public static string eqMathBiLinearInterpolation(
[ExcelArgument(Description = "interpolation obj id")] string objId,
[ExcelArgument(Description = "row variable x ")] double[] x,
[ExcelArgument(Description = "col variable y ")] double[] y,
[ExcelArgument(Description = "variable z ")] double[,] z)
{
if (ExcelUtil.CallFromWizard())
{
return("");
}
string callerAddress = "";
callerAddress = ExcelUtil.getActiveCellAddress();
try
{
if ((x.Length != z.GetLength(0)) || (y.Length != z.GetLength(1)))
{
return("size mismatch");
}
QlArray xa = new QlArray((uint)x.Length);
QlArray ya = new QlArray((uint)y.Length);
for (uint i = 0; i < x.Length; i++)
{
xa.set(i, x[i]);
ya.set(i, y[i]);
}
Matrix ma = new Matrix((uint)x.Length, (uint)y.Length);
for (uint i = 0; i < x.Length; i++)
{
for (uint j = 0; j < y.Length; j++)
{
ma.set(i, j, z[i, j]);
}
}
BilinearInterpolation interp = new BilinearInterpolation(xa, ya, ma);
// Store the futures and return its id
string id = "Int@" + objId;
OHRepository.Instance.storeObject(id, interp, callerAddress);
id += "#" + (String)DateTime.Now.ToString(@"HH:mm:ss");
return(id);
}
catch (Exception e)
{
ExcelUtil.logError(callerAddress, System.Reflection.MethodInfo.GetCurrentMethod().Name.ToString(), e.Message);
return(e.Message);
}
}
public static string eqModelSVI(
[ExcelArgument(Description = "id of option to be constructed ")] string ObjectId,
[ExcelArgument(Description = "ATM forward ")] double forward,
[ExcelArgument(Description = "expiry (years of fraction ")] double tenor,
[ExcelArgument(Description = "Strikes ")] double[] strikes,
[ExcelArgument(Description = "implied vols ")] double[] volatilities,
[ExcelArgument(Description = "initial parameters ")] double[] initials,
[ExcelArgument(Description = "trigger ")] object trigger)
{
if (ExcelUtil.CallFromWizard())
{
return("");
}
string callerAddress = "";
callerAddress = ExcelUtil.getActiveCellAddress();
try
{
if (strikes.Length != volatilities.Length)
{
throw new Exception("SABR input lengths don't match.");
}
if (initials.Length != 5)
{
throw new Exception("SVI has five parameters.");
}
int[] idx = volatilities.Select((v, Index) => new { V = v, idx = Index })
.Where(x => x.V == 0)
.Select(x => x.idx)
.ToArray();
QlArray xx = new QlArray((uint)strikes.Length - (uint)idx.Length);
QlArray yy = new QlArray((uint)volatilities.Length - (uint)idx.Length);
for (uint i = 0, j = 0; i < strikes.Length; i++)
{
if (volatilities[i] == 0) // empty
{
continue;
}
xx.set(j, strikes[i]);
yy.set(j, volatilities[i]);
j++;
}
EndCriteria endcriteria = new EndCriteria(100000, 100, 1e-8, 1e-8, 1e-8);
OptimizationMethod opmodel = new Simplex(0.01);
// alpha: ATM Vol, beta: CEV param, rho: underlying/vol correlation, nu: vol of vol
SVIInterpolation svi = new SVIInterpolation(xx, yy, tenor, forward,
initials[0], initials[1], initials[2], initials[3], initials[4],
endcriteria, opmodel, true);
double err = 0;
err = svi.update();
// Store the option and return its id
string id = "MODEL@" + ObjectId;
OHRepository.Instance.storeObject(id, svi, callerAddress);
id += "#" + (String)DateTime.Now.ToString(@"HH:mm:ss");
return(id);
}
catch (Exception e)
{
ExcelUtil.logError(callerAddress, System.Reflection.MethodInfo.GetCurrentMethod().Name.ToString(), e.Message);
return(e.Message);
}
}
static void Main(string[] args)
{
const int xSteps = 100;
const int tSteps = 25;
const int dampingSteps = 0;
Date today = new Date(15, Month.January, 2020);
Settings.instance().setEvaluationDate(today);
DayCounter dc = new Actual365Fixed();
YieldTermStructureHandle rTS = new YieldTermStructureHandle(
new FlatForward(today, 0.06, dc));
YieldTermStructureHandle qTS = new YieldTermStructureHandle(
new FlatForward(today, 0.02, dc));
const double strike = 110.0;
StrikedTypePayoff payoff = new PlainVanillaPayoff(Option.Type.Put, strike);
Date maturityDate = today.Add(new Period(1, TimeUnit.Years));
double maturity = dc.yearFraction(today, maturityDate);
Exercise exercise = new AmericanExercise(today, maturityDate);
Instrument vanillaOption = new VanillaOption(payoff, exercise);
QuoteHandle spot = new QuoteHandle(new SimpleQuote(100.0));
BlackVolTermStructureHandle volatility = new BlackVolTermStructureHandle(
new BlackConstantVol(today, new TARGET(), 0.20, dc));
BlackScholesMertonProcess process =
new BlackScholesMertonProcess(spot, qTS, rTS, volatility);
vanillaOption.setPricingEngine(new FdBlackScholesVanillaEngine(
process, tSteps, xSteps, dampingSteps));
double expected = vanillaOption.NPV();
// build an PDE engine from scratch
Fdm1dMesher equityMesher = new FdmBlackScholesMesher(
xSteps, process, maturity, strike,
nullDouble(), nullDouble(), 0.0001, 1.5,
new DoublePair(strike, 0.1));
FdmMesherComposite mesher = new FdmMesherComposite(equityMesher);
FdmLinearOpComposite op = new FdmBlackScholesOp(mesher, process, strike);
FdmInnerValueCalculator calc = new FdmLogInnerValue(payoff, mesher, 0);
QlArray x = new QlArray(equityMesher.size());
QlArray rhs = new QlArray(equityMesher.size());
FdmLinearOpIterator iter = mesher.layout().begin();
for (uint i = 0; i < rhs.size(); ++i, iter.increment())
{
x.set(i, mesher.location(iter, 0));
rhs.set(i, calc.avgInnerValue(iter, maturity));
}
FdmBoundaryConditionSet bcSet = new FdmBoundaryConditionSet();
FdmStepConditionComposite stepCondition =
FdmStepConditionComposite.vanillaComposite(
new DividendSchedule(), exercise, mesher, calc, today, dc);
FdmLinearOpComposite proxyOp = new FdmLinearOpCompositeProxy(
new FdmBSDelegate(op));
FdmBackwardSolver solver = new FdmBackwardSolver(
proxyOp, bcSet, stepCondition, FdmSchemeDesc.Douglas());
solver.rollback(rhs, maturity, 0.0, tSteps, dampingSteps);
double logS = Math.Log(spot.value());
double calculated = new CubicNaturalSpline(x, rhs).call(logS);
Console.WriteLine("Homebrew PDE engine : {0:0.0000}", calculated);
Console.WriteLine("FdBlackScholesVanillaEngine: {0:0.0000}", expected);
}
