/usr/include/ql/pricingengines/blackformula.hpp is in libquantlib0-dev 1.12-1.
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/*
Copyright (C) 2001, 2002, 2003 Sadruddin Rejeb
Copyright (C) 2003, 2004, 2005, 2006, 2008 Ferdinando Ametrano
Copyright (C) 2006 Mark Joshi
Copyright (C) 2006 StatPro Italia srl
Copyright (C) 2007 Cristina Duminuco
Copyright (C) 2007 Chiara Fornarola
Copyright (C) 2013 Gary Kennedy
Copyright (C) 2015 Peter Caspers
Copyright (C) 2017 Klaus Spanderen
This file is part of QuantLib, a free-software/open-source library
for financial quantitative analysts and developers - http://quantlib.org/
QuantLib is free software: you can redistribute it and/or modify it
under the terms of the QuantLib license. You should have received a
copy of the license along with this program; if not, please email
<quantlib-dev@lists.sf.net>. The license is also available online at
<http://quantlib.org/license.shtml>.
This program is distributed in the hope that it will be useful, but WITHOUT
ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS
FOR A PARTICULAR PURPOSE. See the license for more details.
*/
/*! \file blackformula.hpp
\brief Black formula
*/
#ifndef quantlib_blackformula_hpp
#define quantlib_blackformula_hpp
#include <ql/option.hpp>
#include <ql/instruments/payoffs.hpp>
namespace QuantLib {
/*! Black 1976 formula
\warning instead of volatility it uses standard deviation,
i.e. volatility*sqrt(timeToMaturity)
*/
Real blackFormula(Option::Type optionType,
Real strike,
Real forward,
Real stdDev,
Real discount = 1.0,
Real displacement = 0.0);
/*! Black 1976 formula
\warning instead of volatility it uses standard deviation,
i.e. volatility*sqrt(timeToMaturity)
*/
Real blackFormula(const boost::shared_ptr<PlainVanillaPayoff>& payoff,
Real forward,
Real stdDev,
Real discount = 1.0,
Real displacement = 0.0);
/*! Approximated Black 1976 implied standard deviation,
i.e. volatility*sqrt(timeToMaturity).
It is calculated using Brenner and Subrahmanyan (1988) and Feinstein
(1988) approximation for at-the-money forward option, with the
extended moneyness approximation by Corrado and Miller (1996)
*/
Real blackFormulaImpliedStdDevApproximation(Option::Type optionType,
Real strike,
Real forward,
Real blackPrice,
Real discount = 1.0,
Real displacement = 0.0);
/*! Approximated Black 1976 implied standard deviation,
i.e. volatility*sqrt(timeToMaturity).
It is calculated using Brenner and Subrahmanyan (1988) and Feinstein
(1988) approximation for at-the-money forward option, with the
extended moneyness approximation by Corrado and Miller (1996)
*/
Real blackFormulaImpliedStdDevApproximation(
const boost::shared_ptr<PlainVanillaPayoff>& payoff,
Real forward,
Real blackPrice,
Real discount = 1.0,
Real displacement = 0.0);
/*! Approximated Black 1976 implied standard deviation,
i.e. volatility*sqrt(timeToMaturity).
It is calculated following "An improved approach to computing
implied volatility", Chambers, Nawalkha, The Financial Review,
2001, 89-100. The atm option price must be known to use this
method.
*/
Real blackFormulaImpliedStdDevChambers(Option::Type optionType,
Real strike,
Real forward,
Real blackPrice,
Real blackAtmPrice,
Real discount = 1.0,
Real displacement = 0.0);
/*! Approximated Black 1976 implied standard deviation,
i.e. volatility*sqrt(timeToMaturity).
It is calculated following "An improved approach to computing
implied volatility", Chambers, Nawalkha, The Financial Review,
2001, 89-100. The atm option price must be known to use this
method.
*/
Real blackFormulaImpliedStdDevChambers(
const boost::shared_ptr<PlainVanillaPayoff> &payoff,
Real forward,
Real blackPrice,
Real blackAtmPrice,
Real discount = 1.0,
Real displacement = 0.0);
/*! Approximated Black 1976 implied standard deviation,
i.e. volatility*sqrt(timeToMaturity).
It is calculated using
"An Explicit Implicit Volatility Formula"
R. Radoicic, D. Stefanica,
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2908494
"Tighter Bounds for Implied Volatility",
J. Gatheral, I. Matic, R. Radoicic, D. Stefanica
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2922742
*/
Real blackFormulaImpliedStdDevApproximationRS(
Option::Type optionType,
Real strike,
Real forward,
Real blackPrice,
Real discount = 1.0,
Real displacement = 0.0);
Real blackFormulaImpliedStdDevApproximationRS(
const boost::shared_ptr<PlainVanillaPayoff> &payoff,
Real forward,
Real blackPrice,
Real discount = 1.0,
Real displacement = 0.0);
/*! Black 1976 implied standard deviation,
i.e. volatility*sqrt(timeToMaturity)
*/
Real blackFormulaImpliedStdDev(Option::Type optionType,
Real strike,
Real forward,
Real blackPrice,
Real discount = 1.0,
Real displacement = 0.0,
Real guess = Null<Real>(),
Real accuracy = 1.0e-6,
Natural maxIterations = 100);
/*! Black 1976 implied standard deviation,
i.e. volatility*sqrt(timeToMaturity)
*/
Real blackFormulaImpliedStdDev(
const boost::shared_ptr<PlainVanillaPayoff>& payoff,
Real forward,
Real blackPrice,
Real discount = 1.0,
Real displacement = 0.0,
Real guess = Null<Real>(),
Real accuracy = 1.0e-6,
Natural maxIterations = 100);
/*! Black 1976 implied standard deviation,
i.e. volatility*sqrt(timeToMaturity)
"An Adaptive Successive Over-relaxation Method for Computing the
Black-Scholes Implied Volatility"
M. Li, http://mpra.ub.uni-muenchen.de/6867/
Starting point of the iteration is calculated based on
"An Explicit Implicit Volatility Formula"
R. Radoicic, D. Stefanica,
https://papers.ssrn.com/sol3/papers.cfm?abstract_id=2908494
*/
Real blackFormulaImpliedStdDevLiRS(
Option::Type optionType,
Real strike,
Real forward,
Real blackPrice,
Real discount = 1.0,
Real displacement = 0.0,
Real guess = Null<Real>(),
Real omega = 1.0,
Real accuracy = 1.0e-6,
Natural maxIterations = 100);
Real blackFormulaImpliedStdDevLiRS(
const boost::shared_ptr<PlainVanillaPayoff>& payoff,
Real forward,
Real blackPrice,
Real discount = 1.0,
Real displacement = 0.0,
Real guess = Null<Real>(),
Real omega = 1.0,
Real accuracy = 1.0e-6,
Natural maxIterations = 100);
/*! Black 1976 probability of being in the money (in the bond martingale
measure), i.e. N(d2).
It is a risk-neutral probability, not the real world one.
\warning instead of volatility it uses standard deviation,
i.e. volatility*sqrt(timeToMaturity)
*/
Real blackFormulaCashItmProbability(Option::Type optionType,
Real strike,
Real forward,
Real stdDev,
Real displacement = 0.0);
/*! Black 1976 probability of being in the money (in the bond martingale
measure), i.e. N(d2).
It is a risk-neutral probability, not the real world one.
\warning instead of volatility it uses standard deviation,
i.e. volatility*sqrt(timeToMaturity)
*/
Real blackFormulaCashItmProbability(
const boost::shared_ptr<PlainVanillaPayoff>& payoff,
Real forward,
Real stdDev,
Real displacement = 0.0);
/*! Black 1976 formula for standard deviation derivative
\warning instead of volatility it uses standard deviation, i.e.
volatility*sqrt(timeToMaturity), and it returns the
derivative with respect to the standard deviation.
If T is the time to maturity Black vega would be
blackStdDevDerivative(strike, forward, stdDev)*sqrt(T)
*/
Real blackFormulaStdDevDerivative(Real strike,
Real forward,
Real stdDev,
Real discount = 1.0,
Real displacement = 0.0);
/*! Black 1976 formula for derivative with respect to implied vol, this
is basically the vega, but if you want 1% change multiply by 1%
*/
Real blackFormulaVolDerivative(Real strike,
Real forward,
Real stdDev,
Real expiry,
Real discount = 1.0,
Real displacement = 0.0);
/*! Black 1976 formula for standard deviation derivative
\warning instead of volatility it uses standard deviation, i.e.
volatility*sqrt(timeToMaturity), and it returns the
derivative with respect to the standard deviation.
If T is the time to maturity Black vega would be
blackStdDevDerivative(strike, forward, stdDev)*sqrt(T)
*/
Real blackFormulaStdDevDerivative(
const boost::shared_ptr<PlainVanillaPayoff>& payoff,
Real forward,
Real stdDev,
Real discount = 1.0,
Real displacement = 0.0);
/*! Black 1976 formula for second derivative by standard deviation
\warning instead of volatility it uses standard deviation, i.e.
volatility*sqrt(timeToMaturity), and it returns the
derivative with respect to the standard deviation.
*/
Real blackFormulaStdDevSecondDerivative(Rate strike,
Rate forward,
Real stdDev,
Real discount,
Real displacement);
/*! Black 1976 formula for second derivative by standard deviation
\warning instead of volatility it uses standard deviation, i.e.
volatility*sqrt(timeToMaturity), and it returns the
derivative with respect to the standard deviation.
*/
Real blackFormulaStdDevSecondDerivative(
const boost::shared_ptr<PlainVanillaPayoff>& payoff,
Real forward,
Real stdDev,
Real discount = 1.0,
Real displacement = 0.0);
/*! Black style formula when forward is normal rather than
log-normal. This is essentially the model of Bachelier.
\warning Bachelier model needs absolute volatility, not
percentage volatility. Standard deviation is
absoluteVolatility*sqrt(timeToMaturity)
*/
Real bachelierBlackFormula(Option::Type optionType,
Real strike,
Real forward,
Real stdDev,
Real discount = 1.0);
/*! Black style formula when forward is normal rather than
log-normal. This is essentially the model of Bachelier.
\warning Bachelier model needs absolute volatility, not
percentage volatility. Standard deviation is
absoluteVolatility*sqrt(timeToMaturity)
*/
Real bachelierBlackFormula(
const boost::shared_ptr<PlainVanillaPayoff>& payoff,
Real forward,
Real stdDev,
Real discount = 1.0);
/*! Approximated Bachelier implied volatility
It is calculated using the analytic implied volatility approximation
of J. Choi, K Kim and M. Kwak (2009), “Numerical Approximation of the
Implied Volatility Under Arithmetic Brownian Motion”,
Applied Math. Finance, 16(3), pp. 261-268.
*/
Real bachelierBlackFormulaImpliedVol(Option::Type optionType,
Real strike,
Real forward,
Real tte,
Real bachelierPrice,
Real discount = 1.0);
/*! Bachelier formula for standard deviation derivative
\warning instead of volatility it uses standard deviation, i.e.
volatility*sqrt(timeToMaturity), and it returns the
derivative with respect to the standard deviation.
If T is the time to maturity Black vega would be
blackStdDevDerivative(strike, forward, stdDev)*sqrt(T)
*/
Real bachelierBlackFormulaStdDevDerivative(Real strike,
Real forward,
Real stdDev,
Real discount = 1.0);
Real bachelierBlackFormulaStdDevDerivative(const boost::shared_ptr<PlainVanillaPayoff>& payoff,
Real forward,
Real stdDev,
Real discount = 1.0);
}
#endif
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