Simulating the Evolution of the Implied Distribution

Motivated by the implied stochastic volatility literature (Britten–Jones and Neuberger, forthcoming; Derman and Kani, 1997; Ledoit and Santa–Clara, 1998) this paper proposes a new and general method for constructing smile–consistent stochastic volatility models. The method is developed by recognising that option pricing and hedging can be accomplished via the simulation of the implied risk neutral distribution. We devise an algorithm for the simulation of the implied distribution, when the first two moments change over time. The algorithm can be implemented easily, and it is based on an economic interpretation of the concept of mixture of distributions. It can also be generalised to cases where more complicated forms for the mixture are assumed.     

Modeling Conditional Yield Densities

Given the increasing interest in agricultural risk, many have sought improved methods to characterize conditional crop-yield densities. While most have postulated the Beta as a flexible alternative to the Normal, others have chosen nonparametric methods. Unfortunately, yield data tends not to be sufficiently abundant to invalidate many reasonable parametric models. This is problematic because conclusions from economic analyses, which require estimated conditional yield densities, tend not to be invariant to the modeling assumption. We propose a semiparametric estimator that, because of its theoretical properties and our simulation results, enables one to empirically proceed with a higher degree of confidence.     

Conditioning as disintegration

Conditional probability distributions seem to have a bad reputation when it comes to rigorous treatment of conditioning. Technical arguments are published as manipulations of Radon–Nikodym derivatives, although we all secretly perform heuristic calculations using elementary definitions of conditional probabilities. In print, measurability and averaging properties substitute for intuitive ideas about random variables behaving like constants given particular conditioning information.
One way to engage in rigorous, guilt-free manipulation of conditional distributions is to treat them as disintegrating measures—families of probability measures concentrating on the level sets of a conditioning statistic. In this paper we present a little theory and a range of examples—from EM algorithms and the Neyman factorization, through Bayes theory and marginalization paradoxes—to suggest that disintegrations have both intuitive appeal and the rigor needed for many problems in mathematical statistics.     

Asymptotically optimal estimation of smooth functionals for interval censoring, part 1

Estimation in the interval censoring model is considered. A class of smooth functionals is introduced, of which the mean is an example. The asymptotic information lower bound for such functionals can be represented as an inner product of two functions. In case 1, i.e. one observation time per unobservable event time, both functions can be given explicitly. We mainly consider case 2, with two observation times for each unobservable event time, in the situation that the observation times can not become arbitrarily close to each other. For case 2, one of the functions in the inner product can only be given implicitly as solution to a Fredholm integral equation. We study properties of this solution and, in a sequel to this paper, prove that the nonparametric maximum likelihood estimator of the functional asymptotically reaches the information lower bound.     

A new continuous distribution and two new families of distributions based on the exponential

Recent work on social status led to derivation of a new continuous distribution based on the exponential. The new variate, termed the ring(2)-exponential, in turn leads to derivation of two closely related new families of continuous distributions, the mirror-exponential and the ring-exponential. Both the standard exponential and the ring(2)-exponential are special cases of both the new families. In this paper, we first focus on the ring(2)-exponential, describing its derivation and examining its properties, and next introduce the two new families, describing their derivation and initiating exploration of their properties. The mirror-exponential arises naturally in the study of status; the ring-exponential arises from the mathematical structure of the ring(2)-exponential. Both have the potential for broad application in diverse contexts across science and engineering. Within sociobehavioral contexts, the new mirror-exponential may have application to the problem of approximating the form and inequality of the wage distribution.     

A Note on Minimax Mixture of Distributions Free Procedure for Inventory Model with Variable Lead Time

In recent papers, Moon and Choi (1998) and Hariga and Ben-Daya (1999)considered a continuous review inventory model with a mixture of backordersand lost sales in which the lead time, the order quantity, and the reorder pointare decision variables was studied. Moreover, they also develop a minimaxdistribution free procedure for the problem. While the demands of differentcustomers are not identical in the lead time, then we can't only use a singledistribution (such as Moon & Choi (1998) and Hariga & Ben-Daya (1999))to describe the demand of the lead time. Hence, we correct and extend the modelof Moon and Choi (1998) and Hariga and Ben-Daya (1999) by considering thelead time demand with the mixture of distributions. In addition, we also applythe minimax mixture of distributions free approach to the model by simultaneouslyoptimizing the order quantity, the reorder point, and the lead time to devise a practical procedure which can be used without specific information on demand distribution.     

Good News and Bad News: Search from Unknown Wage Offer Distributions

The largest market in national economies is the labor market. Labor market contracting is characterized by job search, often from unknown wage offer distributions. This paper reports experimental tests of finite horizon models of job search in which the wage offer distribution is unknown. Theoretically-optimal search from an unknown wage offer distribution can have the seemingly paradoxical property that some offers will be accepted that are lower than other offers that will be rejected in the same period of the search horizon. Thus the reservation wage property (or lowest acceptable wage path) may not exist. This can occur because an offer that is a priori relatively high (good news) can imply that it is highly probable that search is from a favorable distribution, and such an offer can look unattractive when it is an a posteriori relatively low offer from a favorable distribution (bad news). This paper reports results from experimental treatments for search from unknown distributions in which the reservation wage property does exist and treatments in which it does not exist. We find that the consistency of search behavior with search theory reported in earlier papers is robust to the presence or absence of the reservation wage property and to whether the draws come from known or unknown distributions.     

EXTREME VALUE THEORY IN FINANCE: A SURVEY

Extreme value theory is concerned with the study of the asymptotic distribution of extreme events, that is to say events which are rare in frequency and huge in magnitude with respect to the majority of observations. Statistical methods derived from it have been employed increasingly in finance, especially for risk measurement. This paper surveys some of those main applications, namely for testing different distributional assumptions for the data, for Value‐at‐Risk and Expected Shortfall calculations, for asset allocation under safety‐first type constraints, and for the study of contagion and dependence across markets under conditions of stress.