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33
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 p ..."
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Cited by 410 (2 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 remar ..."
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Cited by 208 (52 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 89 (6 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 27 (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
Application of Fourier Inversion Methods to Credit Portfolio Models with Integrated Interest Rate and Credit Spread Risk. Working Paper
"... Most credit portfolio models currently used by the banking industry rely on Monte Carlo simulations for calculating the probability distribution of the future credit portfolio value, which can be quite computer time consuming. Adding market risk factors, such as stochastic interest rates or credit s ..."
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Cited by 1 (1 self)
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Most credit portfolio models currently used by the banking industry rely on Monte Carlo simulations for calculating the probability distribution of the future credit portfolio value, which can be quite computer time consuming. Adding market risk factors, such as stochastic interest rates or credit spreads, as additional ingredients of a credit portfolio model, the computational burden of full Monte Carlo simulations even increases and the need for efficient methods for calculating credit risk measures becomes even more obvious. In this study, based on a version of the wellknown credit portfolio model CreditMetrics extended by correlated interest rate and credit spread risk, it is analyzed whether the use of characteristic functions and inverse Fourier transformation can be an efficient tool for calculating risk measures in the context of integrated credit portfolio models. 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. However, this method can be much faster than a full Monte Carlo simulation of the future credit portfolio distribution. The accuracy of the method depends on the composition of the portfolio. Keywords: credit risk, interest rate risk, credit spread risk, credit portfolio model, Value at Risk, characteristic function, inverse Fourier transforms
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.
Exact optimal inference in regression models under heteroskedasticity and nonnormality of unknown form
, 2009
"... Simple pointoptimal signbased tests are developed for inference on linear and nonlinear regression models with nonGaussian heteroskedastic errors. The tests are exact, distributionfree, robust to heteroskedasticity of unknown form, and may be inverted to build confidence regions for the paramet ..."
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Cited by 1 (0 self)
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Simple pointoptimal signbased tests are developed for inference on linear and nonlinear regression models with nonGaussian heteroskedastic errors. The tests are exact, distributionfree, robust to heteroskedasticity of unknown form, and may be inverted to build confidence regions for the parameters of the regression function. Since pointoptimal sign tests depend on the alternative hypothesis considered, an adaptive approach based on a splitsample technique is proposed in order to choose an alternative that brings power close to the power envelope. The performance of the proposed quasipointoptimal sign tests with respect to size and power is assessed in a Monte Carlo study. The power of quasipointoptimal sign tests is typically close to the power envelope, when approximately 10 % of the sample is used to estimate the alternative and the remaining sample to compute the test statistic. Further, the proposed procedures perform much better than common leastsquaresbased tests which are supposed to be robust against heteroskedasticity.
Analytical ValueatRisk and Expected Shortfall under Regime Switching*
, 2009
"... It is well known that the use of Gaussian models to assess financial risk leads to an underestimation of risk. The reason is because these models are unable to capture some important facts such as heavy tails and volatility clustering which indicate the presence of large fluctuations in returns. An ..."
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Cited by 1 (0 self)
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It is well known that the use of Gaussian models to assess financial risk leads to an underestimation of risk. The reason is because these models are unable to capture some important facts such as heavy tails and volatility clustering which indicate the presence of large fluctuations in returns. An alternative way is to use regimeswitching models, the latter are able to capture the previous facts. Using regimeswitching model, we propose an analytical approximation for multihorizon conditional ValueatRisk and a closedform solution for conditional Expected Shortfall. By comparing the ValueatRisks and Expected Shortfalls calculated analytically and using simulations, we find that the both approaches lead to almost the same result. Further, the analytical approach is less time and computer intensive compared to simulations, which are typically used in risk management.
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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 algorit ..."
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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. 1
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