {
maturity
};
PiecewiseconstantHazardRate flatrate = ih.impliedHazardRate(this.Notional * Upfront - this.accruedamt, this.Notional, this.tradedate,
spread, mat, yt, dayCounter, frequency, firstpaymentdate, this.formerpaymentdate, this.Jump_Nodes, recovery);
this.piecewiseHazardRate = flatrate;
}
}
else
// Construct the credit curve with the predefined term structure
{
dates.Add(firstpaymentdate.AddMonths(6));
dates.Add(firstpaymentdate.AddYears(1));
dates.Add(firstpaymentdate.AddYears(3));
dates.Add(firstpaymentdate.AddYears(5));
dates.Add(firstpaymentdate.AddYears(7));
dates.Add(firstpaymentdate.AddYears(10));
for (int i = 0; i < QuotedSpread.Count(); i++)
{
QuotedSpread[i] = QuotedSpread[i] / 10000;
}
impliedhazardrate implied = new impliedhazardrate();
PiecewiseconstantHazardRate hazardcurve = implied.impliedHazardRate(0, this.Notional, this.tradedate, QuotedSpread, dates, yt, dayCounter,
frequency, this.firstpaymentdate, this.formerpaymentdate, this.Jump_Nodes, recovery);
this.piecewiseHazardRate = hazardcurve;
List <double> survival = new List <double>();
for (int i = 0; i < dates.Count; i++)
{
survival.Add(piecewiseHazardRate.SurvivalProb(dates[i].AddDays(1)));
}
}
}
