VannaVolgaSmileSection Class Reference

#include <qle/termstructures/fxvannavolgasmilesection.hpp>

Inheritance diagram for VannaVolgaSmileSection:

Collaboration diagram for VannaVolgaSmileSection:

Public Member Functions
	VannaVolgaSmileSection (Real spot, Real rd, Real rf, Time t, Volatility atmVol, Volatility rr, Volatility bf, bool firstApprox=false, const DeltaVolQuote::AtmType &atmType=DeltaVolQuote::AtmType::AtmDeltaNeutral, const DeltaVolQuote::DeltaType &deltaType=DeltaVolQuote::DeltaType::Spot, const Real delta=0.25)
Real	k_atm () const
	getters for unit test More...
Real	k_c () const
Real	k_p () const
Volatility	vol_atm () const
Volatility	vol_c () const
Volatility	vol_p () const
Public Member Functions inherited from FxSmileSection
	FxSmileSection ()
	FxSmileSection (Real spot, Real rd, Real rf, Time t)
virtual	~FxSmileSection ()
virtual Volatility	volatility (Real strike) const =0
DiscountFactor	domesticDiscount () const
DiscountFactor	foreignDiscount () const

FxSmileSection interface
Real	k_atm_
Real	k_c_
Real	k_p_
Volatility	atmVol_
Volatility	rr_
Volatility	bf_
Volatility	vol_c_
Volatility	vol_p_
bool	firstApprox_
Volatility	volatility (Real strike) const override
Real	d1 (Real x) const
Real	d2 (Real x) const

Additional Inherited Members
Protected Attributes inherited from FxSmileSection
Real	spot_
Real	rd_
Real	rf_
Time	t_

Detailed Description

Vanna Volga Smile section

Consistent Pricing of FX Options Castagna & Mercurio (2006) http://papers.ssrn.com/sol3/papers.cfm?abstract_id=873788

Definition at line 41 of file fxvannavolgasmilesection.hpp.

Constructor & Destructor Documentation

VannaVolgaSmileSection()

VannaVolgaSmileSection	(	Real	spot,
		Real	rd,
		Real	rf,
		Time	t,
		Volatility	atmVol,
		Volatility	rr,
		Volatility	bf,
		bool	firstApprox = false,
		const DeltaVolQuote::AtmType &	atmType = DeltaVolQuote::AtmType::AtmDeltaNeutral,
		const DeltaVolQuote::DeltaType &	deltaType = DeltaVolQuote::DeltaType::Spot,
		const Real	delta = 0.25
	)

Definition at line 26 of file fxvannavolgasmilesection.cpp.

    : FxSmileSection(spot, rd, rf, t), atmVol_(atmVol), rr_(rr), bf_(bf), firstApprox_(firstApprox) {
 
    // Consistent Pricing of FX Options
    // Castagna & Mercurio (2006)
    // eq(4) + (5).
    vol_c_ = atmVol + bf_ + 0.5 * rr_;
    vol_p_ = atmVol + bf_ - 0.5 * rr_;
 
    // infer strikes from delta and vol quote
    try {
        BlackDeltaCalculator a(Option::Type::Call, deltaType, spot, domesticDiscount(), foreignDiscount(),
                               sqrt(t) * atmVol);
        k_atm_ = a.atmStrike(atmType);
    } catch (const std::exception& e) {
        QL_FAIL("VannaVolgaSmileSection: Error during calculating atm strike: "
                << e.what() << " (t=" << t << ", atmVol=" << atmVol << ", bf=" << bf_ << ", rr=" << rr << ", vol_c="
                << vol_c_ << ", vol_p=" << vol_p_ << ", atmType=" << atmType << ", deltaType=" << deltaType
                << ", spot=" << spot << ", domDsc=" << domesticDiscount() << ", forDsc=" << foreignDiscount() << ")");
    }
 
    try {
        BlackDeltaCalculator c(Option::Type::Call, deltaType, spot, domesticDiscount(), foreignDiscount(),
                               sqrt(t) * vol_c_);
        k_c_ = c.strikeFromDelta(delta);
    } catch (const std::exception& e) {
        QL_FAIL("VannaVolgaSmileSection: Error during calculating call strike at delta "
                << delta << ": " << e.what() << " (t=" << t << ", atmVol=" << atmVol << ", bf=" << bf_ << ", rr=" << rr
                << ", vol_c=" << vol_c_ << ", vol_p=" << vol_p_ << ", deltaType=" << deltaType << ", spot=" << spot
                << ", domDsc=" << domesticDiscount() << ", forDsc=" << foreignDiscount() << ")");
    }
 
    try {
        BlackDeltaCalculator p(Option::Type::Put, deltaType, spot, domesticDiscount(), foreignDiscount(),
                               sqrt(t) * vol_p_);
        k_p_ = p.strikeFromDelta(-delta);
    } catch (const std::exception& e) {
        QL_FAIL("VannaVolgaSmileSection: Error during calculating put strike at delta "
                << delta << ": " << e.what() << " (t=" << t << ", atmVol=" << atmVol << ", bf=" << bf_ << ", rr=" << rr
                << ", vol_c=" << vol_c_ << ", vol_p=" << vol_p_ << ", deltaType=" << deltaType << ", spot=" << spot
                << ", domDsc=" << domesticDiscount() << ", forDsc=" << foreignDiscount() << ")");
    }
}

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Member Function Documentation

k_atm()

Real k_atm

(

)

const

getters for unit test

Definition at line 50 of file fxvannavolgasmilesection.hpp.

{ return k_atm_; }

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k_c()

Real k_c

(

)

const

Definition at line 51 of file fxvannavolgasmilesection.hpp.

{ return k_c_; }

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k_p()

Real k_p

(

)

const

Definition at line 52 of file fxvannavolgasmilesection.hpp.

{ return k_p_; }

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vol_atm()

Volatility vol_atm

(

)

const

Definition at line 53 of file fxvannavolgasmilesection.hpp.

{ return atmVol_; }

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vol_c()

Volatility vol_c

(

)

const

Definition at line 54 of file fxvannavolgasmilesection.hpp.

{ return vol_c_; }

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vol_p()

Volatility vol_p

(

)

const

Definition at line 55 of file fxvannavolgasmilesection.hpp.

{ return vol_p_; }

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volatility()

Volatility volatility ( Real  strike ) const

overridevirtual

Implements FxSmileSection.

Definition at line 80 of file fxvannavolgasmilesection.cpp.

                                                          {
    QL_REQUIRE(k >= 0, "Non-positive strike (" << k << ")");
 
    // eq(14). Note sigma = sigma_ATM here.
    Real k1 = k_p_;
    Real k2 = k_atm_;
    Real k3 = k_c_;
 
    // TODO: Cache the (constant) denominator
    Real r1 = log(k2 / k) * log(k3 / k) / (log(k2 / k1) * log(k3 / k1));
    Real r2 = log(k / k1) * log(k3 / k) / (log(k2 / k1) * log(k3 / k2));
    Real r3 = log(k / k1) * log(k / k2) / (log(k3 / k1) * log(k3 / k2));
 
    Real sigma1_k = r1 * vol_p_ + r2 * atmVol_ + r3 * vol_c_;
    if (firstApprox_) {
        return std::max(sigma1_k, Real(0.0001)); // for extreme ends: cannot return negative impl vols
    }
 
    Real D1 = sigma1_k - atmVol_;
 
    // No middle term as sigma = sigma_atm
    Real D2 = r1 * d1(k1) * d2(k1) * (vol_p_ - atmVol_) * (vol_p_ - atmVol_) +
              r3 * d1(k3) * d2(k3) * (vol_c_ - atmVol_) * (vol_c_ - atmVol_);
 
    Real d1d2k = d1(k) * d2(k);
 
    Real tmp = atmVol_ * atmVol_ + d1d2k * (2 * atmVol_ * D1 + D2);
    QL_REQUIRE(tmp >= 0, "VannaVolga attempting to take square root of negative number in second approximation. "
                         "Consider using first approximation in fxvol config.");
 
    return atmVol_ + (-atmVol_ + sqrt(tmp)) / d1d2k;
}

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d1()

Real d1 ( Real  x ) const

private

Definition at line 72 of file fxvannavolgasmilesection.cpp.

                                            {
    return (log(spot_ / x) + (rd_ - rf_ + 0.5 * atmVol_ * atmVol_) * t_) / (atmVol_ * sqrt(t_));
}

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d2()

Real d2 ( Real  x ) const

private

Definition at line 76 of file fxvannavolgasmilesection.cpp.

                                            {
    return (log(spot_ / x) + (rd_ - rf_ - 0.5 * atmVol_ * atmVol_) * t_) / (atmVol_ * sqrt(t_));
}

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Member Data Documentation

k_atm_

Real k_atm_

private

Definition at line 66 of file fxvannavolgasmilesection.hpp.

k_c_

Real k_c_

private

Definition at line 66 of file fxvannavolgasmilesection.hpp.

k_p_

Real k_p_

private

Definition at line 66 of file fxvannavolgasmilesection.hpp.

atmVol_

Volatility atmVol_

private

Definition at line 67 of file fxvannavolgasmilesection.hpp.

rr_

Volatility rr_

private

Definition at line 67 of file fxvannavolgasmilesection.hpp.

bf_

Volatility bf_

private

Definition at line 67 of file fxvannavolgasmilesection.hpp.

vol_c_

Volatility vol_c_

private

Definition at line 68 of file fxvannavolgasmilesection.hpp.

vol_p_

Volatility vol_p_

private

Definition at line 68 of file fxvannavolgasmilesection.hpp.

firstApprox_

bool firstApprox_

private

Definition at line 69 of file fxvannavolgasmilesection.hpp.