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 PremiumLegNPV_Exact(List <CashFlow> cf, PiecewiseconstantHazardRate hazard,
YieldTermStructure yt, DateTime tradedate, DateTime settlementDate, double notional, double coupon, List <DateTime> Jumps, DateTime lastpayment)
{
if (cf.Count() == 0)
{
return(0.0);
}
double ita = (double)365 / 360;
double totalNPV = 0.0;
for (int i = 0; i < cf.Count; ++i)
{
totalNPV += cf[i].Amount * cf[i].DiscountFactor * cf[i].Survivalprobability;
}
double accrualpaidondefault = calculateSinglePeriodAccrualOnDefault(cf, coupon, tradedate, yt, hazard, Jumps, 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 / yt.discount(settlementDate));
}
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 void curve_output(YieldTermStructure yt, PiecewiseconstantHazardRate ct)
{
double it = ct.SurvivalProb(new DateTime(2021, 06, 20));
List <double> yield = new List <double>();
for (int j = 1; j < 120; j++)
{
DateTime t = this.evalDate.AddMonths(j);
double t_ = (double)j / 12;
yield.Add(-Math.Log(yt.discount(t)) / t_);
}
this.yield_series = yield;
List <double> survival = new List <double>();
for (int j = 1; j < 120; j++)
{
DateTime t = this.tradedate.AddMonths(j);
survival.Add(ct.SurvivalProb(t));
}
this.survival_prob = survival;
}
public List <CashFlow> Calculation(double fixrate, double initialNotional, List <DateTime> fixedSchedule, DateTime tradedate,
YieldTermStructure yt, PiecewiseconstantHazardRate piecewiseFlatHazardRate, int settlement, DateTime lastpaymentdate)
{
List <CashFlow> result = new List <CashFlow>();
OMLib.Conventions.DayCount.Actual360 daycountconvention = new OMLib.Conventions.DayCount.Actual360();
for (int i = 0; i < fixedSchedule.Count; i++)
{
CashFlow cf = new CashFlow();
Calendar calendar = new UnitedStates();
//fixedSchedule[i] = calendar.adjust(fixedSchedule[i], BusinessDayConvention.Following);
cf.CashFlowDate = fixedSchedule[i];
if (i == 0)
{
//The protection buyer pays the next coupon in full on the coupon date,
//(even if this is the next day); in return the buyer receives (from the protection seller) the accrued
//interest[Geoff Chaplin. Credit Derivatives.], which is paid on the cash settlement date.
if (lastpaymentdate != null)
{
lastpaymentdate = calendar.adjust(lastpaymentdate, BusinessDayConvention.Following);
cf.Amount = (double)initialNotional * fixrate * (daycountconvention.DayCount(lastpaymentdate, fixedSchedule[i])) / 360;
}
else
{
cf.Amount = (double)initialNotional * fixrate * (daycountconvention.DayCount(tradedate, fixedSchedule[i])) / 360;
}
}
else
{
//Each coupon is equal to (annual coupon/360) (# of days in accrual period).
//The accrual period always stretches from (previous coupon payment date) through (this coupon
//payment date–1), inclusive; except a contract's last accrual period, which ends with (and
//includes) the unadjusted maturity date.
if (i == fixedSchedule.Count - 1)
{
cf.Amount = (double)initialNotional * fixrate * (daycountconvention.DayCount(fixedSchedule[i - 1], fixedSchedule[i].AddDays(1))) / 360;
}
else
{
cf.Amount = (double)initialNotional * fixrate * (daycountconvention.DayCount(fixedSchedule[i - 1], fixedSchedule[i])) / 360;
}
}
//Assume all cash flows are discounted to the cash settlement date
cf.DiscountFactor = yt.discount(fixedSchedule[i]);
if (i == fixedSchedule.Count - 1)
{
cf.Survivalprobability = piecewiseFlatHazardRate.SurvivalProb(fixedSchedule[i].AddDays(1));
}
else
{
cf.Survivalprobability = piecewiseFlatHazardRate.SurvivalProb(fixedSchedule[i]);
}
result.Add(cf);
}
return(result);
}
