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); }