//! Conventional/standard upfront-to-spread conversion
/*! Under a standard ISDA model and a set of standardised
* instrument characteristics, it is the running only quoted
* spread that will make a CDS contract have an NPV of 0 when
* quoted for that running only spread. Refer to: "ISDA
* Standard CDS converter specification." May 2009.
*
* The conventional recovery rate to apply in the calculation
* is as specified by ISDA, not necessarily equal to the
* market-quoted one. It is typically 0.4 for SeniorSec and
* 0.2 for subordinate.
*
* \note The conversion employs a flat hazard rate. As a result,
* you will not recover the market quotes.
*
* \note This method performs the calculation with the
* instrument characteristics. It will coincide with
* the ISDA calculation if your object has the standard
* characteristics. Notably:
* - The calendar should have no bank holidays, just
* weekends.
* - The yield curve should be LIBOR piecewise ant
* in fwd rates, with a discount factor of 1 on the
* calculation date, which coincides with the trade
* date.
* - Convention should be Following for yield curve and
* contract cashflows.
* - The CDS should pay accrued and mature on standard
* IMM dates, settle on trade date +1 and upfront
* settle on trade date +3.
*/
public double?conventionalSpread(double conventionalRecovery,
Handle <YieldTermStructure> discountCurve,
DayCounter dayCounter)
{
double flatHazardRate = impliedHazardRate(0.0,
discountCurve,
dayCounter,
conventionalRecovery);
Handle <DefaultProbabilityTermStructure> probability = new Handle <DefaultProbabilityTermStructure>(
new FlatHazardRate(0, new WeekendsOnly(), flatHazardRate, dayCounter));
MidPointCdsEngine engine = new MidPointCdsEngine(probability, conventionalRecovery, discountCurve, true);
setupArguments(engine.getArguments());
engine.calculate();
CreditDefaultSwap.Results results = engine.getResults() as CreditDefaultSwap.Results;
return(results.fairSpread);
}
/// <summary>
/// Implied hazard rate calculation
/// </summary>
/// <remarks>
/// This method performs the calculation with the
/// instrument characteristics. It will coincide with
/// the ISDA calculation if your object has the standard
/// characteristics. Notably:
/// - The calendar should have no bank holidays, just
/// weekends.
/// - The yield curve should be LIBOR piecewise ant
/// in fwd rates, with a discount factor of 1 on the
/// calculation date, which coincides with the trade
/// date.
/// - Convention should be Following for yield curve and
/// contract cashflows.
/// - The CDS should pay accrued and mature on standard
/// IMM dates, settle on trade date +1 and upfront
/// settle on trade date +3.
/// </remarks>
/// <param name="targetNPV"></param>
/// <param name="discountCurve"></param>
/// <param name="dayCounter"></param>
/// <param name="recoveryRate"></param>
/// <param name="accuracy"></param>
/// <returns></returns>
public double impliedHazardRate(double targetNPV,
Handle <YieldTermStructure> discountCurve,
DayCounter dayCounter,
double recoveryRate = 0.4,
double accuracy = 1.0e-6,
PricingModel model = PricingModel.Midpoint)
{
SimpleQuote flatRate = new SimpleQuote(0.0);
Handle <DefaultProbabilityTermStructure> probability = new Handle <DefaultProbabilityTermStructure>(
new FlatHazardRate(0, new WeekendsOnly(), new Handle <Quote>(flatRate), dayCounter));
IPricingEngine engine = null;
switch (model)
{
case PricingModel.Midpoint:
engine = new MidPointCdsEngine(probability, recoveryRate, discountCurve);
break;
case PricingModel.ISDA:
engine = new IsdaCdsEngine(probability, recoveryRate, discountCurve);
break;
default:
Utils.QL_FAIL("unknown CDS pricing model: " + model);
break;
}
setupArguments(engine.getArguments());
CreditDefaultSwap.Results results = engine.getResults() as CreditDefaultSwap.Results;
ObjectiveFunction f = new ObjectiveFunction(targetNPV, flatRate, engine, results);
double guess = runningSpread_ / (1 - recoveryRate) * 365.0 / 360.0;
double step = guess * 0.1;
return(new Brent().solve(f, accuracy, guess, step));
}
public double impliedHazardRate(double targetNPV,
Handle <YieldTermStructure> discountCurve,
DayCounter dayCounter,
double recoveryRate = 0.4,
double accuracy = 1.0e-6)
{
SimpleQuote flatRate = new SimpleQuote(0.0);
Handle <DefaultProbabilityTermStructure> probability = new Handle <DefaultProbabilityTermStructure>(
new FlatHazardRate(0, new WeekendsOnly(), new Handle <Quote>(flatRate), dayCounter));
MidPointCdsEngine engine = new MidPointCdsEngine(probability, recoveryRate, discountCurve);
setupArguments(engine.getArguments());
CreditDefaultSwap.Results results = engine.getResults() as CreditDefaultSwap.Results;
ObjectiveFunction f = new ObjectiveFunction(targetNPV, flatRate, engine, results);
double guess = 0.001;
double step = guess * 0.1;
return(new Brent().solve(f, accuracy, guess, step));
}
public void testFairUpfront()
{
// Testing fair-upfront calculation for credit-default swaps...
SavedSettings backup = new SavedSettings();
// Initialize curves
Calendar calendar = new TARGET();
Date today = calendar.adjust(Date.Today);
Settings.setEvaluationDate(today);
Handle<Quote> hazardRate = new Handle<Quote>(new SimpleQuote(0.01234));
RelinkableHandle<DefaultProbabilityTermStructure> probabilityCurve =
new RelinkableHandle<DefaultProbabilityTermStructure>();
probabilityCurve.linkTo(new FlatHazardRate(0, calendar, hazardRate, new Actual360()));
RelinkableHandle<YieldTermStructure> discountCurve =
new RelinkableHandle<YieldTermStructure>();
discountCurve.linkTo(new FlatForward(today,0.06,new Actual360()));
// Build the schedule
Date issueDate = today;
Date maturity = calendar.advance(issueDate, 10, TimeUnit.Years);
BusinessDayConvention convention = BusinessDayConvention.Following;
Schedule schedule =
new MakeSchedule().from(issueDate)
.to(maturity)
.withFrequency(Frequency.Quarterly)
.withCalendar(calendar)
.withTerminationDateConvention(convention)
.withRule(DateGeneration.Rule.TwentiethIMM).value();
// Build the CDS
double fixedRate = 0.05;
double upfront = 0.001;
DayCounter dayCount = new Actual360();
double notional = 10000.0;
double recoveryRate = 0.4;
IPricingEngine engine = new MidPointCdsEngine(probabilityCurve, recoveryRate, discountCurve, true);
CreditDefaultSwap cds = new CreditDefaultSwap(Protection.Side.Seller, notional, upfront, fixedRate,
schedule, convention, dayCount, true, true);
cds.setPricingEngine(engine);
double fairUpfront = cds.fairUpfront();
CreditDefaultSwap fairCds = new CreditDefaultSwap(Protection.Side.Seller, notional,
fairUpfront, fixedRate, schedule, convention, dayCount, true, true);
fairCds.setPricingEngine(engine);
double fairNPV = fairCds.NPV();
double tolerance = 1e-10;
if (Math.Abs(fairNPV) > tolerance)
Assert.Fail(
"Failed to reproduce null NPV with calculated fair upfront\n"
+ " calculated upfront: " + fairUpfront + "\n"
+ " calculated NPV: " + fairNPV);
// same with null upfront to begin with
upfront = 0.0;
CreditDefaultSwap cds2 = new CreditDefaultSwap(Protection.Side.Seller, notional, upfront, fixedRate,
schedule, convention, dayCount, true, true);
cds2.setPricingEngine(engine);
fairUpfront = cds2.fairUpfront();
CreditDefaultSwap fairCds2 = new CreditDefaultSwap(Protection.Side.Seller, notional,
fairUpfront, fixedRate, schedule, convention, dayCount, true, true);
fairCds2.setPricingEngine(engine);
fairNPV = fairCds2.NPV();
if (Math.Abs(fairNPV) > tolerance)
Assert.Fail(
"Failed to reproduce null NPV with calculated fair upfront\n"
+ " calculated upfront: " + fairUpfront + "\n"
+ " calculated NPV: " + fairNPV);
}
