public override void partialRollback(DiscretizedAsset asset, double to)
{
double from = asset.time();
if (Utils.close(from, to))
{
return;
}
Utils.QL_REQUIRE(from > to, () => "cannot roll the asset back to" + to + " (it is already at t = " + from + ")");
int iFrom = t_.index(from);
int iTo = t_.index(to);
for (int i = iFrom - 1; i >= iTo; --i)
{
Vector newValues = new Vector(impl().size(i));
impl().stepback(i, asset.values(), newValues);
asset.setTime(t_[i]);
asset.setValues(newValues);
// skip the very last adjustment
if (i != iTo)
{
asset.adjustValues();
}
}
}
protected void applyExerciseCondition()
{
for (int i = 0; i < values_.size(); i++)
{
values_[i] = Math.Max(underlying_.values()[i], values_[i]);
}
}
//! Computes the present value of an asset using Arrow-Debrew prices
public override double presentValue(DiscretizedAsset asset)
{
int i = t_.index(asset.time());
return(Vector.DotProduct(asset.values(), statePrices(i)));
}
public override void calculate()
{
DayCounter rfdc = process_.riskFreeRate().link.dayCounter();
DayCounter divdc = process_.dividendYield().link.dayCounter();
DayCounter voldc = process_.blackVolatility().link.dayCounter();
Calendar volcal = process_.blackVolatility().link.calendar();
double s0 = process_.stateVariable().link.value();
Utils.QL_REQUIRE(s0 > 0.0, () => "negative or null underlying given");
double v = process_.blackVolatility().link.blackVol(arguments_.exercise.lastDate(), s0);
Date maturityDate = arguments_.exercise.lastDate();
double r = process_.riskFreeRate().link.zeroRate(maturityDate, rfdc, Compounding.Continuous, Frequency.NoFrequency).value();
double q = process_.dividendYield().link.zeroRate(maturityDate, divdc, Compounding.Continuous, Frequency.NoFrequency).value();
Date referenceDate = process_.riskFreeRate().link.referenceDate();
// binomial trees with constant coefficient
Handle <YieldTermStructure> flatRiskFree = new Handle <YieldTermStructure>(new FlatForward(referenceDate, r, rfdc));
Handle <YieldTermStructure> flatDividends = new Handle <YieldTermStructure>(new FlatForward(referenceDate, q, divdc));
Handle <BlackVolTermStructure> flatVol = new Handle <BlackVolTermStructure>(new BlackConstantVol(referenceDate, volcal, v, voldc));
StrikedTypePayoff payoff = arguments_.payoff as StrikedTypePayoff;
Utils.QL_REQUIRE(payoff != null, () => "non-striked payoff given");
double maturity = rfdc.yearFraction(referenceDate, maturityDate);
StochasticProcess1D bs = new GeneralizedBlackScholesProcess(process_.stateVariable(),
flatDividends, flatRiskFree, flatVol);
// correct timesteps to ensure a (local) minimum, using Boyle and Lau
// approach. See Journal of Derivatives, 1/1994,
// "Bumping up against the barrier with the binomial method"
// Note: this approach works only for CoxRossRubinstein lattices, so
// is disabled if T is not a CoxRossRubinstein or derived from it.
int optimum_steps = timeSteps_;
if (maxTimeSteps_ > timeSteps_ && s0 > 0 && arguments_.barrier > 0) // boost::is_base_of<CoxRossRubinstein, T>::value &&
{
double divisor;
if (s0 > arguments_.barrier)
{
divisor = Math.Pow(Math.Log(s0 / arguments_.barrier.Value), 2);
}
else
{
divisor = Math.Pow(Math.Log(arguments_.barrier.Value / s0), 2);
}
if (!Utils.close(divisor, 0))
{
for (int i = 1; i < timeSteps_; ++i)
{
int optimum = (int)((i * i * v * v * maturity) / divisor);
if (timeSteps_ < optimum)
{
optimum_steps = optimum;
break; // found first minimum with iterations>=timesteps
}
}
}
if (optimum_steps > maxTimeSteps_)
{
optimum_steps = maxTimeSteps_; // too high, limit
}
}
TimeGrid grid = new TimeGrid(maturity, optimum_steps);
ITree tree = getTree_(bs, maturity, optimum_steps, payoff.strike());
BlackScholesLattice <ITree> lattice = new BlackScholesLattice <ITree>(tree, r, maturity, optimum_steps);
DiscretizedAsset option = getAsset_(arguments_, process_, grid);
option.initialize(lattice, maturity);
// Partial derivatives calculated from various points in the
// binomial tree
// (see J.C.Hull, "Options, Futures and other derivatives", 6th edition, pp 397/398)
// Rollback to third-last step, and get underlying prices (s2) &
// option values (p2) at this point
option.rollback(grid[2]);
Vector va2 = new Vector(option.values());
Utils.QL_REQUIRE(va2.size() == 3, () => "Expect 3 nodes in grid at second step");
double p2u = va2[2]; // up
double p2m = va2[1]; // mid
double p2d = va2[0]; // down (low)
double s2u = lattice.underlying(2, 2); // up price
double s2m = lattice.underlying(2, 1); // middle price
double s2d = lattice.underlying(2, 0); // down (low) price
// calculate gamma by taking the first derivate of the two deltas
double delta2u = (p2u - p2m) / (s2u - s2m);
double delta2d = (p2m - p2d) / (s2m - s2d);
double gamma = (delta2u - delta2d) / ((s2u - s2d) / 2);
// Rollback to second-last step, and get option values (p1) at
// this point
option.rollback(grid[1]);
Vector va = new Vector(option.values());
Utils.QL_REQUIRE(va.size() == 2, () => "Expect 2 nodes in grid at first step");
double p1u = va[1];
double p1d = va[0];
double s1u = lattice.underlying(1, 1); // up (high) price
double s1d = lattice.underlying(1, 0); // down (low) price
double delta = (p1u - p1d) / (s1u - s1d);
// Finally, rollback to t=0
option.rollback(0.0);
double p0 = option.presentValue();
// Store results
results_.value = p0;
results_.delta = delta;
results_.gamma = gamma;
// theta can be approximated by calculating the numerical derivative
// between mid value at third-last step and at t0. The underlying price
// is the same, only time varies.
results_.theta = (p2m - p0) / grid[2];
}
public override void calculate()
{
DayCounter rfdc = process_.riskFreeRate().link.dayCounter();
DayCounter divdc = process_.dividendYield().link.dayCounter();
DayCounter voldc = process_.blackVolatility().link.dayCounter();
Calendar volcal = process_.blackVolatility().link.calendar();
double s0 = process_.stateVariable().link.value();
Utils.QL_REQUIRE(s0 > 0.0, () => "negative or null underlying given");
double v = process_.blackVolatility().link.blackVol(arguments_.exercise.lastDate(), s0);
Date maturityDate = arguments_.exercise.lastDate();
double r = process_.riskFreeRate().link.zeroRate(maturityDate, rfdc, Compounding.Continuous, Frequency.NoFrequency).value();
double q = process_.dividendYield().link.zeroRate(maturityDate, divdc, Compounding.Continuous, Frequency.NoFrequency).value();
Date referenceDate = process_.riskFreeRate().link.referenceDate();
// binomial trees with constant coefficient
Handle <YieldTermStructure> flatRiskFree = new Handle <YieldTermStructure>(new FlatForward(referenceDate, r, rfdc));
Handle <YieldTermStructure> flatDividends = new Handle <YieldTermStructure>(new FlatForward(referenceDate, q, divdc));
Handle <BlackVolTermStructure> flatVol = new Handle <BlackVolTermStructure>(new BlackConstantVol(referenceDate, volcal, v, voldc));
StrikedTypePayoff payoff = arguments_.payoff as StrikedTypePayoff;
Utils.QL_REQUIRE(payoff != null, () => "non-striked payoff given");
double maturity = rfdc.yearFraction(referenceDate, maturityDate);
StochasticProcess1D bs = new GeneralizedBlackScholesProcess(process_.stateVariable(),
flatDividends, flatRiskFree, flatVol);
TimeGrid grid = new TimeGrid(maturity, timeSteps_);
ITree tree = getTree_(bs, maturity, timeSteps_, payoff.strike());
BlackScholesLattice <ITree> lattice = new BlackScholesLattice <ITree>(tree, r, maturity, timeSteps_);
DiscretizedAsset option = getAsset_(arguments_, process_, grid);
option.initialize(lattice, maturity);
// Partial derivatives calculated from various points in the
// binomial tree
// (see J.C.Hull, "Options, Futures and other derivatives", 6th edition, pp 397/398)
// Rollback to third-last step, and get underlying prices (s2) &
// option values (p2) at this point
option.rollback(grid[2]);
Vector va2 = new Vector(option.values());
Utils.QL_REQUIRE(va2.size() == 3, () => "Expect 3 nodes in grid at second step");
double p2u = va2[2]; // up
double p2m = va2[1]; // mid
double p2d = va2[0]; // down (low)
double s2u = lattice.underlying(2, 2); // up price
double s2m = lattice.underlying(2, 1); // middle price
double s2d = lattice.underlying(2, 0); // down (low) price
// calculate gamma by taking the first derivate of the two deltas
double delta2u = (p2u - p2m) / (s2u - s2m);
double delta2d = (p2m - p2d) / (s2m - s2d);
double gamma = (delta2u - delta2d) / ((s2u - s2d) / 2);
// Rollback to second-last step, and get option values (p1) at
// this point
option.rollback(grid[1]);
Vector va = new Vector(option.values());
Utils.QL_REQUIRE(va.size() == 2, () => "Expect 2 nodes in grid at first step");
double p1u = va[1];
double p1d = va[0];
double s1u = lattice.underlying(1, 1); // up (high) price
double s1d = lattice.underlying(1, 0); // down (low) price
double delta = (p1u - p1d) / (s1u - s1d);
// Finally, rollback to t=0
option.rollback(0.0);
double p0 = option.presentValue();
// Store results
results_.value = p0;
results_.delta = delta;
results_.gamma = gamma;
// theta can be approximated by calculating the numerical derivative
// between mid value at third-last step and at t0. The underlying price
// is the same, only time varies.
results_.theta = (p2m - p0) / grid[2];
}