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mcPrdMulti.h
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#pragma once
#include "mcPrd.h"
/* A test class, computing statistics on multiple assets on multiple dates
On each date T, the payoffs are xi and xixj so their expectations give expectations and covariances
We also export yi and yiyj where y = xi(Tk) - xi(Tk-1) so we get stats on increments too
Finally, xi(Tk) is the fwd fixed at Tk for the corresponding maturity Tk' >= Tk
*/
template <class T>
class MultiStats : public Product<T>
{
// Timeline
vector<Time> myFixDates;
vector<Time> myFwdDates;
// Assets
size_t myNumAssets;
vector<string> myAssetNames;
// Defline and labels
vector<SampleDef> myDefline;
size_t myNumPayoffs;
vector<string> myLabels;
public:
// Constructor: store data and build timeline
MultiStats(const vector<string>& assets, const vector<Time>& fixDates, const vector<Time>& fwdDates) :
myNumAssets(assets.size()), myAssetNames(assets), myFixDates(fixDates), myFwdDates(fwdDates)
{
// Defline = num and forward(Tfix, Tfwd) on every fix date, for all assets
const size_t nTimes = fixDates.size();
myDefline.resize(nTimes);
for (size_t i = 0; i < nTimes; ++i)
{
myDefline[i].numeraire = false;
myDefline[i].forwardMats.resize(myNumAssets);
fill(myDefline[i].forwardMats.begin(), myDefline[i].forwardMats.end(), vector<Time>(1, myFwdDates[i]));
}
// Identify the payoffs
myNumPayoffs = (nTimes + (nTimes > 1 ? nTimes - 1: 0)) * (myNumAssets + myNumAssets * (myNumAssets + 3) / 2);
// First, fwd fixings on fix dates
for (size_t t = 0; t < nTimes; ++t)
{
for (size_t a1 = 0; a1 < myNumAssets; ++a1)
{
ostringstream ost;
ost.precision(2);
ost << fixed;
ost << myAssetNames[a1] << " " << myFixDates[t] << " " << myFwdDates[t];
myLabels.push_back(ost.str());
}
for (size_t a1 = 0; a1 < myNumAssets; ++a1) for (size_t a2 = 0; a2 <= a1; ++a2)
{
ostringstream ost;
ost.precision(2);
ost << fixed;
ost << myAssetNames[a1] << " " << myAssetNames[a2] << " " << myFixDates[t] << " " << myFwdDates[t];
myLabels.push_back(ost.str());
}
}
// Next, differences
for (size_t t2 = 1; t2 < nTimes; ++t2)
{
const size_t t1 = t2 - 1;
for (size_t a1 = 0; a1 < myNumAssets; ++a1)
{
ostringstream ost;
ost.precision(2);
ost << fixed;
ost << myAssetNames[a1] << " " << myFixDates[t1] << " " << myFwdDates[t1] << " - " << myFixDates[t2] << " " << myFwdDates[t2];
myLabels.push_back(ost.str());
}
for (size_t a1 = 0; a1 < myNumAssets; ++a1) for (size_t a2 = 0; a2 <= a1; ++a2)
{
ostringstream ost;
ost.precision(2);
ost << fixed;
ost << myAssetNames[a1] << " " << myAssetNames[a2] << " " << myFixDates[t1] << " " << myFwdDates[t1] << " - " << myFixDates[t2] << " " << myFwdDates[t2];
myLabels.push_back(ost.str());
}
}
}
// Read access to parameters
const size_t numAssets() const override
{
return myNumAssets;
}
const vector<string>& assetNames() const override
{
return myAssetNames;
}
const vector<Time>& fixDates() const
{
return myFixDates;
}
const vector<Time>& fwdDates() const
{
return myFwdDates;
}
// Virtual copy constructor
unique_ptr<Product<T>> clone() const override
{
return make_unique<MultiStats<T>>(*this);
}
// Timeline
const vector<Time>& timeline() const override
{
return myFixDates;
}
// Defline
const vector<SampleDef>& defline() const override
{
return myDefline;
}
// Labels
const vector<string>& payoffLabels() const override
{
return myLabels;
}
// Evaluation on scenario
void payoffs(
// path, one entry per time step
const Scenario<T>& path,
// pre-allocated space for resulting payoffs
vector<T>& payoffs)
const override
{
const size_t nTimes = myFixDates.size();
size_t payIdx = 0;
// First, fwd fixings on fix dates
for (size_t t = 0; t < nTimes; ++t)
{
for (size_t a1 = 0; a1 < myNumAssets; ++a1)
{
payoffs[payIdx++] = path[t].forwards[a1].front();
}
for (size_t a1 = 0; a1 < myNumAssets; ++a1) for (size_t a2 = 0; a2 <= a1; ++a2)
{
payoffs[payIdx++] = path[t].forwards[a1].front() * path[t].forwards[a2].front();
}
}
// Next, differences
for (size_t t2 = 1; t2 < nTimes; ++t2)
{
const size_t t1 = t2 - 1;
for (size_t a1 = 0; a1 < myNumAssets; ++a1)
{
payoffs[payIdx++] = path[t2].forwards[a1].front() - path[t1].forwards[a1].front();
}
for (size_t a1 = 0; a1 < myNumAssets; ++a1) for (size_t a2 = 0; a2 <= a1; ++a2)
{
payoffs[payIdx++] = (path[t2].forwards[a1].front() - path[t1].forwards[a1].front())
* (path[t2].forwards[a2].front() - path[t1].forwards[a2].front());
}
}
}
};
template <class T>
class Baskets : public Product<T>
{
// Assets and weights
size_t myNumAssets;
vector<string> myAssetNames;
vector<double> myWeights;
// Timeline
Time myMaturity;
// Vector of strikes
vector<double> myStrikes;
vector<Time> myTimeline;
vector<SampleDef> myDefline;
vector<string> myLabels;
public:
// Constructor: store data and build timeline
Baskets(const vector<string>& assets, const vector<double> weights, const Time maturity, const vector<double>& strikes) :
myNumAssets(assets.size()), myAssetNames(assets), myWeights(weights), myMaturity(maturity), myStrikes(strikes),
myTimeline(1, maturity), myDefline(1)
{
const size_t n = strikes.size();
// Defline = num and spot(t) = forward(t,t) on maturity for all assets
myDefline[0].numeraire = true;
myDefline[0].forwardMats = vector<vector<Time>>(myNumAssets, { maturity });
// Identify the payoffs
myLabels.reserve(strikes.size());
for (const double strike : strikes)
{
ostringstream ost;
ost.precision(2);
ost << fixed;
ost << "basket strike " << strike;
myLabels.push_back(ost.str());
}
}
const size_t numAssets() const override
{
return myNumAssets;
}
const vector<string>& assetNames() const override
{
return myAssetNames;
}
// access to weights, maturity and strikes
const vector<double>& weights() const
{
return myWeights;
}
Time maturity() const
{
return myMaturity;
}
const vector<double>& strikes() const
{
return myStrikes;
}
// Virtual copy constructor
unique_ptr<Product<T>> clone() const override
{
return make_unique<Baskets<T>>(*this);
}
// Timeline
const vector<Time>& timeline() const override
{
return myTimeline;
}
// Defline
const vector<SampleDef>& defline() const override
{
return myDefline;
}
// Labels
const vector<string>& payoffLabels() const override
{
return myLabels;
}
// Payoffs, maturity major
void payoffs(
// path, one entry per time step
const Scenario<T>& path,
// pre-allocated space for resulting payoffs
vector<T>& payoffs)
const override
{
T basket = inner_product(myWeights.begin(), myWeights.end(), path[0].forwards.begin(), T(0.0),
plus<T>(), [](const double weight, const vector<T>& fwds) { return weight * fwds[0]; });
transform(myStrikes.begin(), myStrikes.end(), payoffs.begin(),
[&basket, num = path[0].numeraire](const double k) {return max(basket - k, 0.0) / num; });
}
};
template <class T>
class Autocall : public Product<T>
{
// Assets and weights
size_t myNumAssets;
vector<string> myAssetNames;
// Timeline
Time myMaturity;
int myNumPeriods;
// References
vector<double> myRefs;
// Barriers
double myKO;
double myStrike;
double myCpn;
double mySmooth;
vector<Time> myTimeline;
vector<SampleDef> myDefline;
vector<string> myLabels;
public:
// Constructor: store data and build timeline
Autocall(const vector<string>& assets, const vector<double> refs, const Time maturity, const int periods, const double ko, const double strike, const double cpn, const double smooth) :
myNumAssets(assets.size()), myAssetNames(assets), myRefs(refs), myMaturity(maturity), myNumPeriods(periods), myKO(ko), myStrike(strike), myCpn(cpn), mySmooth(max(smooth, EPS)),
myTimeline(periods), myDefline(periods), myLabels(1)
{
// Timeline and defline
// Periods
Time time = systemTime;
const double dt = maturity / periods;
for (size_t step=0; step<periods; ++step)
{
time += dt;
myTimeline[step] = time;
myDefline[step].numeraire = true;
myDefline[step].forwardMats = vector<vector<Time>>(myNumAssets, { time }); // spot(t) = forward(t,t) on maturity for all assets
}
// Identify the payoff
myLabels[0] = "autocall strike " + to_string(int(100 * myStrike + EPS))
+ " KO " + to_string(int(100 * myKO + EPS))
+ " CPN " + to_string(int(100 * myCpn + EPS)) + " "
+ to_string(periods) + " periods of " + to_string(int(12 * maturity / periods + EPS)) + "m";
}
const size_t numAssets() const override
{
return myNumAssets;
}
const vector<string>& assetNames() const override
{
return myAssetNames;
}
const vector<double>& refs() const
{
return myRefs;
}
// access to maturity, strike, KO and cpn
Time maturity() const { return myMaturity; }
double strike() const { return myStrike; }
double ko() const { return myKO; }
double cpn() const { return myCpn; }
// Virtual copy constructor
unique_ptr<Product<T>> clone() const override
{
return make_unique<Autocall<T>>(*this);
}
// Timeline
const vector<Time>& timeline() const override
{
return myTimeline;
}
// Defline
const vector<SampleDef>& defline() const override
{
return myDefline;
}
// Labels
const vector<string>& payoffLabels() const override
{
return myLabels;
}
// Payoff
void payoffs(
// path, one entry per time step
const Scenario<T>& path,
// pre-allocated space for resulting payoffs
vector<T>& payoffs)
const override
{
// Temporaries
static thread_local vector<T> perfs;
perfs.resize(myNumAssets);
// Periods
const double dt = myMaturity / myNumPeriods;
T notionalAlive(1.0);
payoffs[0] = 0.0;
for (int step=0; step<myNumPeriods-1; ++step)
{
auto& state = path[step];
transform(state.forwards.begin(), state.forwards.end(), myRefs.begin(), perfs.begin(), [](const vector<T>& fwds, const double ref) { return fwds[0] / ref; });
T worst = *min_element(perfs.begin(), perfs.end());
// receive cpn
payoffs[0] += notionalAlive * myCpn * dt / state.numeraire;
// apply ko smoothly
T notionalSurviving = notionalAlive * min(1.0, max(0.0, (myKO + mySmooth - worst) / 2 / mySmooth));
T notionalDead = notionalAlive - notionalSurviving;
// receive redemption on dead notional
payoffs[0] += notionalDead / state.numeraire;
// continue with the rest
notionalAlive = notionalSurviving;
}
// last
{
int step = myNumPeriods-1;
auto& state = path[step];
transform(state.forwards.begin(), state.forwards.end(), myRefs.begin(), perfs.begin(), [](const vector<T>& fwds, const double ref) { return fwds[0] / ref; });
T worst = *min_element(perfs.begin(), perfs.end());
// receive cpn
payoffs[0] += notionalAlive * myCpn * dt / state.numeraire;
// receive redemption
payoffs[0] += notionalAlive / state.numeraire;
// pay put
payoffs[0] -= notionalAlive * max(myStrike - worst, 0.0) / myStrike / state.numeraire;
}
}
};