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));
}
//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);
}
