BlackVolatilitySurfaceProxy Class Reference

Wrapper class for a BlackVolTermStructure that allows us to proxy one equity vol surface off another. More...

#include <qle/termstructures/blackvolsurfaceproxy.hpp>

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Public Member Functions
	BlackVolatilitySurfaceProxy (const QuantLib::ext::shared_ptr< BlackVolTermStructure > &proxySurface, const QuantLib::ext::shared_ptr< EqFxIndexBase > &index, const QuantLib::ext::shared_ptr< EqFxIndexBase > &proxyIndex, const QuantLib::ext::shared_ptr< BlackVolTermStructure > &fxSurface=nullptr, const QuantLib::ext::shared_ptr< FxIndex > &fxIndex=nullptr, const QuantLib::ext::shared_ptr< CorrelationTermStructure > &correlation=nullptr)
	Constructor. This is a floating term structure (settlement days is zero) More...
TermStructure interface
DayCounter	dayCounter () const override
Date	maxDate () const override
Time	maxTime () const override
const Date &	referenceDate () const override
Calendar	calendar () const override
Natural	settlementDays () const override
VolatilityTermStructure interface
Rate	minStrike () const override
Rate	maxStrike () const override

Inspectors
QuantLib::ext::shared_ptr< BlackVolTermStructure >	proxySurface_
QuantLib::ext::shared_ptr< EqFxIndexBase >	index_
QuantLib::ext::shared_ptr< EqFxIndexBase >	proxyIndex_
QuantLib::ext::shared_ptr< BlackVolTermStructure >	fxSurface_
QuantLib::ext::shared_ptr< FxIndex >	fxIndex_
QuantLib::ext::shared_ptr< CorrelationTermStructure >	correlation_
QuantLib::ext::shared_ptr< BlackVolTermStructure >	proxySurface () const
QuantLib::ext::shared_ptr< EqFxIndexBase >	index () const
QuantLib::ext::shared_ptr< EqFxIndexBase >	proxyIndex () const
Volatility	blackVolImpl (Time t, Real strike) const override

Detailed Description

Wrapper class for a BlackVolTermStructure that allows us to proxy one equity vol surface off another.

This class implements BlackVolatilityTermStructure and takes a surface (well, any BlackVolTermStructure) as an input. It also takes Handles to two EquityIndices (index and proxyIndex), where index is the 'EquityIndex' of the underlying for the surface being constructed and proxyIndex is the 'EquityIndex' for the surface being proxied off.

The vol returned from the new surface is proxied from the base, adjusting by the forward prices to match ATM:

\begin{eqnarray} \sigma_2(K,T) = \sigma_1(\frac{K}{F_2}*F_1,T) \end{eqnarray}

Where

\( \sigma_1 = \text{Volatility of underlying being proxied against}\)
\( \sigma_2 = \text{Volatility of underlying being proxied}\)
\( F_1 = \text{Forward at time T of the underlying being proxied against}\)
\( F_2 = \text{Forward at time T of the underlying being proxied}\)
\( T = \text{Time}\)
Note: This surface only proxies equity volatilities, this is because we are forced to look up the equity fixings using time instead of date and use the forecastFixing method in an EquityIndex. A more general class could be developed if need, using Index instead of EquityIndex, if the time lookup could be overcome.

Definition at line 62 of file blackvolsurfaceproxy.hpp.

Constructor & Destructor Documentation

BlackVolatilitySurfaceProxy()

BlackVolatilitySurfaceProxy	(	const QuantLib::ext::shared_ptr< BlackVolTermStructure > &	proxySurface,
		const QuantLib::ext::shared_ptr< EqFxIndexBase > &	index,
		const QuantLib::ext::shared_ptr< EqFxIndexBase > &	proxyIndex,
		const QuantLib::ext::shared_ptr< BlackVolTermStructure > &	fxSurface = nullptr,
		const QuantLib::ext::shared_ptr< FxIndex > &	fxIndex = nullptr,
		const QuantLib::ext::shared_ptr< CorrelationTermStructure > &	correlation = nullptr
	)

Constructor. This is a floating term structure (settlement days is zero)

Definition at line 25 of file blackvolsurfaceproxy.cpp.

    : BlackVolatilityTermStructure(0, proxySurface->calendar(), proxySurface->businessDayConvention(),
                                   proxySurface->dayCounter()),
      proxySurface_(proxySurface), index_(index), proxyIndex_(proxyIndex), fxSurface_(fxSurface), 
      fxIndex_(fxIndex), correlation_(correlation) {
 
    if (proxySurface->allowsExtrapolation())
        this->enableExtrapolation();
 
    registerWith(proxySurface);
    registerWith(index);
    registerWith(proxyIndex);
}

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Member Function Documentation

dayCounter()

DayCounter dayCounter ( ) const

override

Definition at line 74 of file blackvolsurfaceproxy.hpp.

{ return proxySurface_->dayCounter(); }

maxDate()

Date maxDate ( ) const

override

Definition at line 75 of file blackvolsurfaceproxy.hpp.

{ return proxySurface_->maxDate(); }

maxTime()

Time maxTime ( ) const

override

Definition at line 76 of file blackvolsurfaceproxy.hpp.

{ return proxySurface_->maxTime(); }

referenceDate()

const Date & referenceDate ( ) const

override

Definition at line 77 of file blackvolsurfaceproxy.hpp.

{ return proxySurface_->referenceDate(); }

calendar()

Calendar calendar ( ) const

override

Definition at line 78 of file blackvolsurfaceproxy.hpp.

{ return proxySurface_->calendar(); }

settlementDays()

Natural settlementDays ( ) const

override

Definition at line 79 of file blackvolsurfaceproxy.hpp.

{ return proxySurface_->settlementDays(); }

minStrike()

Rate minStrike ( ) const

override

Definition at line 77 of file blackvolsurfaceproxy.cpp.

                                                  {
    return proxySurface_->minStrike() * index_->forecastFixing(0.0) / proxyIndex_->forecastFixing(0.0);
}

maxStrike()

Rate maxStrike ( ) const

override

Definition at line 81 of file blackvolsurfaceproxy.cpp.

                                                  {
    return proxySurface_->maxStrike() * index_->forecastFixing(0.0) / proxyIndex_->forecastFixing(0.0);
}

proxySurface()

QuantLib::ext::shared_ptr< BlackVolTermStructure > proxySurface

(

)

const

Definition at line 90 of file blackvolsurfaceproxy.hpp.

{ return proxySurface_; }

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index()

QuantLib::ext::shared_ptr< EqFxIndexBase > index

(

)

const

Definition at line 91 of file blackvolsurfaceproxy.hpp.

{ return index_; }

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proxyIndex()

QuantLib::ext::shared_ptr< EqFxIndexBase > proxyIndex

(

)

const

Definition at line 92 of file blackvolsurfaceproxy.hpp.

{ return proxyIndex_; }

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blackVolImpl()

Volatility blackVolImpl ( Time  t, Real  strike  ) const

overrideprotected

Definition at line 42 of file blackvolsurfaceproxy.cpp.

                                                                              {
 
    t = std::max(t, 1E-6);
 
    Volatility vol;
    if (fxSurface_) {
        // Get the Fx forward value at time t, and hence the ATM vol
        Real fxForward = fxIndex_->forecastFixing(t);
        Volatility fxVol = fxSurface_->blackVol(t, fxForward);
 
        // Get the ATM vol for the proxy surface
        Volatility proxyAtmVol = proxySurface_->blackVol(t, proxyIndex_->forecastFixing(t));
        
        // Convert the atm vol for this surface using sqrt( sigma^2 + sigma_X^2 + 2 rho sigma sigma_X)
        Volatility atmVol = sqrt(proxyAtmVol * proxyAtmVol + fxVol * fxVol + 2 * correlation_->correlation(t) * proxyAtmVol * fxVol);
 
        // Get the moneyness in this surface of the strike requested
        Real forward = index_->forecastFixing(t);
        Real moneyness = std::log(strike / forward) / (atmVol * sqrt(t));
 
        // Find the strike in the proxy surface that gives the same moneyness
        Real proxyForward = proxyIndex_->forecastFixing(t);
        Real proxyStrike = proxyForward * exp(moneyness * proxyAtmVol * sqrt(t));
 
        // Look up the vol in the proxy surface for the proxyStrike and convert using sqrt( sigma^2 + sigma_X^2 + 2 rho sigma sigma_X)
        Volatility proxyVol = proxySurface_->blackVol(t, proxyStrike);        
        vol = sqrt(proxyVol * proxyVol + fxVol * fxVol + 2 * correlation_->correlation(t) * proxyVol * fxVol);
        
    } else {
        Real adjustedStrike = strike * proxyIndex_->forecastFixing(t) / index_->forecastFixing(t);
        vol = proxySurface_->blackVol(t, adjustedStrike);
    } 
    return vol;
}

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Member Data Documentation

proxySurface_

QuantLib::ext::shared_ptr<BlackVolTermStructure> proxySurface_

private

Definition at line 100 of file blackvolsurfaceproxy.hpp.

index_

QuantLib::ext::shared_ptr<EqFxIndexBase> index_

private

Definition at line 101 of file blackvolsurfaceproxy.hpp.

proxyIndex_

QuantLib::ext::shared_ptr<EqFxIndexBase> proxyIndex_

private

Definition at line 101 of file blackvolsurfaceproxy.hpp.

fxSurface_

QuantLib::ext::shared_ptr<BlackVolTermStructure> fxSurface_

private

Definition at line 102 of file blackvolsurfaceproxy.hpp.

fxIndex_

QuantLib::ext::shared_ptr<FxIndex> fxIndex_

private

Definition at line 103 of file blackvolsurfaceproxy.hpp.

correlation_

QuantLib::ext::shared_ptr<CorrelationTermStructure> correlation_

private

Definition at line 104 of file blackvolsurfaceproxy.hpp.