BlackCdsOptionEngine Class Reference

#include <qle/pricingengines/blackcdsoptionengine.hpp>

Inheritance diagram for BlackCdsOptionEngine:

Collaboration diagram for BlackCdsOptionEngine:

Public Member Functions
	BlackCdsOptionEngine (const QuantLib::Handle< QuantLib::DefaultProbabilityTermStructure > &probability, QuantLib::Real recovery, const QuantLib::Handle< QuantLib::YieldTermStructure > &discount, const QuantLib::Handle< QuantExt::CreditVolCurve > &volatility)
Inspectors
const QuantLib::Handle< QuantLib::DefaultProbabilityTermStructure > &	probability () const
QuantLib::Real	recovery () const
const QuantLib::Handle< QuantLib::YieldTermStructure >	discount () const
const QuantLib::Handle< QuantExt::CreditVolCurve >	volatility () const

Instrument interface
QuantLib::Handle< QuantLib::DefaultProbabilityTermStructure >	probability_
QuantLib::Real	recovery_
QuantLib::Handle< QuantLib::YieldTermStructure >	discount_
QuantLib::Handle< QuantExt::CreditVolCurve >	volatility_
void	calculate () const override

Detailed Description

Black single name CDS option engine

Prices single name CDS option instruments quoted in terms of strike spread. It is assumed that the volatility structure's strike dimension, if there is one, is in terms of spread also. This is the standard situation for single name CDS options.

The valuation follows the approach outlined in Modeling Single-name and Multi-name Credit Derivatives, Dominic O'Kane, 2008, Section 9.3.7. This is also the approach in A CDS Option Miscellany, Richard J. Martin, 2019, Section 2.1 and 2.2. If we need the approach in Section 2.4 of that paper, we would need to make adjustments to the forward spread and RPV01 in our calculation which may in turn need access to the ISDA supplied interest rate curve. We leave that as a possible future enhancement.

Definition at line 45 of file blackcdsoptionengine.hpp.

Constructor & Destructor Documentation

BlackCdsOptionEngine()

BlackCdsOptionEngine	(	const QuantLib::Handle< QuantLib::DefaultProbabilityTermStructure > &	probability,
		QuantLib::Real	recovery,
		const QuantLib::Handle< QuantLib::YieldTermStructure > &	discount,
		const QuantLib::Handle< QuantExt::CreditVolCurve > &	volatility
	)

Definition at line 29 of file blackcdsoptionengine.cpp.

    : probability_(probability), recovery_(recovery), discount_(discount), volatility_(volatility) {
    registerWith(probability_);
    registerWith(discount_);
    registerWith(volatility_);
}

Member Function Documentation

probability()

const Handle< DefaultProbabilityTermStructure > & probability

(

)

const

Definition at line 38 of file blackcdsoptionengine.cpp.

                                                                                       {
    return probability_;
}

recovery()

Real recovery

(

)

const

Definition at line 42 of file blackcdsoptionengine.cpp.

                                          {
    return recovery_;
}

discount()

const Handle< YieldTermStructure > discount

(

)

const

Definition at line 46 of file blackcdsoptionengine.cpp.

                                                                      {
    return discount_;
}

volatility()

const Handle< CreditVolCurve > volatility

(

)

const

Definition at line 50 of file blackcdsoptionengine.cpp.

                                                                    {
    return volatility_;
}

calculate()

void calculate ( ) const

override

Definition at line 55 of file blackcdsoptionengine.cpp.

                                           {
 
    QL_REQUIRE(arguments_.strikeType == CdsOption::Spread, "BlackCdsOptionEngine does not support valuation" <<
        " of single name options quoted in terms of strike price.");
 
    // Reference to the underlying forward starting CDS, from expiry date $t_E$ to maturity $T$.
    const auto& cds = *arguments_.swap;
 
    // Get the additional results of the underlying CDS (need to call NPV first for calculation).
    cds.NPV();
    results_.additionalResults = cds.additionalResults();
 
    // Add some entries to additional results.
    Real forward = cds.fairSpreadClean();
    results_.additionalResults["forwardSpread"] = forward;
    const Real& strike = arguments_.strike;
    results_.additionalResults["strikeSpread"] = strike;
 
    // Calculate risky PV01, as of the valuation date i.e. time 0, for the period from $t_E$ to underlying 
    // CDS maturity $T$. This risky PV01 does not include the non-risky accrual from the CDS premium leg coupon date 
    // immediately preceding the expiry date up to the expiry date.
    Real rpv01 = std::abs(cds.couponLegNPV() + cds.accrualRebateNPV()) / (cds.notional() * cds.runningSpread());
    results_.additionalResults["riskyAnnuity"] = rpv01;
 
    // Read the volatility from the volatility surface, assumed to have strike dimension in terms of spread.
    const Date& exerciseDate = arguments_.exercise->dates().front();
    Real underlyingLength = volatility_->dayCounter().yearFraction(exerciseDate, cds.maturity());
    Real vol = volatility_->volatility(exerciseDate, underlyingLength, strike, CreditVolCurve::Type::Spread);
    Real stdDev = vol * std::sqrt(volatility_->timeFromReference(exerciseDate));
    results_.additionalResults["volatility"] = vol;
    results_.additionalResults["standardDeviation"] = stdDev;
 
    // Option type
    Option::Type callPut = cds.side() == Protection::Buyer ? Option::Call : Option::Put;
    results_.additionalResults["callPut"] = callPut == Option::Call ? string("Call") : string("Put");
 
    // NPV, Section 9.3.7 O'Kane 2008.
    results_.value = rpv01 * cds.notional() * blackFormula(callPut, strike, forward, stdDev, 1.0);
 
    // If it is non-knockout and a payer, add the value of the default payout.
    // Section 2.2 of Richard J.Martin, 2019 or Section 9.3.7 O'Kane 2008.
    if (!arguments_.knocksOut && cds.side() == Protection::Buyer) {
 
        DiscountFactor disc = discount_->discount(exerciseDate);
        results_.additionalResults["discountToExercise"] = disc;
 
        Probability sp = probability_->survivalProbability(exerciseDate);
        results_.additionalResults["survivalProbabilityToExercise"] = sp;
 
        Real nonKoPv = disc * sp * (1 - recovery_);
        results_.additionalResults["nonKnockoutPv"] = nonKoPv;
 
        results_.value += nonKoPv;
    }
}

Member Data Documentation

probability_

QuantLib::Handle<QuantLib::DefaultProbabilityTermStructure> probability_

private

Definition at line 66 of file blackcdsoptionengine.hpp.

recovery_

QuantLib::Real recovery_

private

Definition at line 67 of file blackcdsoptionengine.hpp.

discount_

QuantLib::Handle<QuantLib::YieldTermStructure> discount_

private

Definition at line 68 of file blackcdsoptionengine.hpp.

volatility_

QuantLib::Handle<QuantExt::CreditVolCurve> volatility_

private

Definition at line 69 of file blackcdsoptionengine.hpp.