//! Implied internal rate of return.
// The function verifies
// the theoretical existance of an IRR and numerically
// establishes the IRR to the desired precision.
public static double yield(Leg leg, double npv, DayCounter dayCounter, Compounding compounding, Frequency frequency,
bool includeSettlementDateFlows, Date settlementDate = null, Date npvDate = null,
double accuracy = 1.0e-10, int maxIterations = 100, double guess = 0.05)
{
NewtonSafe solver = new NewtonSafe();
solver.setMaxEvaluations(maxIterations);
IrrFinder objFunction = new IrrFinder(leg, npv,
dayCounter, compounding, frequency,
includeSettlementDateFlows,
settlementDate, npvDate);
return(solver.solve(objFunction, accuracy, guess, guess / 10.0));
}
//! implied volatility
public double impliedVolatility(double targetValue,
Handle <YieldTermStructure> discountCurve,
double guess,
double accuracy = 1.0e-4,
int maxEvaluations = 100,
double minVol = 1.0e-7,
double maxVol = 4.0,
VolatilityType type = VolatilityType.ShiftedLognormal,
double?displacement = 0.0)
{
calculate();
if (isExpired())
{
throw new ArgumentException("instrument expired");
}
ImpliedVolHelper_ f = new ImpliedVolHelper_(this, discountCurve, targetValue, displacement, type);
NewtonSafe solver = new NewtonSafe();
solver.setMaxEvaluations(maxEvaluations);
return(solver.solve(f, accuracy, guess, minVol, maxVol));
}
protected override double solveImpl(ISolver1d f, double xAccuracy)
{
/* The implementation of the algorithm was inspired by Press, Teukolsky, Vetterling, and Flannery,
* "Numerical Recipes in C", 2nd edition, Cambridge University Press */
double froot, dfroot, dx;
froot = f.value(root_);
dfroot = f.derivative(root_);
if (dfroot.IsEqual(default(double)))
{
throw new ArgumentException("Newton requires function's derivative");
}
++evaluationNumber_;
while (evaluationNumber_ <= maxEvaluations_)
{
dx = froot / dfroot;
root_ -= dx;
// jumped out of brackets, switch to NewtonSafe
if ((xMin_ - root_) * (root_ - xMax_) < 0.0)
{
NewtonSafe s = new NewtonSafe();
s.setMaxEvaluations(maxEvaluations_ - evaluationNumber_);
return(s.solve(f, xAccuracy, root_ + dx, xMin_, xMax_));
}
if (Math.Abs(dx) < xAccuracy)
{
return(root_);
}
froot = f.value(root_);
dfroot = f.derivative(root_);
evaluationNumber_++;
}
Utils.QL_FAIL("maximum number of function evaluations (" + maxEvaluations_ + ") exceeded",
QLNetExceptionEnum.MaxNumberFuncEvalExceeded);
return(0);
}
public double impliedVolatility(
double targetValue,
Handle <YieldTermStructure> discountCurve,
double guess,
double accuracy,
int maxEvaluations,
double minVol,
double maxVol,
VolatilityType type,
double displacement)
{
calculate();
if (isExpired())
{
throw new ArgumentException("instrument expired");
}
ImpliedVolHelper f = new ImpliedVolHelper(this, discountCurve, targetValue, displacement, type);
NewtonSafe solver = new NewtonSafe();
solver.setMaxEvaluations(maxEvaluations);
return(solver.solve(f, accuracy, guess, minVol, maxVol));
}
/*! Black 1976 implied standard deviation,
* i.e. volatility*sqrt(timeToMaturity)
*/
public static double blackFormulaImpliedStdDev(Option.Type optionType,
double strike,
double forward,
double blackPrice,
double discount = 1.0,
double displacement = 0.0,
double?guess = null,
double accuracy = 1.0e-6,
int maxIterations = 100)
{
checkParameters(strike, forward, displacement);
QL_REQUIRE(discount > 0.0, () =>
"discount (" + discount + ") must be positive");
QL_REQUIRE(blackPrice >= 0.0, () =>
"option price (" + blackPrice + ") must be non-negative");
// check the price of the "other" option implied by put-call paity
double otherOptionPrice = blackPrice - (int)optionType * (forward - strike) * discount;
QL_REQUIRE(otherOptionPrice >= 0.0, () =>
"negative " + (-1 * (int)optionType) +
" price (" + otherOptionPrice +
") implied by put-call parity. No solution exists for " +
optionType + " strike " + strike +
", forward " + forward +
", price " + blackPrice +
", deflator " + discount);
// solve for the out-of-the-money option which has
// greater vega/price ratio, i.e.
// it is numerically more robust for implied vol calculations
if (optionType == Option.Type.Put && strike > forward)
{
optionType = Option.Type.Call;
blackPrice = otherOptionPrice;
}
if (optionType == Option.Type.Call && strike < forward)
{
optionType = Option.Type.Put;
blackPrice = otherOptionPrice;
}
strike = strike + displacement;
forward = forward + displacement;
if (guess == null)
{
guess = blackFormulaImpliedStdDevApproximation(optionType, strike, forward, blackPrice, discount, displacement);
}
else
{
QL_REQUIRE(guess >= 0.0, () => "stdDev guess (" + guess + ") must be non-negative");
}
BlackImpliedStdDevHelper f = new BlackImpliedStdDevHelper(optionType, strike, forward, blackPrice / discount);
NewtonSafe solver = new NewtonSafe();
solver.setMaxEvaluations(maxIterations);
double minSdtDev = 0.0, maxStdDev = 24.0; // 24 = 300% * sqrt(60)
double stdDev = solver.solve(f, accuracy, guess.Value, minSdtDev, maxStdDev);
QL_REQUIRE(stdDev >= 0.0, () => "stdDev (" + stdDev + ") must be non-negative");
return(stdDev);
}
