CarrMadanMarginalProbabilitySafeStrikes Class Reference

#include <qle/models/carrmadanarbitragecheck.hpp>

Collaboration diagram for CarrMadanMarginalProbabilitySafeStrikes:

Public Member Functions
	CarrMadanMarginalProbabilitySafeStrikes (const std::vector< Real > &strikes, const Real forward, const std::vector< Real > &callPrices, const VolatilityType volType=ShiftedLognormal, const Real shift=0.0)
const std::vector< Real > &	strikes () const
Real	forward () const
const std::vector< Real > &	callPrices () const
VolatilityType	volatilityType () const
Real	shift () const
bool	arbitrageFree () const
const std::vector< bool > &	callSpreadArbitrage () const
const std::vector< bool > &	butterflyArbitrage () const
const std::vector< Real > &	density () const

Private Attributes
std::vector< Real >	strikes_
Real	forward_
std::vector< Real >	callPrices_
VolatilityType	volType_
Real	shift_
std::vector< bool >	validStrike_
std::vector< bool >	callSpreadArbitrage_
std::vector< bool >	butterflyArbitrage_
std::vector< Real >	q_
bool	smileIsArbitrageFree_

Detailed Description

Definition at line 68 of file carrmadanarbitragecheck.hpp.

Constructor & Destructor Documentation

CarrMadanMarginalProbabilitySafeStrikes()

CarrMadanMarginalProbabilitySafeStrikes	(	const std::vector< Real > &	strikes,
		const Real	forward,
		const std::vector< Real > &	callPrices,
		const VolatilityType	volType = ShiftedLognormal,
		const Real	shift = 0.0
	)

The callPrices should be non-discounted

Definition at line 274 of file carrmadanarbitragecheck.cpp.

    : strikes_(strikes), forward_(forward), callPrices_(callPrices), volType_(volType), shift_(shift) {
 
    QL_REQUIRE(strikes_.size() == callPrices_.size(), "CarrMadanMarginalProbabilitySafeStrikes: strike size ("
                                                          << strikes_.size() << ") must match callPrices size ("
                                                          << callPrices_.size() << ")");
 
    // handle edge cases (no strikes given, invalid forward given)
 
    if (strikes_.empty()) {
        smileIsArbitrageFree_ = true;
        return;
    }
 
    if (volType == ShiftedLognormal && forward < -shift && !close_enough(forward, -shift)) {
        smileIsArbitrageFree_ = true;
        callSpreadArbitrage_ = std::vector<bool>(strikes_.size(), false);
        butterflyArbitrage_ = std::vector<bool>(strikes_.size(), false);
        q_ = std::vector<Real>(strikes_.size(), 0.0);
        return;
    }
 
    // identify the strikes that are not valid (i.e. < -shift)
 
    validStrike_.resize(strikes_.size(), true);
    for (Size i = 0; i < strikes_.size(); ++i) {
        if (volType_ == ShiftedLognormal && (strikes_[i] < -shift && !close_enough(strikes[i], -shift))) {
            validStrike_[i] = false;
        }
    }
 
    // build input for regular CM class
 
    std::vector<Real> regStrikes;
    std::vector<Real> regCallPrices;
 
    for (Size i = 0; i < validStrike_.size(); ++i) {
        if (validStrike_[i]) {
            regStrikes.push_back(strikes_[i]);
            regCallPrices.push_back(callPrices_[i]);
        }
    }
 
    // check if we have at least one strike > -shift
 
    bool haveNonBoundaryStrike = false;
    if (volType == Normal) {
        haveNonBoundaryStrike = true;
    } else {
        for (auto const& k : regStrikes) {
            if (volType_ == ShiftedLognormal && k > -shift && !close_enough(k, -shift)) {
                haveNonBoundaryStrike = true;
            }
        }
    }
 
    // if no such strike exists, the result is trivial
 
    if (!haveNonBoundaryStrike) {
        smileIsArbitrageFree_ = true;
        callSpreadArbitrage_ = std::vector<bool>(1, false);
        butterflyArbitrage_ = std::vector<bool>(1, false);
        q_ = std::vector<Real>(1, 1.0);
    }
 
    // otherwise we call the regular CM class on the regular strikes
 
    CarrMadanMarginalProbability cm(regStrikes, forward_, regCallPrices, volType_, shift_);
 
    // the results are set for the regular strikes and filled with reasonable values for invalid strike positions
 
    smileIsArbitrageFree_ = cm.arbitrageFree();
    callSpreadArbitrage_ = std::vector<bool>(strikes_.size(), false);
    butterflyArbitrage_ = std::vector<bool>(strikes_.size(), false);
    q_ = std::vector<Real>(strikes_.size(), 0.0);
 
    for (Size i = 0; i < validStrike_.size(); ++i) {
        if (validStrike_[i]) {
            callSpreadArbitrage_[i] = cm.callSpreadArbitrage()[i];
            butterflyArbitrage_[i] = cm.butterflyArbitrage()[i];
            q_[i] = cm.density()[i];
        }
    }
}

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Member Function Documentation

strikes()

const std::vector< Real > & strikes

(

)

const

Definition at line 363 of file carrmadanarbitragecheck.cpp.

{ return strikes_; }

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forward()

Real forward

(

)

const

Definition at line 364 of file carrmadanarbitragecheck.cpp.

{ return forward_; }

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callPrices()

const std::vector< Real > & callPrices

(

)

const

Definition at line 365 of file carrmadanarbitragecheck.cpp.

{ return callPrices_; }

volatilityType()

VolatilityType volatilityType

(

)

const

Definition at line 366 of file carrmadanarbitragecheck.cpp.

{ return volType_; }

shift()

Real shift

(

)

const

Definition at line 367 of file carrmadanarbitragecheck.cpp.

{ return shift_; }

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arbitrageFree()

bool arbitrageFree

(

)

const

Definition at line 369 of file carrmadanarbitragecheck.cpp.

{ return smileIsArbitrageFree_; }

callSpreadArbitrage()

const std::vector< bool > & callSpreadArbitrage

(

)

const

Definition at line 371 of file carrmadanarbitragecheck.cpp.

                                                                                          {
    return callSpreadArbitrage_;
}

butterflyArbitrage()

const std::vector< bool > & butterflyArbitrage

(

)

const

Definition at line 374 of file carrmadanarbitragecheck.cpp.

                                                                                         {
    return butterflyArbitrage_;
}

density()

const std::vector< Real > & density

(

)

const

Definition at line 377 of file carrmadanarbitragecheck.cpp.

{ return q_; }

Member Data Documentation

strikes_

std::vector<Real> strikes_

private

Definition at line 88 of file carrmadanarbitragecheck.hpp.

forward_

Real forward_

private

Definition at line 89 of file carrmadanarbitragecheck.hpp.

callPrices_

std::vector<Real> callPrices_

private

Definition at line 90 of file carrmadanarbitragecheck.hpp.

volType_

VolatilityType volType_

private

Definition at line 91 of file carrmadanarbitragecheck.hpp.

shift_

Real shift_

private

Definition at line 92 of file carrmadanarbitragecheck.hpp.

validStrike_

std::vector<bool> validStrike_

private

Definition at line 94 of file carrmadanarbitragecheck.hpp.

callSpreadArbitrage_

std::vector<bool> callSpreadArbitrage_

private

Definition at line 96 of file carrmadanarbitragecheck.hpp.

butterflyArbitrage_

std::vector<bool> butterflyArbitrage_

private

Definition at line 96 of file carrmadanarbitragecheck.hpp.

q_

std::vector<Real> q_

private

Definition at line 97 of file carrmadanarbitragecheck.hpp.

smileIsArbitrageFree_

bool smileIsArbitrageFree_

private

Definition at line 98 of file carrmadanarbitragecheck.hpp.