6,291 research outputs found
USLV: Unspanned Stochastic Local Volatility Model
We propose a new framework for modeling stochastic local volatility, with
potential applications to modeling derivatives on interest rates, commodities,
credit, equity, FX etc., as well as hybrid derivatives. Our model extends the
linearity-generating unspanned volatility term structure model by Carr et al.
(2011) by adding a local volatility layer to it. We outline efficient numerical
schemes for pricing derivatives in this framework for a particular four-factor
specification (two "curve" factors plus two "volatility" factors). We show that
the dynamics of such a system can be approximated by a Markov chain on a
two-dimensional space (Z_t,Y_t), where coordinates Z_t and Y_t are given by
direct (Kroneker) products of values of pairs of curve and volatility factors,
respectively. The resulting Markov chain dynamics on such partly "folded" state
space enables fast pricing by the standard backward induction. Using a
nonparametric specification of the Markov chain generator, one can accurately
match arbitrary sets of vanilla option quotes with different strikes and
maturities. Furthermore, we consider an alternative formulation of the model in
terms of an implied time change process. The latter is specified
nonparametrically, again enabling accurate calibration to arbitrary sets of
vanilla option quotes.Comment: Sections 3.2 and 3.3 are re-written, 3 figures adde
Analog, hybrid, and digital simulation
Analog, hybrid, and digital computerized simulation technique
Co-regularized Alignment for Unsupervised Domain Adaptation
Deep neural networks, trained with large amount of labeled data, can fail to
generalize well when tested with examples from a \emph{target domain} whose
distribution differs from the training data distribution, referred as the
\emph{source domain}. It can be expensive or even infeasible to obtain required
amount of labeled data in all possible domains. Unsupervised domain adaptation
sets out to address this problem, aiming to learn a good predictive model for
the target domain using labeled examples from the source domain but only
unlabeled examples from the target domain. Domain alignment approaches this
problem by matching the source and target feature distributions, and has been
used as a key component in many state-of-the-art domain adaptation methods.
However, matching the marginal feature distributions does not guarantee that
the corresponding class conditional distributions will be aligned across the
two domains. We propose co-regularized domain alignment for unsupervised domain
adaptation, which constructs multiple diverse feature spaces and aligns source
and target distributions in each of them individually, while encouraging that
alignments agree with each other with regard to the class predictions on the
unlabeled target examples. The proposed method is generic and can be used to
improve any domain adaptation method which uses domain alignment. We
instantiate it in the context of a recent state-of-the-art method and observe
that it provides significant performance improvements on several domain
adaptation benchmarks.Comment: NIPS 2018 accepted versio
A finite model of two-dimensional ideal hydrodynamics
A finite-dimensional su() Lie algebra equation is discussed that in the
infinite limit (giving the area preserving diffeomorphism group) tends to
the two-dimensional, inviscid vorticity equation on the torus. The equation is
numerically integrated, for various values of , and the time evolution of an
(interpolated) stream function is compared with that obtained from a simple
mode truncation of the continuum equation. The time averaged vorticity moments
and correlation functions are compared with canonical ensemble averages.Comment: (25 p., 7 figures, not included. MUTP/92/1
A Comparison of Three Random Number Generators for Aircraft Dynamic Modeling Applications
Three random number generators, which produce Gaussian white noise sequences, were compared to assess their suitability in aircraft dynamic modeling applications. The first generator considered was the MATLAB (registered) implementation of the Mersenne-Twister algorithm. The second generator was a website called Random.org, which processes atmospheric noise measured using radios to create the random numbers. The third generator was based on synthesis of the Fourier series, where the random number sequences are constructed from prescribed amplitude and phase spectra. A total of 200 sequences, each having 601 random numbers, for each generator were collected and analyzed in terms of the mean, variance, normality, autocorrelation, and power spectral density. These sequences were then applied to two problems in aircraft dynamic modeling, namely estimating stability and control derivatives from simulated onboard sensor data, and simulating flight in atmospheric turbulence. In general, each random number generator had good performance and is well-suited for aircraft dynamic modeling applications. Specific strengths and weaknesses of each generator are discussed. For Monte Carlo simulation, the Fourier synthesis method is recommended because it most accurately and consistently approximated Gaussian white noise and can be implemented with reasonable computational effort
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