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xlExport.cpp
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xlExport.cpp
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/*
Written by Antoine Savine in 2018
This code is the strict IP of Antoine Savine
License to use and alter this code for personal and commercial applications
is freely granted to any person or company who purchased a copy of the book
Modern Computational Finance: AAD and Parallel Simulations
Antoine Savine
Wiley, 2018
As long as this comment is preserved at the top of the file
*/
// Excel export wrappers to functions in main.h
#pragma warning(disable:4996)
#pragma warning(disable:4267)
#include "ThreadPool.h"
#include "main.h"
#include "toyCode.h"
#define WIN32_LEAN_AND_MEAN
#define NOMINMAX
#include <windows.h>
#include "xlcall.h"
#include "xlframework.h"
#include "xlOper.h"
// Helpers
NumericalParam xl2num(
const double useSobol,
const double seed1,
const double seed2,
const double numPath,
const double parallel)
{
NumericalParam num;
num.numPath = static_cast<int>(numPath + EPS);
num.parallel = parallel > EPS;
if (seed1 >= 1)
{
num.seed1 = static_cast<int>(seed1 + EPS);
}
else
{
num.seed1 = 1234;
}
if (seed2 >= 1)
{
num.seed2 = static_cast<int>(seed2 + EPS);
}
else
{
num.seed2 = num.seed1 + 1;
}
num.useSobol = useSobol > EPS;
return num;
}
// Wrappers
// change number of threads in the pool
extern "C" __declspec(dllexport)
double xRestartThreadPool(
double xNthread)
{
const int numThread = int(xNthread + EPS);
ThreadPool::getInstance()->stop();
ThreadPool::getInstance()->start(numThread);
return numThread;
}
extern "C" __declspec(dllexport)
LPXLOPER12 xPutDupire(
// model parameters
double spot,
FP12* spots,
FP12* times,
FP12* vols,
double maxDt,
LPXLOPER12 xid)
{
FreeAllTempMemory();
const string id = getString(xid);
// Make sure we have an id
if (maxDt <= 0.0 || id.empty()) return TempErr12(xlerrNA);
// Unpack
if (spots->rows * spots->columns * times->rows * times->columns != vols->rows * vols->columns)
{
return TempErr12(xlerrNA);
}
vector<double> vspots = to_vector(spots);
vector<double> vtimes = to_vector(times);
matrix<double> vvols = to_matrix(vols);
// Call and return
putDupire(spot, vspots, vtimes, vvols, maxDt, id);
return TempStr12(id);
}
extern "C" __declspec(dllexport)
LPXLOPER12 xPutBlackScholes(
double spot,
double vol,
double qSpot,
double rate,
double div,
LPXLOPER12 xid)
{
FreeAllTempMemory();
const string id = getString(xid);
// Make sure we have an id
if (id.empty()) return TempErr12(xlerrNA);
// Call and return
putBlackScholes(spot, vol, qSpot > 0, rate, div, id);
return TempStr12(id);
}
extern "C" __declspec(dllexport)
LPXLOPER12 xPutDLM(
// model parameters
LPXLOPER12 assets,
FP12* spots,
FP12* atms,
FP12* skews,
double discRate,
FP12* repoSpreads,
FP12* divDates,
FP12* divs,
FP12* correl,
double lambda,
LPXLOPER12 xid)
{
FreeAllTempMemory();
const string id = getString(xid);
// Make sure we have an id
if (id.empty()) return TempErr12(xlerrNA);
// Assets
vector<string> vassets = to_strVector(assets);
if (vassets.empty()) return TempErr12(xlerrNA);
for (const auto& asset : vassets) if (asset.empty()) return TempErr12(xlerrNA);
const size_t vnumassets = vassets.size();
// Check dimensions
if ( spots->rows * spots->columns != vnumassets
|| repoSpreads->rows * repoSpreads->columns != vnumassets
|| atms->rows * atms->columns != vnumassets
|| skews->rows * skews->columns != vnumassets
|| divs->rows != divDates->rows || divs->columns != vnumassets || divDates->columns != 1
|| correl->rows != vnumassets || correl->columns != vnumassets)
{
return TempErr12(xlerrNA);
}
// Unpack
vector<double> vspots = to_vector(spots);
vector<double> vspreads = to_vector(repoSpreads);
vector<double> vatms = to_vector(atms);
vector<double> vskews = to_vector(skews);
vector<double> vdivtimes = to_vector(divDates);
matrix<double> vdivs = to_matrix(divs);
matrix<double> vcorrel = to_matrix(correl);
// Call and return
putDisplaced(vassets, vspots, vatms, vskews, discRate, vspreads, vdivtimes, vdivs, vcorrel, lambda, id);
return TempStr12(id);
}
extern "C" __declspec(dllexport)
LPXLOPER12 xViewDLM(
LPXLOPER12 xid)
{
FreeAllTempMemory();
const string id = getString(xid);
// Make sure we have an id
if (id.empty()) return TempErr12(xlerrNA);
try
{
Model<double>* mdl = const_cast<Model<double>*>(getModel<double>(id));
// Make sure we have a model
if (!mdl) return TempErr12(xlerrNA);
MultiDisplaced<double>* dlm = dynamic_cast<MultiDisplaced<double>*>(mdl);
// Make sure it is a DLM
if (!dlm) return TempErr12(xlerrNA);
// Initialize it
vector<Time> timeline = { 1.0 };
vector<SampleDef> defline(1);
defline[0].numeraire = false;
defline[0].discountMats = {};
defline[0].liborDefs = {};
defline[0].forwardMats = vector<vector<Time>>(dlm->numAssets(), { 1.0 });
dlm->allocate(timeline, defline);
dlm->init(timeline, defline);
const size_t n = dlm->numAssets() + 1, m = 4;
LPXLOPER12 oper = TempXLOPER12();
resize(oper, n, m);
setString(oper, "dynamics", 0, 1);
setString(oper, "alpha", 0, 2);
setString(oper, "beta", 0, 3);
for (size_t i = 0; i < dlm->numAssets(); ++i)
{
setString(oper, dlm->assetNames()[i], i + 1, 0);
switch(dlm->dynamics()[i])
{
case 0:
setString(oper, "lognormal", i + 1, 1);
break;
case 1:
setString(oper, "normal", i + 1, 1);
break;
case 2:
setString(oper, "surnormal", i + 1, 1);
break;
case 3:
setString(oper, "subnormal", i + 1, 1);
break;
default:
setString(oper, "invalid", i + 1, 1);
break;
}
setNum(oper, dlm->alphas()[i], i + 1, 2);
setNum(oper, dlm->betas()[i], i + 1, 3);
}
return oper;
}
catch (const exception&)
{
return TempErr12(xlerrNA);
}
}
extern "C" __declspec(dllexport)
LPXLOPER12 xPutEuropean(
double strike,
double exerciseDate,
double settlementDate,
LPXLOPER12 xid)
{
FreeAllTempMemory();
const string id = getString(xid);
// Make sure we have an id
if (id.empty()) return TempErr12(xlerrNA);
if (settlementDate <= 0) settlementDate = exerciseDate;
// Call and return
putEuropean(strike, exerciseDate, settlementDate, id);
return TempStr12(id);
}
extern "C" __declspec(dllexport)
LPXLOPER12 xPutBarrier(
double strike,
double barrier,
double maturity,
double monitorFreq,
double smoothing,
LPXLOPER12 xcallput,
LPXLOPER12 xid)
{
FreeAllTempMemory();
const string id = getString(xid);
// Make sure we have an id
if (id.empty()) return TempErr12(xlerrNA);
// Call or put?
const string cpStr = getString(xcallput);
bool callPut = !cpStr.empty() && (cpStr[0] == 'p' || cpStr[0] == 'P');
// Call and return
putBarrier(strike, barrier, maturity, monitorFreq, smoothing, callPut, id);
return TempStr12(id);
}
extern "C" __declspec(dllexport)
LPXLOPER12 xPutContingent(
double coupon,
double maturity,
double payFreq,
double smoothing,
LPXLOPER12 xid)
{
FreeAllTempMemory();
const string id = getString(xid);
// Make sure we have an id
if (id.empty()) return TempErr12(xlerrNA);
// Call and return
putContingent(coupon, maturity, payFreq, smoothing, id);
return TempStr12(id);
}
extern "C" __declspec(dllexport)
LPXLOPER12 xPutEuropeans(
FP12* maturities,
FP12* strikes,
LPXLOPER12 xid)
{
FreeAllTempMemory();
const string id = getString(xid);
// Make sure we have an id
if (id.empty()) return TempErr12(xlerrNA);
// Make sure we have options
if (!strikes->rows || !strikes->columns) return TempErr12(xlerrNA);
// Maturities and strikes, removing blanks
vector<double> vmats;
vector<double> vstrikes;
{
size_t rows = maturities->rows;
size_t cols = maturities->columns;
if (strikes->rows * strikes->columns != rows * cols) return TempErr12(xlerrNA);
double* mats= maturities->array;
double* strs = strikes->array;
for (size_t i = 0; i < cols * rows; ++i)
{
if (mats[i] > EPS && strs[i] > EPS)
{
vmats.push_back(mats[i]);
vstrikes.push_back(strs[i]);
}
}
}
// Make sure we still have options
if (vmats.empty()) return TempErr12(xlerrNA);
// Call and return
putEuropeans(vmats, vstrikes, id);
return TempStr12(id);
}
extern "C" __declspec(dllexport)
LPXLOPER12 xPutMultiStats(
LPXLOPER12 assets,
FP12* fix,
FP12* fwd,
LPXLOPER12 xid)
{
FreeAllTempMemory();
const string id = getString(xid);
// Make sure we have an id
if (id.empty()) return TempErr12(xlerrNA);
vector<string> vassets = to_strVector(assets);
// Make sure we have assets
if (vassets.empty()) return TempErr12(xlerrNA);
// Fixing and fwd dates, removing blanks and zeros (not today)
vector<Time> vfix;
vector<Time> vfwd;
{
size_t rows = fix->rows;
size_t cols = fix->columns;
if (fwd->rows * fwd->columns != rows * cols) return TempErr12(xlerrNA);
Time* fixs = fix->array;
Time* fwds = fwd->array;
for (size_t i = 0; i < cols * rows; ++i)
{
if (fixs[i] > EPS && fwds[i] > EPS)
{
// Check
if (i > 0 && fixs[i] <= fixs[i-1]) return TempErr12(xlerrNA);
if (fixs[i] > fwds[i]) return TempErr12(xlerrNA);
// Set
vfix.push_back(fixs[i]);
vfwd.push_back(fwds[i]);
}
}
}
// Call and return
putMultiStats(vassets, vfix, vfwd, id);
return TempStr12(id);
}
extern "C" __declspec(dllexport)
LPXLOPER12 xPutBaskets(
LPXLOPER12 assets,
FP12* weights,
double maturity,
FP12* strikes,
LPXLOPER12 xid)
{
FreeAllTempMemory();
const string id = getString(xid);
// Make sure we have an id
if (id.empty()) return TempErr12(xlerrNA);
vector<string> vassets = to_strVector(assets);
// Make sure we have assets
if (vassets.empty()) return TempErr12(xlerrNA);
// Maturity
if (maturity <= 0) return TempErr12(xlerrNA);
// Weights and strikes
vector<double> vweights = to_vector(weights);
vector<double> vstrikes = to_vector(strikes);
if (vweights.empty() || vstrikes.empty()) TempErr12(xlerrNA);
// Call and return
putBaskets(vassets, vweights, maturity, vstrikes, id);
return TempStr12(id);
}
extern "C" __declspec(dllexport)
LPXLOPER12 xPutAutocall(
LPXLOPER12 assets,
FP12* refs,
double maturity,
double periods,
double ko,
double strike,
double cpn,
double smooth,
LPXLOPER12 xid)
{
FreeAllTempMemory();
const string id = getString(xid);
// Make sure we have an id
if (id.empty()) return TempErr12(xlerrNA);
vector<string> vassets = to_strVector(assets);
vector<double> vrefs = to_vector(refs);
// Make sure we have assets and dimensions are consistent
if (vassets.empty()) return TempErr12(xlerrNA);
if (vassets.size() != vrefs.size()) return TempErr12(xlerrNA);
// Maturity
if (maturity <= 0) return TempErr12(xlerrNA);
if (int(periods + EPS) <= 0) return TempErr12(xlerrNA);
// Call and return
putAutocall(vassets, vrefs, maturity, int(periods + EPS), ko, strike, cpn, smooth, id);
return TempStr12(id);
}
// Access payoff identifiers and parameters
extern "C" __declspec(dllexport)
LPXLOPER12 xPayoffIds(
LPXLOPER12 xid)
{
FreeAllTempMemory();
const string id = getString(xid);
// Make sure we have an id
if (id.empty()) return TempErr12(xlerrNA);
const auto* prd = getProduct<double>(id);
// Make sure we have a product
if (!prd) return TempErr12(xlerrNA);
return from_strVector(prd->payoffLabels());
}
extern "C" __declspec(dllexport)
LPXLOPER12 xParameters(
LPXLOPER12 xid)
{
FreeAllTempMemory();
const string id = getString(xid);
// Make sure we have an id
if (id.empty()) return TempErr12(xlerrNA);
Model<double>* mdl = const_cast<Model<double>*>(getModel<double>(id));
// Make sure we have a model
if (!mdl) return TempErr12(xlerrNA);
const auto& paramLabels = mdl->parameterLabels();
const auto& params = mdl->parameters();
vector<double> paramsCopy(params.size());
transform(params.begin(), params.end(), paramsCopy.begin(), [](const double* p) { return *p; });
return from_labelsAndNumbers(paramLabels, paramsCopy);
}
extern "C" __declspec(dllexport)
LPXLOPER12 xValue(
LPXLOPER12 modelid,
LPXLOPER12 productid,
// numerical parameters
double useSobol,
double seed1,
double seed2,
double numPath,
double parallel)
{
FreeAllTempMemory();
const string pid = getString(productid);
// Make sure we have an id
if (pid.empty()) return TempErr12(xlerrNA);
const auto* prd = getProduct<double>(pid);
// Make sure we have a product
if (!prd) return TempErr12(xlerrNA);
const string mid = getString(modelid);
// Make sure we have an id
if (mid.empty()) return TempErr12(xlerrNA);
Model<double>* mdl = const_cast<Model<double>*>(getModel<double>(mid));
// Make sure we have a model
if (!mdl) return TempErr12(xlerrNA);
// Numerical params
const auto num = xl2num(useSobol, seed1, seed2, numPath, parallel);
// Make sure we have a numPath
if (!num.numPath) return TempErr12(xlerrNA);
// Call and return;
try
{
auto results = value(mid, pid, num);
return from_labelsAndNumbers(results.identifiers, results.values);
}
catch (const exception&)
{
return TempErr12(xlerrNA);
}
}
extern "C" __declspec(dllexport)
LPXLOPER12 xValueTime(
LPXLOPER12 modelid,
LPXLOPER12 productid,
// numerical parameters
double useSobol,
double seed1,
double seed2,
double numPath,
double parallel)
{
FreeAllTempMemory();
const string pid = getString(productid);
// Make sure we have an id
if (pid.empty()) return TempErr12(xlerrNA);
const auto* prd = getProduct<double>(pid);
// Make sure we have a product
if (!prd) return TempErr12(xlerrNA);
const string mid = getString(modelid);
// Make sure we have an id
if (mid.empty()) return TempErr12(xlerrNA);
Model<double>* mdl = const_cast<Model<double>*>(getModel<double>(mid));
// Make sure we have a model
if (!mdl) return TempErr12(xlerrNA);
// Numerical params
const auto num = xl2num(useSobol, seed1, seed2, numPath, parallel);
// Make sure we have a numPath
if (!num.numPath) return TempErr12(xlerrNA);
// Call and return;
try
{
clock_t t0 = clock();
auto results = value(mid, pid, num);
clock_t t1 = clock();
LPXLOPER12 oper = TempXLOPER12();
resize(oper, results.values.size() + 1, 1);
for (int i = 0; i < results.values.size(); ++i) setNum(oper, results.values[i], i, 0);
setNum(oper, t1 - t0, results.values.size(), 0);
return oper;
}
catch (const exception&)
{
return TempErr12(xlerrNA);
}
}
extern "C" __declspec(dllexport)
LPXLOPER12 xAADrisk(
LPXLOPER12 modelid,
LPXLOPER12 productid,
LPXLOPER12 xRiskPayoff,
// numerical parameters
double useSobol,
double seed1,
double seed2,
double numPath,
double parallel)
{
FreeAllTempMemory();
const string pid = getString(productid);
// Make sure we have an id
if (pid.empty()) return TempErr12(xlerrNA);
const string mid = getString(modelid);
// Make sure we have an id
if (mid.empty()) return TempErr12(xlerrNA);
// Numerical params
const auto num = xl2num(useSobol, seed1, seed2, numPath, parallel);
// Make sure we have a numPath
if (!num.numPath) return TempErr12(xlerrNA);
// Risk payoff
const string riskPayoff = getString(xRiskPayoff);
try
{
auto results = AADriskOne(mid, pid, num, riskPayoff);
const size_t n = results.risks.size(), N = n + 1;
LPXLOPER12 oper = TempXLOPER12();
resize(oper, N, 2);
setString(oper, "value", 0, 0);
setNum(oper, results.riskPayoffValue, 0, 1);
for (size_t i = 0; i < n; ++i)
{
setString(oper, results.paramIds[i], i + 1, 0);
setNum(oper, results.risks[i], i + 1, 1);
}
return oper;
}
catch (const exception&)
{
return TempErr12(xlerrNA);
}
}
extern "C" __declspec(dllexport)
LPXLOPER12 xAADriskAggregate(
LPXLOPER12 modelid,
LPXLOPER12 productid,
LPXLOPER12 xPayoffs,
FP12* xNotionals,
// numerical parameters
double useSobol,
double seed1,
double seed2,
double numPath,
double parallel)
{
FreeAllTempMemory();
const string pid = getString(productid);
// Make sure we have an id
if (pid.empty()) return TempErr12(xlerrNA);
const string mid = getString(modelid);
// Make sure we have an id
if (mid.empty()) return TempErr12(xlerrNA);
// Numerical params
const auto num = xl2num(useSobol, seed1, seed2, numPath, parallel);
// Make sure we have a numPath
if (!num.numPath) return TempErr12(xlerrNA);
// Payoffs and notionals, removing blanks
map<string, double> notionals;
{
size_t rows = getRows(xPayoffs);
size_t cols = getCols(xPayoffs);
if (rows * cols == 0 ||
xNotionals->rows * xNotionals->columns != rows * cols)
return TempErr12(xlerrNA);
size_t idx = 0;
for (size_t i = 0; i < rows; ++i) for (size_t j = 0; j < cols; ++j)
{
string payoff = getString(xPayoffs, i, j);
double notional = xNotionals->array[idx++];
if (payoff != "" && fabs(notional) > EPS)
{
notionals[payoff] = notional;
}
}
}
try
{
auto results = AADriskAggregate(mid, pid, notionals, num);
const size_t n = results.risks.size(), N = n + 1;
LPXLOPER12 oper = TempXLOPER12();
resize(oper, N, 2);
setString(oper, "value", 0, 0);
setNum(oper, results.riskPayoffValue, 0, 1);
for (size_t i = 0; i < n; ++i)
{
setString(oper, results.paramIds[i], i + 1, 0);
setNum(oper, results.risks[i], i + 1, 1);
}
return oper;
}
catch (const exception&)
{
return TempErr12(xlerrNA);
}
}
unordered_map<string, RiskReports> riskStore;
extern "C" __declspec(dllexport)
LPXLOPER12 xBumprisk(
LPXLOPER12 modelid,
LPXLOPER12 productid,
// numerical parameters
double useSobol,
double seed1,
double seed2,
double numPath,
double parallel,
// display now or put in memory?
double displayNow,
LPXLOPER12 storeid)
{
FreeAllTempMemory();
const string pid = getString(productid);
// Make sure we have an id
if (pid.empty()) return TempErr12(xlerrNA);
const string mid = getString(modelid);
// Make sure we have an id
if (mid.empty()) return TempErr12(xlerrNA);
// Numerical params
const auto num = xl2num(useSobol, seed1, seed2, numPath, parallel);
// Make sure we have a numPath
if (!num.numPath) return TempErr12(xlerrNA);
try
{
auto results = bumpRisk(mid, pid, num);
if (displayNow > 0.5)
{
return from_labelledMatrix(results.params, results.payoffs, results.risks, "value", results.values);
}
else
{
const string riskId = getString(storeid);
if (riskId == "") return TempErr12(xlerrNA);
riskStore[riskId] = results;
return storeid;
}
}
catch (const exception&)
{
return TempErr12(xlerrNA);
}
}
extern "C" __declspec(dllexport)
LPXLOPER12 xAADriskMulti(
LPXLOPER12 modelid,
LPXLOPER12 productid,
// numerical parameters
double useSobol,
double seed1,
double seed2,
double numPath,
double parallel,
// display now or put in memory?
double displayNow,
LPXLOPER12 storeid)
{
FreeAllTempMemory();
const string pid = getString(productid);
// Make sure we have an id
if (pid.empty()) return TempErr12(xlerrNA);
const string mid = getString(modelid);
// Make sure we have an id
if (mid.empty()) return TempErr12(xlerrNA);
// Numerical params
const auto num = xl2num(useSobol, seed1, seed2, numPath, parallel);
// Make sure we have a numPath
if (!num.numPath) return TempErr12(xlerrNA);
try
{
auto results = AADriskMulti(mid, pid, num);
if (displayNow > 0.5)
{
return from_labelledMatrix(results.params, results.payoffs, results.risks, "value", results.values);
}
else
{
const string riskId = getString(storeid);
if (riskId == "") return TempErr12(xlerrNA);
riskStore[riskId] = results;
return storeid;
}
}
catch (const exception&)
{
return TempErr12(xlerrNA);
}
}
extern "C" __declspec(dllexport)
LPXLOPER12 xDisplayRisk(
LPXLOPER12 riskid,
LPXLOPER12 displayid)
{
FreeAllTempMemory();
RiskReports* results;
const string riskId = getString(riskid);
auto it = riskStore.find(riskId);
if (it == riskStore.end()) return TempErr12(xlerrNA);
else results = &it->second;
const vector<string> riskIds = to_strVector(displayid);
vector<size_t> riskCols;
for (const auto& id : riskIds)
{
auto it2 = find(results->payoffs.begin(), results->payoffs.end(), id);
if (it2 == results->payoffs.end()) return TempErr12(xlerrNA);
riskCols.push_back(distance(results->payoffs.begin(), it2));
}
if (riskCols.empty()) return TempErr12(xlerrNA);
const size_t nParam = results->risks.rows();
const size_t nPayoffs = riskCols.size();
vector<double> showVals(nPayoffs);
matrix<double> showRisks(nParam, nPayoffs);
for (size_t j = 0; j < nPayoffs; ++j)
{
for (size_t i = 0; i < nParam; ++i)
{
showRisks[i][j] = results->risks[i][riskCols[j]];
}
showVals[j] = results->values[riskCols[j]];
}
return from_labelledMatrix(results->params, riskIds, showRisks, "value", showVals);
}
extern "C" __declspec(dllexport)
LPXLOPER12 xDupireCalib(
// Merton market parameters
const double spot,
const double vol,
const double jmpIntens,
const double jmpAverage,
const double jmpStd,
// Discretization
FP12* spots,
const double maxDs,
FP12* times,
const double maxDt)
{
FreeAllTempMemory();
// Make sure the last input is given
if (maxDs == 0 || maxDt == 0) return 0;
// Unpack
vector<double> vspots;
{
size_t rows = spots->rows;
size_t cols = spots->columns;
double* numbers = spots->array;
vspots.resize(rows*cols);
copy(numbers, numbers + rows*cols, vspots.begin());
}
vector<double> vtimes;
{
size_t rows = times->rows;
size_t cols = times->columns;
double* numbers = times->array;
vtimes.resize(rows*cols);
copy(numbers, numbers + rows*cols, vtimes.begin());
}
auto results = dupireCalib(vspots, maxDs, vtimes, maxDt,
spot, vol, jmpIntens, jmpAverage, jmpStd);
// Return
return from_labelledMatrix(results.spots, results.times, results.lVols);
}
extern "C" __declspec(dllexport)
LPXLOPER12 xDupireSuperbucket(
// Merton market parameters
const double spot,
const double vol,
const double jmpIntens,
const double jmpAverage,
const double jmpStd,
// risk view
FP12* strikes,
FP12* mats,
// calibration
FP12* spots,
double maxDs,
FP12* times,
double maxDtVol,
// MC
double maxDtSimul,
// product
LPXLOPER12 productid,
LPXLOPER12 xPayoffs,
FP12* xNotionals,
// numerical parameters
double useSobol,
double seed1,
double seed2,
double numPath,
double parallel,
// bump or AAD?
double bump)
{
FreeAllTempMemory();
// Make sure the last input is given
if (numPath <= 0) return TempErr12(xlerrNA);