noarbsabr.hpp File Reference

No-arbitrage SABR. More...

#include <ql/qldefines.hpp>
#include <ql/types.hpp>
#include <ql/math/integrals/gausslobattointegral.hpp>
#include <vector>

Go to the source code of this file.

Classes
class	NoArbSabrModel
class	D0Interpolator

Namespaces
namespace	QuantLib
namespace	QuantLib::detail
namespace	QuantLib::detail::NoArbSabrModel

Variables
const Real	beta_min = 0.01
const Real	beta_max = 0.99
const Real	expiryTime_max = 30.0
const Real	sigmaI_min = 0.05
const Real	sigmaI_max = 1.00
const Real	nu_min = 0.01
const Real	nu_max = 0.80
const Real	rho_min = -0.99
const Real	rho_max = 0.99
const Real	phiByTau_cutoff = 124.587
const Real	nsim = 2500000.0
const Real	tiny_prob = 1E-5
const Real	strike_min = 1E-6
const Real	i_accuracy = 1E-7
const Size	i_max_iterations = 10000
const Real	forward_accuracy = 1E-6
const Real	forward_search_step = 0.0010
const Real	density_lower_bound = 1E-50
const Real	density_threshold = 1E-100
const unsigned long	sabrabsprob [1209600]

Detailed Description

No-arbitrage SABR.

Reference: Paul Doust, No-arbitrage SABR, The Journal of Computational Finance (3–31) Volume 15/Number 3, Spring 2012

The parameters are bounded as follows (see also below)

beta [0.01, 0.99] expiryTime (0.0, 30.0] sigmaI = alpha*forward^(beta-1) [0.05, 1.0] nu [0.0001, 0.8] rho [-0.99, 0.99]

As suggested in the paper, d0 is interpolated (linearly) in phi space. For beta > 0.9 phi is extrapolated to a value corresponding to d0 = tiny_prob = 1E-5 at beta = 1. For tau < 0.25 phi is extrapolated flat. For rho outside [-0.75, 0.75] phi is extrapolated linearly.

There are some parameter sets that are admissable, yet do not allow for the adjustment procedure as suggested in the paper to force the model implied forward to the correct value. In this case, no adjustment is done, leading to a model implied forward different from the desired one. This situation can be identified by comparing forward() and numericalForward().

Definition in file noarbsabr.hpp.