60 research outputs found
Stochastic volatility and leverage effect
We prove that a wide class of correlated stochastic volatility models exactly
measure an empirical fact in which past returns are anticorrelated with future
volatilities: the so-called ``leverage effect''. This quantitative measure
allows us to fully estimate all parameters involved and it will entail a deeper
study on correlated stochastic volatility models with practical applications on
option pricing and risk management.Comment: 4 pages, 2 figure
Bessel Process and Conformal Quantum Mechanics
Different aspects of the connection between the Bessel process and the
conformal quantum mechanics (CQM) are discussed. The meaning of the possible
generalizations of both models is investigated with respect to the other model,
including self adjoint extension of the CQM. Some other generalizations such as
the Bessel process in the wide sense and radial Ornstein- Uhlenbeck process are
discussed with respect to the underlying conformal group structure.Comment: 28 Page
A robust spectral method for solving Heston’s model
In this paper, we consider the Heston’s volatility model (Heston in Rev.
Financ. Stud. 6: 327–343, 1993]. We simulate this model using a combination of the
spectral collocation method and the Laplace transforms method. To approximate the
two dimensional PDE, we construct a grid which is the tensor product of the two
grids, each of which is based on the Chebyshev points in the two spacial directions.
The resulting semi-discrete problem is then solved by applying the Laplace transform
method based on Talbot’s idea of deformation of the contour integral (Talbot in IMA
J. Appl. Math. 23(1): 97–120, 1979)
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