/**
* The intrinsic annuity of a CDS portfolio (index) for a unit (initial) notional.
* The value of the premium leg is this multiplied by the <b> initial</b> notional of the index
* and the index coupon (as a fraction).
*
* @param indexCDS representation of the index cashflows (seen from today).
* @param yieldCurve The current yield curves
* @param intrinsicData credit curves, weights and recovery rates of the intrinsic names
* @param valuationTime Valuation time. The leg value is calculated for today (t=0), then rolled
* forward (using the risk free yield curve) to the valuation time.
* This is because cash payments occur on the cash-settlement-date, which is usually
* three working days after the trade date (today)
* @return The intrinsic annuity of a CDS portfolio (index)
*/
public double indexAnnuity(
CDS indexCDS,
YieldTermStructure yieldCurve,
IntrinsicIndexDataBundle intrinsicData,
double valuationTime)
{
return(indexAnnuity(indexCDS, yieldCurve, intrinsicData, CdsPriceType.CLEAN, valuationTime));
}
/**
* The intrinsic annuity of a CDS portfolio (index) for a unit (initial) notional.
* The value of the premium leg is this multiplied by the <b> initial</b> notional of the index
* and the index coupon (as a fraction).
*
* @param indexCDS representation of the index cashflows (seen from today).
* @param yieldCurve The current yield curves
* @param intrinsicData credit curves, weights and recovery rates of the intrinsic names
* @param priceType Clean or dirty
* @return The normalised intrinsic annuity of a CDS portfolio (index)
*/
public double indexAnnuity(
CDS indexCDS,
YieldTermStructure yieldCurve,
IntrinsicIndexDataBundle intrinsicData,
CdsPriceType priceType)
{
return(indexAnnuity(indexCDS, yieldCurve, intrinsicData, priceType, indexCDS.getCashSettleTime()));
}
public double ProtectionLegNPV_Exact(CDS cds, double notional, PiecewiseconstantHazardRate hazard,
YieldTermStructure yt, DateTime tradedate, DateTime settlementDate, double recoveryrate, List <double> Jumps, List <double> creditCurveKnot)
{
DateTime Stepindate = tradedate.AddDays(1);
OMLib.Conventions.DayCount.Actual360 dc = new OMLib.Conventions.DayCount.Actual360();
double t0 = 0;
double T = cds.getProtectionEnd();
List <double> JumpNodes = new List <double>();
JumpNodes.Add(t0);
for (int j = 0; j < Jumps.Count; j++)
{
if (Jumps[j] < T)
{
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));
}
/**
* 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));
}
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 Points-Up-Front (PUF) of an index. This is the (clean) price of a unit notional index.
* The actual clean price is this multiplied by the (current) index notional
* (i.e. the initial notional times the index factor).
*
* @param indexCDS analytic description of a CDS traded at a certain time
* @param indexCoupon The coupon of the index (as a fraction)
* @param yieldCurve The yield curve
* @param intrinsicData credit curves, weights and recover
* @return PUF of an index
*/
public double indexPUF(
CDS indexCDS,
double indexCoupon,
YieldTermStructure yieldCurve,
IntrinsicIndexDataBundle intrinsicData)
{
if (intrinsicData.getNumOfDefaults() == intrinsicData.getIndexSize())
{
}
return(indexPV(indexCDS, indexCoupon, yieldCurve, intrinsicData) / intrinsicData.getIndexFactor());
}
/**
* Intrinsic (normalised) price an index from the credit curves of the individual single names.
* To get the actual index value, this multiplied by the <b>initial</b> notional of the index.
*
* @param indexCDS analytic description of a CDS traded at a certain time
* @param indexCoupon The coupon of the index (as a fraction)
* @param yieldCurve The yield curve
* @param intrinsicData credit curves, weights and recovery rates of the intrinsic names
* @return The index value for a unit notional.
*/
public double indexPV(
CDS indexCDS,
double indexCoupon,
YieldTermStructure yieldCurve,
IntrinsicIndexDataBundle intrinsicData)
{
double prot = indexProtLeg(indexCDS, yieldCurve, intrinsicData);
double annuity = indexAnnuity(indexCDS, yieldCurve, intrinsicData);
return(prot - indexCoupon * annuity);
}
/**
* 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);
}
/**
* Intrinsic (normalised) price an index from the credit curves of the individual single names.
* To get the actual index value, this multiplied by the <b>initial</b> notional of the index.
*
* @param indexCDS analytic description of a CDS traded at a certain time
* @param indexCoupon The coupon of the index (as a fraction)
* @param yieldCurve The yield curve
* @param intrinsicData credit curves, weights and recovery rates of the intrinsic names
* @param priceType Clean or dirty price
* @param valuationTime The leg value is calculated for today (t=0), then rolled
* forward (using the risk free yield curve) to the valuation time.
* This is because cash payments occur on the cash-settlement-date, which is usually
* three working days after the trade date (today)
* @return The index value for a unit notional.
*/
public double indexPV(
CDS indexCDS,
double indexCoupon,
YieldTermStructure yieldCurve,
IntrinsicIndexDataBundle intrinsicData,
CdsPriceType priceType,
double valuationTime)
{
double prot = indexProtLeg(indexCDS, yieldCurve, intrinsicData, valuationTime);
double annuity = indexAnnuity(indexCDS, yieldCurve, intrinsicData, priceType, valuationTime);
return(prot - indexCoupon * annuity);
}
private double decomposedValueOnDefault(
CDS indexCDS,
double indexCoupon,
YieldTermStructure yieldCurve,
IntrinsicIndexDataBundle intrinsicData,
int singleName)
{
double weight = intrinsicData.getWeight(singleName);
double protection = intrinsicData.getLGD(singleName);
double singleNamePV = _pricer.pv(indexCDS, yieldCurve, intrinsicData.getCreditCurves()[singleName], indexCoupon);
return(weight * (protection - singleNamePV));
}
/**
* The intrinsic index spread. this is defined as the ratio of the intrinsic protection leg to the intrinsic annuity.
*
* @see #averageSpread
* @param indexCDS analytic description of a CDS traded at a certain time
* @param yieldCurve The yield curve
* @param intrinsicData credit curves, weights and recovery rates of the intrinsic names
* @return intrinsic index spread (as a fraction)
*/
public double intrinsicIndexSpread(
CDS indexCDS,
YieldTermStructure yieldCurve,
IntrinsicIndexDataBundle intrinsicData)
{
if (intrinsicData.getNumOfDefaults() == intrinsicData.getIndexSize())
{
}
double prot = indexProtLeg(indexCDS, yieldCurve, intrinsicData);
double annuity = indexAnnuity(indexCDS, yieldCurve, intrinsicData);
return(prot / annuity);
}
//*******************************************************************************************************************
//* Forward values adjusted for defaults
//****************************************************************************************************************
/**
* 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).
*
* @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.
* @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 intrinsicData credit curves, weights and recovery rates of the intrinsic names
* initially 100 entries, and the realised recovery rates are 0.2 and 0.35, the this value is (0.8 + 0.65)/100 )
* @return the default adjusted forward index value
*/
public double defaultAdjustedForwardIndexValue(
CDS fwdStartingCDS,
double timeToExpiry,
YieldTermStructure yieldCurve,
double indexCoupon,
IntrinsicIndexDataBundle intrinsicData)
{
//the expected value of the index (not including default settlement) at the expiry settlement date
double indexPV1 = indexPV(fwdStartingCDS, indexCoupon, yieldCurve, intrinsicData);
double d = expectedDefaultSettlementValue(timeToExpiry, intrinsicData);
return(indexPV1 + d);
}
public IntrinsicIndexDataBundle adjustCurves(
double indexPUF,
CDS indexCDS,
double indexCoupon,
YieldTermStructure yieldCurve,
IntrinsicIndexDataBundle intrinsicData)
{
Func <double, double> func = getHazardRateAdjFunction(indexPUF, indexCDS, indexCoupon, yieldCurve, intrinsicData);
double x = ROOTFINDER.getRoot(func, 1.0);
PiecewiseconstantHazardRate[] adjCC = adjustCurves(intrinsicData.getCreditCurves(), x);
return(intrinsicData.withCreditCurves(adjCC));
}
/**
* 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.
*
* @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 the time in years between the trade date and expiry.
* This should use the same DCC as the curves (ACT365F unless manually changed).
* @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 intrinsicData credit curves, weights and recovery rates of the intrinsic names
* initially 100 entries, and the realised recovery rates are 0.2 and 0.35, the this value is (0.8 + 0.65)/100 )
* @return The (default adjusted) forward spread (as a fraction)
*/
public double defaultAdjustedForwardSpread(
CDS fwdStartingCDS,
double timeToExpiry,
YieldTermStructure yieldCurve,
IntrinsicIndexDataBundle intrinsicData)
{
// Note: these values are all calculated for payment on the (forward) cash settlement date
// there is no point discounting to today
double protLeg = indexProtLeg(fwdStartingCDS, yieldCurve, intrinsicData);
double defSettle = expectedDefaultSettlementValue(timeToExpiry, intrinsicData);
double ann = indexAnnuity(fwdStartingCDS, yieldCurve, intrinsicData);
return((protLeg + defSettle) / ann);
}
private Func <double, double> getHazardRateAdjFunction(
double indexPUF,
CDS indexCDS,
double indexCoupon,
YieldTermStructure yieldCurve,
IntrinsicIndexDataBundle intrinsicData)
{
PiecewiseconstantHazardRate[] creditCurves = intrinsicData.getCreditCurves();
double clean = intrinsicData.getIndexFactor() * indexPUF;
Func <double, double> function = x => _pricer.indexPV(indexCDS, indexCoupon,
yieldCurve, intrinsicData.withCreditCurves(adjustCurves(creditCurves, x))) - clean;
return(function);
}
/**
* Make a set of CDS by specifying all dates.
*
* @param tradeDate the trade date
* @param stepinDate (aka Protection Effective sate or assignment date). Date when party assumes ownership.
* This is usually T+1. This is when protection (and risk) starts in terms of the model.
* Note, this is sometimes just called the Effective Date, however this can cause
* confusion with the legal effective date which is T-60 or T-90.
* @param valueDate the valuation date. The date that values are PVed to.
* Is is normally today + 3 business days. Aka cash-settle date.
* @param accStartDate this is when the CDS nominally starts in terms of premium payments. i.e. the number
* of days in the first period (and thus the amount of the first premium payment) is counted from this date.
* @param maturities The maturities of the CDSs. For a standard CDS these are IMM dates
* @return an array of CDS analytic descriptions
*/
public CDS[] makeCds(
DateTime tradeDate,
DateTime stepinDate,
DateTime valueDate,
DateTime accStartDate,
DateTime[] maturities)
{
int n = maturities.Length;
CDS[] cds = new CDS[n];
for (int i = 0; i < n; i++)
{
cds[i] = new CDS(Coupon, notional, maturities[i], getNextIMMDate(tradeDate), tradeDate, accStartDate, frequency, _recoveryRate, DEFAULT_STEPIN, DEFAULT_CASH_SETTLE);
}
return(cds);
}
/**
* 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 void testMethod()
{
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();
}
int accrualDays = targentCDX.getAccuredDays();
double accruedPremium = targentCDX.getAccruedPremium(INDEX_COUPON) * INTRINSIC_DATA.getIndexFactor() * NOTIONAL; // indexFactor = (initialIndexSize - numDefaults) / initialIndexSize
/*
* Using credit curves for constituent single name CDSs.
* The curves are adjusted by using only the target CDX.
*/
IntrinsicIndexDataBundle adjCurves = PSA.adjustCurves(indexPUF[pos], CDX[pos], INDEX_COUPON, YIELD_CURVE,
INTRINSIC_DATA);
double cleanPV = INDEX_CAL.indexPV(targentCDX, INDEX_COUPON, YIELD_CURVE, adjCurves) * NOTIONAL; // should be consistent with 1 - PRICES[pos]
double dirtyPV = INDEX_CAL.indexPV(targentCDX, INDEX_COUPON, YIELD_CURVE, adjCurves, CdsPriceType.DIRTY) * NOTIONAL;
double expectedLoss = INDEX_CAL.expectedDefaultSettlementValue(targentCDX.getProtectionEnd(), adjCurves) * NOTIONAL;
double cleanRPV01 = INDEX_CAL.indexAnnuity(targentCDX, YIELD_CURVE, adjCurves);
double dirtyRPV01 = INDEX_CAL.indexAnnuity(targentCDX, YIELD_CURVE, adjCurves, CdsPriceType.DIRTY);
double durationWeightedAverageSpread = INDEX_CAL.intrinsicIndexSpread(targentCDX, YIELD_CURVE, adjCurves) *
TEN_THOUSAND;
double parallelIR01 = INDEX_CAL.parallelIR01(targentCDX, INDEX_COUPON, YIELD_CURVE, adjCurves) * NOTIONAL;
double[] jumpToDefault = INDEX_CAL.jumpToDefault(targentCDX, INDEX_COUPON, YIELD_CURVE, adjCurves);
for (int i = 0; i < jumpToDefault.Length; ++i)
{
jumpToDefault[i] *= NOTIONAL;
}
double[] recovery01 = INDEX_CAL.recovery01(targentCDX, INDEX_COUPON, YIELD_CURVE, adjCurves);
for (int i = 0; i < recovery01.Length; ++i)
{
recovery01[i] *= NOTIONAL;
}
}
/**
* The change in the intrinsic value of a CDS index when zero rate at node points of the yield curve is bumped by 1bps.
* If the index is priced as a single name CDS, use {@link InterestRateSensitivityCalculator}.
*
* @param indexCDS The CDS index
* @param indexCoupon The index coupon
* @param yieldCurve The yield curve
* @param intrinsicData Credit curves, weights and recovery rates of the intrinsic names
* @return bucketed IR01
*/
public double[] bucketedIR01(
CDS indexCDS,
double indexCoupon,
YieldTermStructure yieldCurve,
IntrinsicIndexDataBundle intrinsicData)
{
double basePV = indexPV(indexCDS, indexCoupon, yieldCurve, intrinsicData, CdsPriceType.DIRTY);
int n = yieldCurve.t.Count;
double[] res = new double[n];
for (int i = 0; i < n; ++i)
{
YieldTermStructure bumpedYieldCurve = yieldCurve.withRate(yieldCurve.getZeroRateAtIndex(i) + ONE_BPS, i);
double bumpedPV = indexPV(indexCDS, indexCoupon, bumpedYieldCurve, intrinsicData, CdsPriceType.DIRTY);
res[i] = bumpedPV - basePV;
}
return(res);
}
/**
* The change in the intrinsic value of a CDS index when the yield curve is bumped by 1bps.
* If the index is priced as a single name CDS, use {@link InterestRateSensitivityCalculator}.
*
* @param indexCDS The CDS index
* @param indexCoupon The index coupon
* @param yieldCurve The yield curve
* @param intrinsicData Credit curves, weights and recovery rates of the intrinsic names
* @return parallel IR01
*/
public double parallelIR01(
CDS indexCDS,
double indexCoupon,
YieldTermStructure yieldCurve,
IntrinsicIndexDataBundle intrinsicData)
{
double pv = indexPV(indexCDS, indexCoupon, yieldCurve, intrinsicData, CdsPriceType.DIRTY);
int nKnots = yieldCurve.t.Count;
double[] rates = yieldCurve.getKnotZeroRates().ToArray();
for (int i = 0; i < nKnots; ++i)
{
rates[i] += ONE_BPS;
}
YieldTermStructure yieldCurveUp = yieldCurve.withRates(rates.ToList());
double pvUp = indexPV(indexCDS, indexCoupon, yieldCurveUp, intrinsicData, CdsPriceType.DIRTY);
return(pvUp - pv);
}
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())));
}
/**
* The normalised intrinsic value of the protection leg of a CDS portfolio (index).
* The actual value of the leg is this multiplied by the <b>initial</b> notional of the index.
*
* @param indexCDS representation of the index cashflows (seen from today).
* @param yieldCurve The current yield curves
* @param intrinsicData credit curves, weights and recovery rates of the intrinsic names
* @param valuationTime Valuation time. The leg value is calculated for today (t=0),
* then rolled forward (using the risk free yield curve) to the valuation time.
* This is because cash payments occur on the cash-settlement-date, which is usually
* three working days after the trade date (today)
* @return The normalised intrinsic value of the protection leg.
*/
public double indexProtLeg(
CDS indexCDS,
YieldTermStructure yieldCurve,
IntrinsicIndexDataBundle intrinsicData,
double valuationTime)
{
CDS cds = indexCDS.withRecoveryRate(0.0);
int n = intrinsicData.getIndexSize();
double protLeg = 0;
for (int i = 0; i < n; i++)
{
if (!intrinsicData.isDefaulted(i))
{
protLeg += intrinsicData.getWeight(i) * intrinsicData.getLGD(i) *
_pricer.protectionLeg(cds, yieldCurve, intrinsicData.getCreditCurve(i), 0);
}
}
protLeg /= Math.Exp(-yieldCurve.getRT_(valuationTime));
return(protLeg);
}
/**
* The intrinsic annuity of a CDS portfolio (index) for a unit (initial) notional.
* The value of the premium leg is this multiplied by the <b> initial</b> notional of the index
* and the index coupon (as a fraction).
*
* @param indexCDS representation of the index cashflows (seen from today).
* @param yieldCurve The current yield curves
* @param intrinsicData credit curves, weights and recovery rates of the intrinsic names
* @param priceType Clean or dirty
* @param valuationTime Valuation time. The leg value is calculated for today (t=0),
* then rolled forward (using the risk free yield curve) to the valuation time.
* This is because cash payments occur on the cash-settlement-date, which is usually
* three working days after the trade date (today)
* @return The intrinsic annuity of a CDS portfolio (index)
*/
public double indexAnnuity(
CDS indexCDS,
YieldTermStructure yieldCurve,
IntrinsicIndexDataBundle intrinsicData,
CdsPriceType priceType,
double valuationTime)
{
int n = intrinsicData.getIndexSize();
double a = 0;
for (int i = 0; i < n; i++)
{
if (!intrinsicData.isDefaulted(i))
{
a += intrinsicData.getWeight(i) * _pricer.annuity(indexCDS, yieldCurve, intrinsicData.getCreditCurve(i), priceType, 0);
}
}
a /= Math.Exp(-yieldCurve.getRT_(valuationTime));
return(a);
}
/**
* Values on per-name default
* @param indexCDS The CDS index
* @param indexCoupon The index coupon
* @param yieldCurve The yield curve
* @param intrinsicData Credit curves, weights and recovery rates of the intrinsic names
* @return The jump to default
*/
public double[] jumpToDefault(
CDS indexCDS,
double indexCoupon,
YieldTermStructure yieldCurve,
IntrinsicIndexDataBundle intrinsicData)
{
int indexSize = intrinsicData.getIndexSize();
double[] res = new double[indexSize];
for (int i = 0; i < indexSize; ++i)
{
if (intrinsicData.isDefaulted(i))
{
res[i] = 0.0;
}
else
{
res[i] = decomposedValueOnDefault(indexCDS, indexCoupon, yieldCurve, intrinsicData, i);
}
}
return(res);
}
/**
* Sensitivity of the intrinsic value of a CDS index to intrinsic CDS recovery rates.
*
* @param indexCDS The CDS index
* @param indexCoupon The index coupon
* @param yieldCurve The yield curve
* @param intrinsicData Credit curves, weights and recovery rates of the intrinsic names
* @return The sensitivity
*/
public double[] recovery01(
CDS indexCDS,
double indexCoupon,
YieldTermStructure yieldCurve,
IntrinsicIndexDataBundle intrinsicData)
{
CDS zeroRR = indexCDS.withRecoveryRate(0.0);
int indexSize = intrinsicData.getIndexSize();
double[] res = new double[indexSize];
for (int i = 0; i < indexSize; ++i)
{
if (intrinsicData.isDefaulted(i))
{
res[i] = 0.0;
}
else
{
res[i] = -_pricer.protectionLeg(zeroRR, yieldCurve, intrinsicData.getCreditCurve(i)) *
intrinsicData.getWeight(i);
}
}
return(res);
}
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 void Pricing()
{
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();
}
defaultedNames = new int[] { 2, 15, 37, 51 };
IntrinsicIndexDataBundle dataDefaulted = INTRINSIC_DATA.withDefault(defaultedNames);
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.
*/
IntrinsicIndexDataBundle adjCurves = PSA.adjustCurves(indexPUF[pos], CDX[pos], INDEX_COUPON, YIELD_CURVE,
dataDefaulted);
cleanPV = INDEX_CAL.indexPV(targentCDX, INDEX_COUPON, YIELD_CURVE, adjCurves) * NOTIONAL;
dirtyPV = INDEX_CAL.indexPV(targentCDX, INDEX_COUPON, YIELD_CURVE, adjCurves, CdsPriceType.DIRTY) * NOTIONAL; // should be consistent with 1 - PRICES[pos]
expectedLoss = INDEX_CAL.expectedDefaultSettlementValue(targentCDX.getProtectionEnd(), adjCurves) * NOTIONAL;
cleanRPV01 = INDEX_CAL.indexAnnuity(targentCDX, YIELD_CURVE, adjCurves);
dirtyRPV01 = INDEX_CAL.indexAnnuity(targentCDX, YIELD_CURVE, adjCurves, CdsPriceType.DIRTY);
durationWeightedAverageSpread = INDEX_CAL.intrinsicIndexSpread(targentCDX, YIELD_CURVE, adjCurves) *
TEN_THOUSAND;
parallelIR01 = INDEX_CAL.parallelIR01(targentCDX, INDEX_COUPON, YIELD_CURVE, adjCurves) * NOTIONAL;
double[] jumpToDefault = INDEX_CAL.jumpToDefault(targentCDX, INDEX_COUPON, YIELD_CURVE, adjCurves);
for (int i = 0; i < jumpToDefault.Length; ++i)
{
jumpToDefault[i] *= NOTIONAL;
}
recovery01 = INDEX_CAL.recovery01(targentCDX, INDEX_COUPON, YIELD_CURVE, adjCurves);
//Build Cash flow
QLNet.UnitedStates cal = new QLNet.UnitedStates();
CdsCoupon[] coupons = targentCDX.getCoupons();
int npayments = coupons.Count();
cashflow = new List <CouponPayment>();
for (int i = 0; i < npayments; i++)
{
CouponPayment cf = new CouponPayment();
cf.Amount = (-coupons[i].getEffStart() + coupons[i].getEffEnd()) * NOTIONAL * INDEX_COUPON;
cf.Amount = Math.Round(cf.Amount, 2);
double days = coupons[i].getEffEnd() * 365;
cf.CashFlowDate = i == 0? CdsAnalyticFactory.getNextIMMDate(TRADE_DATE):
CdsAnalyticFactory.getNextIMMDate(cashflow[i - 1].CashFlowDate);
cf.CashFlowDate = cal.adjust(cf.CashFlowDate);
cashflow.Add(cf);
}
for (int i = 0; i < recovery01.Length; ++i)
{
recovery01[i] *= NOTIONAL;
}
}
