1,160 research outputs found
Computationally intensive Value at Risk calculations
Market risks are the prospect of financial losses- or gains- due to unexpected changes in market prices and rates. Evaluating the exposure to such risks is nowadays of primary concern to risk managers in financial and non-financial institutions alike. Until late 1980s market risks were estimated through gap and duration analysis (interest rates), portfolio theory (securities), sensitivity analysis (derivatives) or "what-if" scenarios. However, all these methods either could be applied only to very specific assets or relied on subjective reasoning. --
Calculation of Weibull strength parameters and Batdorf flow-density constants for volume- and surface-flaw-induced fracture in ceramics
The calculation of shape and scale parameters of the two-parameter Weibull distribution is described using the least-squares analysis and maximum likelihood methods for volume- and surface-flaw-induced fracture in ceramics with complete and censored samples. Detailed procedures are given for evaluating 90 percent confidence intervals for maximum likelihood estimates of shape and scale parameters, the unbiased estimates of the shape parameters, and the Weibull mean values and corresponding standard deviations. Furthermore, the necessary steps are described for detecting outliers and for calculating the Kolmogorov-Smirnov and the Anderson-Darling goodness-of-fit statistics and 90 percent confidence bands about the Weibull distribution. It also shows how to calculate the Batdorf flaw-density constants by uing the Weibull distribution statistical parameters. The techniques described were verified with several example problems, from the open literature, and were coded. The techniques described were verified with several example problems from the open literature, and were coded in the Structural Ceramics Analysis and Reliability Evaluation (SCARE) design program
Models for Heavy-tailed Asset Returns
Many of the concepts in theoretical and empirical finance developed over the past decades â including the classical portfolio theory, the Black-Scholes-Merton option pricing model or the RiskMetrics variance-covariance approach to VaR â rest upon the assumption that asset returns follow a normal distribution. But this assumption is not justified by empirical data! Rather, the empirical observations exhibit excess kurtosis, more colloquially known as fat tails or heavy tails. This chapter is intended as a guide to heavy-tailed models. We first describe the historically oldest heavy-tailed model â the stable laws. Next, we briefly characterize their recent lighter-tailed generalizations, the socalled truncated and tempered stable distributions. Then we study the class of generalized hyperbolic laws, which â like tempered stable distributions â can be classified somewhere between infinite variance stable laws and the Gaussian distribution. Finally, we provide numerical examples.Heavy-tailed distribution; Stable distribution; Tempered stable distribution; Generalized hyperbolic distribution; Asset return; Random number generation; Parameter estimation;
Models for Heavy-tailed Asset Returns
Many of the concepts in theoretical and empirical finance developed over the past decades â including the classical portfolio theory, the Black-Scholes-Merton option pricing model or the RiskMetrics variance-covariance approach to VaR â rest upon the assumption that asset returns follow a normal distribution. But this assumption is not justified by empirical data! Rather, the empirical observations exhibit excess kurtosis, more colloquially known as fat tails or heavy tails. This chapter is intended as a guide to heavy-tailed models. We first describe the historically oldest heavy-tailed model â the stable laws. Next, we briefly characterize their recent lighter-tailed generalizations, the so-called truncated and tempered stable distributions. Then we study the class of generalized hyperbolic laws, which â like tempered stable distributions â can be classified somewhere between infinite variance stable laws and the Gaussian distribution. Finally, we provide numerical examples.Heavy-tailed distribution; Stable distribution; Tempered stable distribution; Generalized hyperbolic distribution; Asset return; Random number generation; Parameter estimation
Models for Heavy-tailed Asset Returns
Many of the concepts in theoretical and empirical finance developed over the past decades â including the classical portfolio theory, the Black- Scholes-Merton option pricing model or the RiskMetrics variance-covariance approach to VaR â rest upon the assumption that asset returns follow a normal distribution. But this assumption is not justified by empirical data! Rather, the empirical observations exhibit excess kurtosis, more colloquially known as fat tails or heavy tails. This chapter is intended as a guide to heavy-tailed models. We first describe the historically oldest heavy-tailed model â the stable laws. Next, we briefly characterize their recent lighter-tailed generalizations, the socalled truncated and tempered stable distributions. Then we study the class of generalized hyperbolic laws, which â like tempered stable distributions â can be classified somewhere between infinite variance stable laws and the Gaussian distribution. Finally, we provide numerical examples.Heavy-tailed distribution; Stable distribution; Tempered stable distribution; Generalized hyperbolic distribution; Asset return; Random number generation; Parameter estimation
Goodness-of-Fit Tests for Symmetric Stable Distributions -- Empirical Characteristic Function Approach
We consider goodness-of-fit tests of symmetric stable distributions based on
weighted integrals of the squared distance between the empirical characteristic
function of the standardized data and the characteristic function of the
standard symmetric stable distribution with the characteristic exponent
estimated from the data. We treat as an unknown parameter,
but for theoretical simplicity we also consider the case that is
fixed. For estimation of parameters and the standardization of data we use
maximum likelihood estimator (MLE) and an equivariant integrated squared error
estimator (EISE) which minimizes the weighted integral. We derive the
asymptotic covariance function of the characteristic function process with
parameters estimated by MLE and EISE. For the case of MLE, the eigenvalues of
the covariance function are numerically evaluated and asymptotic distribution
of the test statistic is obtained using complex integration. Simulation studies
show that the asymptotic distribution of the test statistics is very accurate.
We also present a formula of the asymptotic covariance function of the
characteristic function process with parameters estimated by an efficient
estimator for general distributions
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