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