7,977 research outputs found
Pricing Bermudan options under local L\'evy models with default
We consider a defaultable asset whose risk-neutral pricing dynamics are
described by an exponential L\'evy-type martingale. This class of models allows
for a local volatility, local default intensity and a locally dependent L\'evy
measure. We present a pricing method for Bermudan options based on an
analytical approximation of the characteristic function combined with the COS
method. Due to a special form of the obtained characteristic function the price
can be computed using a Fast Fourier Transform-based algorithm resulting in a
fast and accurate calculation. The Greeks can be computed at almost no
additional computational cost. Error bounds for the approximation of the
characteristic function as well as for the total option price are given
Bayesian interpretation of periodograms
The usual nonparametric approach to spectral analysis is revisited within the
regularization framework. Both usual and windowed periodograms are obtained as
the squared modulus of the minimizer of regularized least squares criteria.
Then, particular attention is paid to their interpretation within the Bayesian
statistical framework. Finally, the question of unsupervised hyperparameter and
window selection is addressed. It is shown that maximum likelihood solution is
both formally achievable and practically useful
Calculation of Densities of States and Spectral Functions by Chebyshev Recursion and Maximum Entropy
We present an efficient algorithm for calculating spectral properties of
large sparse Hamiltonian matrices such as densities of states and spectral
functions. The combination of Chebyshev recursion and maximum entropy achieves
high energy resolution without significant roundoff error, machine precision or
numerical instability limitations. If controlled statistical or systematic
errors are acceptable, cpu and memory requirements scale linearly in the number
of states. The inference of spectral properties from moments is much better
conditioned for Chebyshev moments than for power moments. We adapt concepts
from the kernel polynomial approximation, a linear Chebyshev approximation with
optimized Gibbs damping, to control the accuracy of Fourier integrals of
positive non-analytic functions. We compare the performance of kernel
polynomial and maximum entropy algorithms for an electronic structure example.Comment: 8 pages RevTex, 3 postscript figure
The Evaluation Of Barrier Option Prices Under Stochastic Volatility
This paperc onsiders the problem o fnumerically evaluating barrier option prices when the dynamics of the underlying are driven by stochastic volatility following the square root process of Heston (1993). We develop a method of lines approach to evaluate the price as well as the delta and gamma of the option. The method is able to effciently handle bothc ontinuously monitored and discretely monitored barrier options and can also handle barrier options with early exercise features. In the latter case, we can calculate the early exercise boundary of an American barrier option in both the continuously and discretely monitored cases.barrier option; stochastic volatility; continuously monitored; discretely monitored; free boundary problem; method of lines; Monte Carlo simulation
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