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12
The JumpRisk Premia Implicit in Options: Evidence from an Integrated TimeSeries Study
 Journal of Financial Economics
"... Abstract: This paper examines the joint time series of the S&P 500 index and nearthemoney shortdated option prices with an arbitragefree model, capturing both stochastic volatility and jumps. Jumprisk premia uncovered from the joint data respond quickly to market volatility, becoming more promi ..."
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Cited by 210 (1 self)
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Abstract: This paper examines the joint time series of the S&P 500 index and nearthemoney shortdated option prices with an arbitragefree model, capturing both stochastic volatility and jumps. Jumprisk premia uncovered from the joint data respond quickly to market volatility, becoming more prominent during volatile markets. This form of jumprisk premia is important not only in reconciling the dynamics implied by the joint data, but also in explaining the volatility “smirks” of crosssectional options data.
The FourierSeries Method For Inverting Transforms Of Probability Distributions
, 1991
"... This paper reviews the Fourierseries method for calculating cumulative distribution functions (cdf's) and probability mass functions (pmf's) by numerically inverting characteristic functions, Laplace transforms and generating functions. Some variants of the Fourierseries method are remarkably easy ..."
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Cited by 149 (51 self)
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This paper reviews the Fourierseries method for calculating cumulative distribution functions (cdf's) and probability mass functions (pmf's) by numerically inverting characteristic functions, Laplace transforms and generating functions. Some variants of the Fourierseries method are remarkably easy to use, requiring programs of less than fifty lines. The Fourierseries method can be interpreted as numerically integrating a standard inversion integral by means of the trapezoidal rule. The same formula is obtained by using the Fourier series of an associated periodic function constructed by aliasing; this explains the name of the method. This Fourier analysis applies to the inversion problem because the Fourier coefficients are just values of the transform. The mathematical centerpiece of the Fourierseries method is the Poisson summation formula, which identifies the discretization error associated with the trapezoidal rule and thus helps bound it. The greatest difficulty is approximately calculating the infinite series obtained from the inversion integral. Within this framework, lattice cdf's can be calculated from generating functions by finite sums without truncation. For other cdf's, an appropriate truncation of the infinite series can be determined from the transform based on estimates or bounds. For Laplace transforms, the numerical integration can be made to produce a nearly alternating series, so that the convergence can be accelerated by techniques such as Euler summation. Alternatively, the cdf can be perturbed slightly by convolution smoothing or windowing to produce a truncation error bound independent of the original cdf. Although error bounds can be determined, an effective approach is to use two different methods without elaborate error analysis. For this...
Option Pricing by Transform Methods: Extensions, Unification, and Error Control
 Journal of Computational Finance
"... We extend and unify Fourieranalytic methods for pricing a wide class of options on any underlying state variable whose characteristic function is known. In this general setting, we bound the numerical pricing error of discretized transform computations, such as DFT/FFT. These bounds enable algorith ..."
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Cited by 37 (3 self)
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We extend and unify Fourieranalytic methods for pricing a wide class of options on any underlying state variable whose characteristic function is known. In this general setting, we bound the numerical pricing error of discretized transform computations, such as DFT/FFT. These bounds enable algorithms to select efficient quadrature parameters and to price with guaranteed numerical accuracy.
Probabilistic Arithmetic
, 1989
"... This thesis develops the idea of probabilistic arithmetic. The aim is to replace arithmetic operations on numbers with arithmetic operations on random variables. Specifically, we are interested in numerical methods of calculating convolutions of probability distributions. The longterm goal is to ..."
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Cited by 13 (0 self)
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This thesis develops the idea of probabilistic arithmetic. The aim is to replace arithmetic operations on numbers with arithmetic operations on random variables. Specifically, we are interested in numerical methods of calculating convolutions of probability distributions. The longterm goal is to be able to handle random problems (such as the determination of the distribution of the roots of random algebraic equations) using algorithms which have been developed for the deterministic case. To this end, in this thesis we survey a number of previously proposed methods for calculating convolutions and representing probability distributions and examine their defects. We develop some new results for some of these methods (the Laguerre transform and the histogram method), but ultimately find them unsuitable. We find that the details on how the ordinary convolution equations are calculated are
On the Applicability of Fourier Based Methods to Credit Portfolio Models with Integrated Interest Rate and Credit Spread Risk
, 2004
"... In this paper it is analyzed whether a Fourier based approach can be an efficient tool for calculating risk measures in the context of a credit portfolio model with integrated market risk factors. For this purpose, this technique is applied to a version of the wellknown credit portfolio model Credi ..."
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In this paper it is analyzed whether a Fourier based approach can be an efficient tool for calculating risk measures in the context of a credit portfolio model with integrated market risk factors. For this purpose, this technique is applied to a version of the wellknown credit portfolio model CreditMetrics extended by correlated interest rate and credit spread risk. Unfortunately, the characteristic function of the credit portfolio value at the risk horizon can not be calculated in closedform, but has to be computed by Monte Carlo simulations. Due to this drawback, in the considered numerical examples the performance of the Fourier based approach is not better than that of a full Monte Carlo simulation of the future credit portfolio distribution, especially for inhomogeneous portfolios and when percentiles corresponding to high confidence levels are needed. The application of standard Importance Sampling techniques for improving the performance of the Fourier based approach is problematic, too. Keywords: credit risk, interest rate risk, credit spread risk, credit portfolio model, Value at Risk, characteristic
ON THE ASYMPTOTIC DISTRIBUTION OF USTATISTICS by
"... The asymptotic distribution of a Ustatistic is found in the case when the corresponding Von Mises functional is stationary of order I. Practical methods for the tabulation of the limit distributions are discussed, and the results extended to certain incomplete Ustatistics. Key Words and Phrases: a ..."
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The asymptotic distribution of a Ustatistic is found in the case when the corresponding Von Mises functional is stationary of order I. Practical methods for the tabulation of the limit distributions are discussed, and the results extended to certain incomplete Ustatistics. Key Words and Phrases: asymptotic distribution, stationary statistical functional, incomplete Ustatistic.e
Exact Asymptotic GoodnessofFit Testing For Discrete Circular Data, With Applications
, 2012
"... We show that the full asymptotic null distribution for Watson’s 2 U N statistic, modified for discrete data, can be computed simply and exactly by standard methods. Previous approximate quantiles for the uniform multinomial case are found to be accurate. More extensive quantiles are presented for th ..."
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We show that the full asymptotic null distribution for Watson’s 2 U N statistic, modified for discrete data, can be computed simply and exactly by standard methods. Previous approximate quantiles for the uniform multinomial case are found to be accurate. More extensive quantiles are presented for this distribution, as well as for the betabinomial distribution and for the distributions associated with “Benford’s Laws”. The latter distributions are for the first one, two, or three significant digits in a sequence of “naturally occurring ” numbers. A simulation experiment compares the power of the 2 modified U N test with that of Kuiper’s VN test. In addition, four illustrative empirical applications are provided to illustrate the usefulness of the 2 U N test. (This paper supercedes EWP0607.) Keywords: Mathematics Subject
2006 IEEE Ninth International Symposium on Spread Spectrum Techniques and Applications On Preamble Detection in PacketBased Wireless Networks
"... Abstract — Performance bounds on detecting a preamble embedded at the start of every packet for communication over an additive white Gaussian noise channel are derived. The preamble sequence consists of blocks of spreading sequences whose length is at most the coherence time of the channel. These bl ..."
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Abstract — Performance bounds on detecting a preamble embedded at the start of every packet for communication over an additive white Gaussian noise channel are derived. The preamble sequence consists of blocks of spreading sequences whose length is at most the coherence time of the channel. These blocks are differentially combined. A correlationbased detection is employed to locate the boundaries of the preamble. Simulation results closely follow the analysis. Furthermore, the effects of frequency offset on the system performance are discussed. I.
Differential Preamble Detection in PacketBased Wireless Networks
"... Abstract — A novel hypothesisbased preamble detection method for uncoordinated, highdensity packetbased communication over an additive white Gaussian noise channel is proposed and analyzed. Received samples are observed over a window of length equal to that of the preamble and a metric is compute ..."
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Abstract — A novel hypothesisbased preamble detection method for uncoordinated, highdensity packetbased communication over an additive white Gaussian noise channel is proposed and analyzed. Received samples are observed over a window of length equal to that of the preamble and a metric is computed for each sample shift of the window. A metric exceeding a noise dependent precomputed threshold flags the presence of a preamble. The preamble sequence consists of concatenated sections of spreading sequences whose length is at most the coherence time of the channel. These sections are then differentially combined. A differential correlationbased detection is employed to locate the boundaries of the preamble. A theoretical framework is developed to provide exact analytical solutions for missing and falsely detecting a preamble using matrix analysis of quadratic Gaussian statistics. Furthermore, the robustness of the proposed methodology in a two path channel is studied. The effects of frequency and timing offsets on the system performance is evaluated. Simulation results are presented to validate the analytical expressions. Additionally, a performance comparison of the proposed differential detection scheme with that of a noncoherent squarelaw detector is presented.
NEW INSIGHTS INTO THE PPP PUZZLE
, 2007
"... We derive saddlepoint approximations for the density and distribution functions of the halflife estimated by OLS from an AR(1) or AR(p) model. Our analytic results are used to prove that none of the integerorder moments of these halflife estimators exist. This provides an explanation for the unre ..."
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We derive saddlepoint approximations for the density and distribution functions of the halflife estimated by OLS from an AR(1) or AR(p) model. Our analytic results are used to prove that none of the integerorder moments of these halflife estimators exist. This provides an explanation for the unreasonably large estimates of persistency associated with the purchasing power parity “puzzle”, and it also explains the excessively wide confidence intervals reported in the empirical PPP literature.