/**
* 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));
}
/**
* 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);
}
/**
* 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);
}
/**
* 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));
}
