183 research outputs found
Exact Model for Mode-Dependent Gains and Losses in Multimode Fiber
In the strong mode coupling regime, the model for mode-dependent gains and
losses (collectively referred as MDL) of a multimode fiber is extended to the
region with large MDL. The MDL is found to have the same statistical properties
as the eigenvalues of the summation of two matrices. The first matrix is a
random Gaussian matrix with standard deviation proportional to the accumulated
MDL. The other matrix is a deterministic matrix with uniform eigenvalues
proportional to the square of the accumulated MDL. The results are analytically
correct for fibers with two or large number of modes, and also numerically
verified for other cases.Comment: 7 pages, 2 figures, 2 table
Performance of DPSK Signals with Quadratic Phase Noise
Nonlinear phase noise induced by the interaction of fiber Kerr effect and
amplifier noises is a quadratic function of the electric field. When the
dependence between the additive Gaussian noise and the quadratic phase noise is
taking into account, the joint statistics of quadratic phase noise and additive
Gaussian noise is derived analytically. When the error probability for
differential phase-shift keying (DPSK) signals is evaluated, depending on the
number of fiber spans, the signal-to-noise ratio (SNR) penalty is increased by
up to 0.23 dB due to the dependence between the Gaussian noise and the
quadratic phase noise.Comment: 15 pages, 2 figure
Error Probability of DPSK Signals with Intrachannel Four-Wave-Mixing in Highly Dispersive Transmission Systems
A semi-analytical method evaluates the error probability of DPSK signals with
intrachannel four-wave-mixing (IFWM) in a highly dispersive fiber link with
strong pulse overlap. Depending on initial pulse width, the mean nonlinear
phase shift of the system can be from 1 to 2 rad for signal-to-noise ratio
(SNR) penalty less than 1 dB. An approximated empirical formula, valid for
penalty less than 2 dB, uses the variance of the differential phase of the
ghost pulses to estimate the penalty.Comment: 3 pages, 3 figure
Applications of New Diffusion Models to Barrier Option Pricing and First Hitting Time in Finance
The main focus of this thesis is in the application of a new family of analytical solvable diffusion models to arbitrage-free pricing exotic financial derivatives, such as barrier options. The family of diffusions is the so-called “Drifted Bessel family” having nonlinear (smile-like) local volatility with multiple adjustable parameters. In particular, the drifted Bessel-K diffusion is used to model asset (stock) price processes under a risk-neutral measure whereby discounted asset price are martingales.
Closed-form spectral expansions for barrier option values are derived within the Bessel-K family of models. This follow from the closed-form spectral expansions for the transition probability densities which are obtained for the Bessel family of processes with imposed killing boundaries. We also show that the commonly adopted CEV model is recovered as a special parametric limit of our Bessel family of models for the case of zero drift.
The rapid convergence of the spectral expansions leads to very efficient numerical implementations of barrier option pricing and sensitivity analysis. We hence carry out various numerical computations in order to study the relative effects of the parameters (state dependencies) of the Bessel family of models with respect to barrier option pricing and hedging. We compare our results with the standard Black-Scholes (GBM) and CEV models, demonstrating that model specification leads to important differences when pricing non-vanilla options, such as barrier options
Comparison of Nonlinear Phase Noise and Intrachannel Four-Wave-Mixing for RZ-DPSK Signals in Dispersive Transmission Systems
Self-phase modulation induced nonlinear phase noise is reduced with the
increase of fiber dispersion but intrachannel four-wave-mixing (IFWM) is
increased with dispersion. Both degrading DPSK signals, the standard deviation
of nonlinear phase noise induced differential phase is about three times that
from IFWM even in highly dispersive transmission systems.Comment: 3 pages, 2 figure
Asymptotic Probability Density Function of Nonlinear Phase Noise
The asymptotic probability density function of nonlinear phase noise, often
called the Gordon-Mollenauer effect, is derived analytically when the number of
fiber spans is very large. The nonlinear phase noise is the summation of
infinitely many independently distributed noncentral chi-square random
variables with two degrees of freedom. The mean and standard deviation of those
random variables are both proportional to the square of the reciprocal of all
odd natural numbers. The nonlinear phase noise can also be accurately modeled
as the summation of a noncentral chi-square random variable with two degrees of
freedom and a Gaussian random variable.Comment: 13 pages, 3 figure
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