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Keywords
(5)
Characteristic Function
Heston Model
Option Pricing
Parameter Space
riccati equation
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(2)
Notsocomplex Logarithms in the Heston Model
Moment explosions in stochastic volatility models
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The Little Heston Trap
The Little Heston Trap,Hansjorg Albrecher,Philipp Mayer,Wim Schoutens,Jurgen Tistaert
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The Little Heston Trap
(
Citations: 24
)
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Hansjorg Albrecher
,
Philipp Mayer
,
Wim Schoutens
,
Jurgen Tistaert
Abstract The role of characteristic functions in finance has been strongly amplified by the develop ment of the general
option pricing
formula by Carr and Madan. As these functions are defined and operating in the complex plane, they potentially encompass a few well known numerical issues due to ”branching”. A number,of elegant publications have emerged tackling these effects specifically for the Heston model. For the latter however we have two specifications for the
characteristic function
as they are the solutions to a Riccati equation. In this article we put the i’s and cross the t’s by formally pointing out the properties of and relations be tween both versions. For the first specification we show that for nearly any parameter choice, instabilities will occur for large enough maturities. We subsequently establish  under an addi tional parameter restriction  the existence of a “threshold” maturity from which the complex operations become,a spoilsport. For the second specification of the
characteristic function
it is proved that stability is guaranteed under the full dimensional and unrestricted parameter space. We blend the theoretical results with a few examples. 2
Published in 2006.
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Citation Context
(12)
...In the finance literature various approaches have been taken to efficiently evaluate the objective function of such calibration problems, see for example Carr and Madan [6] or Albrecher et al. [
2
]...
F. Gerlich
,
et al.
Parameter identification in financial market models with a feasible po...
...The vanilla option prices are computed by using the CarrMadan formula (see Carr and Madan 1998 and
Albrecher et al. 2007
for the closedform expression of the Heston characteristic function)...
Florence Guillaume
,
et al.
Calibration risk: Illustrating the impact of calibration risk under th...
...Taking the contrapositive, if (29) does not hold, then (30) does not hold and p = 2 [0;
1
] (recall that p¡ < 0 and p+ > 1); thus, by Proposition 3.1 in [2], E(ep(Xt¡x0)) = 1 for t su‐ciently large, and (3) holds...
Martin Forde
,
et al.
The largematurity smile for the Heston model
... (
2005
) and Gatheral (
2005
) and is free of a numerical difficulty called branch cutting, while another representation can be found in the original Heston (
1993
) paper or Kahl and Jäckel (
2005
), which may cause some numerical difficulties for certain model parameters (Albrecher
et al...
Alexander van Haastrecht
,
et al.
Generic pricing of FX, inflation and stock options under stochastic in...
... (
2007
) and Kahl and Lord (
2010
) there exist two representations of the univariate characteristic function ln
S
_{ T }
in the Heston model...
Susanne A. Griebsch
,
et al.
On the valuation of fader and discrete barrier options in Heston's sto...
References
(8)
A ClosedForm Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options
(
Citations: 1117
)
Steven L. Heston
Published in 2008.
Why the Rotation Count Algorithm works
(
Citations: 12
)
Roger Lord
,
Christian Kahl
Published in 2006.
Exact Simulation of Stochastic Volatility and Other Affine Jump Diffusion Processes
(
Citations: 87
)
Mark Broadie
,
Özgür Kaya
Journal:
Operations Research
, vol. 54, no. 2, pp. 217231, 2006
Option valuation using fast Fourier transform
(
Citations: 362
)
P. Carr
,
D. Madan
Published in 1999.
Notsocomplex Logarithms in the Heston Model
(
Citations: 21
)
Christian Kahl
Published in 1993.
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Citations
(24)
Parameter identification in financial market models with a feasible point SQP algorithm
F. Gerlich
,
A. M. Giese
,
J. H. Maruhn
,
E. W. Sachs
Journal:
Computational Optimization and Applications  COMPUT OPTIM APPL
, pp. 125, 2012
Calibration risk: Illustrating the impact of calibration risk under the Heston model
Florence Guillaume
,
Wim Schoutens
Journal:
Review of Derivatives Research
, vol. 15, no. 1, pp. 123, 2012
The largematurity smile for the Heston model
(
Citations: 3
)
Martin Forde
,
Antoine Jacquierz
Journal:
Finance and Stochastics
, pp. 126, 2011
Generic pricing of FX, inflation and stock options under stochastic interest rates and stochastic volatility
(
Citations: 2
)
Alexander van Haastrecht
,
Antoon Pelsser
Journal:
Quantitative Finance  QUANT FINANC
, vol. 11, no. 5, pp. 665691, 2011
On the valuation of fader and discrete barrier options in Heston's stochastic volatility model
Susanne A. Griebsch
,
Uwe Wystup
Journal:
Quantitative Finance  QUANT FINANC
, vol. 11, no. 5, pp. 693709, 2011