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The weighted Monte Carlo method is an elegant technique to calibrate asset pricing models to market prices. Unfortunately, the accuracy can drop quite quickly for out-of-sample options as one moves away from the strike range and maturity range of the benchmark options. To improve the accuracy, we propose a generalized version of the weighted Monte Carlo calibration method with two distinguishing features. First, we use a probability distortion scheme to produce a non-uniform prior distribution for the simulated paths. Second, we assign multiple weights per path to fit with the different maturities present in the set of benchmark options. Our tests on S&amp, P500 options data show that the new calibration method proposed here produces a significantly better out-of-sample fit than the original method for two commonly used asset pricing models.

For many kinds of derivative valuation problems, especially those that try for greater realism using return processes that are more consistent with empirical evidence, Monte Carlo simulation is the only feasible solution technique. Among the well-known strategies to improve its efficiency, the use of a well-chosen control variate is often very effective. But a good selection can make a lot of difference. This article explains how the mathematical concept of comonotonicity can be applied as a new way to create a control variate. A remarkable improvement in performance can be achieved using the comonotonic upper bound as the control variate. The article illustrates the power of Comonotonic Monte Carlo simulation in estimating tail value at risk and pricing arithmetic Asian options.

We propose a new stochastic volatility model for pricing options on assets that exhibit seasonal trends in volatility. Such assets are prevalent among commodities, with futures on grains and energy being an example. The model is based on the 3/2 stochastic volatility model, but includes a cyclical long-run volatility component. The model yields a closed-form characteristic function which can be used to rapidly calibrate the model to benchmark options. We test the model on market data and show that the model proposed here allows for significantly better empirical fit to option prices on corn and wheat futures than the unmodified 3/2 model.

We give a decision-theoretic procedure for the calibration of option pricing models. The inspiration behind it comes from the Weighted Monte Carlo (WMC) approach. The procedure incorporates rare-event probability distortion in style of Cumulative Prospect Theory (CPT) by Kahneman and Tversky. We also propose an intertemporal interpolation scheme to use with the probability distortion when more than one option maturity is present in the calibration. We show how the procedure significantly improves the out-of-sample accuracy for the arbitrage models we calibrate compared to the original WMC procedure. To our knowledge, this is the first instance where CPT is used to improve the performance of option pricing models in a practical way.

We introduce a new and easy-to-calculate measure for the expected degree of herd behavior or co-movement between stock prices. This forward looking measure is model-independent and based on observed option data. It is baptized the Herd Behavior Index (HIX). The degree of co-movement in a stock market can be determined by comparing the observed market situation with the extreme (theoretical) situation under which the whole system is driven by a single factor. The HIX is then defined as the ratio of an option-based estimate of the risk-neutral variance of the market index and an option-based estimate of the corresponding variance in case of the extreme single factor market situation. The HIX can be determined for any market index provided an appropriate series of vanilla options is traded on this index as well as on its components. As an illustration, we determine historical values of the 30-days HIX for the Dow Jones Industrial Average, covering the period January 2003 to October 2009.

Monte Carlo (MC) simulation is a technique that provides approximate solutions to a broad range of mathematical problems. A drawback of the method is its high computational cost, especially in a high-dimensional setting, such as estimating the Tail Value-at-Risk for large portfolios or pricing basket options and Asian options. For these types of problems, one can construct an upper bound in the convex order by replacing the copula by the comonotonic copula. This comonotonic upper bound can be computed very quickly, but it gives only a rough approximation. In this paper we introduce the Comonotonic Monte Carlo (CoMC) simulation, by using the comonotonic approximation as a control variate. The CoMC is of broad applicability and numerical results show a remarkable speed improvement. We illustrate the method for estimating Tail Value-at-Risk and pricing basket options and Asian options when the logreturns follow a Black-Scholes model or a variance gamma model., La méthode de Monte Carlo est une technique qui permet la résolution d'un grand nombre de problèmes en mathématiques. L'inconvénient de la méthode est la lourdeur des calculs spécialement dans le cadre multidimensionnel. L'estimation de la « Tail Value-at-Risk » dans le cas d'un grand portefeuille ou la tarification d'un portefeuille d'actions comme les options asiatiques peuvent être relativement longues. Dans ce genre de cas, on peut définir une borne supérieure d'ordre convexe en remplaçant la copula par une copula comonotone. Dans cet article, nous introduisons la méthode de Monte Carlo comonotone qui combine les avantages des deux approches. En utilisant l'approximation comonotone comme variable aléatoire de contrôle, nous obtenons une estimation plus précise et donc une simulation moins longue. La CoMc a une large application et les résultats obtenus montrent une amélioration remarquable en terme de vitesse de résolution. Nous illustrerons cette méthode par l'estimation de la TVar, la tarification d'un portefeuille d'actions et des options asiatiques.

Considering that a natural way of sharing risks in insurance companies is to require risk by risk Pareto optimality, we offer in case of strong risk aversion, a simple computable method for deriving all Pareto optima. More importantly all Individually Rational Pareto optima can be computed according to our method., En considérant qu'une manière naturelle pour plusieurs compagnies d'assurance est de partager les risques en imposant la Pareto optimalité risque par risque, nous proposons dans le cas de l'aversion forte au risque une méthode simple et calculable d'obtenir tous les optima de Pareto. De plus, tout optimum de Pareto individuellement rationnel peut être calculé à l'aide de notre méthode.

In this paper we examine and summarize properties of several well-known risk measuresthat can be used in the framework of setting solvency capital requirements for a risky business.Special attention is given to the class of (concave) distortion risk measures. We investigatethe relationship between these risk measures and theories of choice under risk. Furthermore weconsider the problem of how to evaluate risk measures for sums of non-independent randomvariables. Approximations for such sums, based on the concept of comonotonicity, are proposed.Several examples are provided to illustrate properties or to prove that certain properties donot hold. Although the paper contains several new results, it is written as an overview andpedagogical introduction to the subject of risk measurement. The paper is an extended versionof Dhaene et al.[11].Keywords Comonotonicity; Distortion; Lognormal; Risk measurer; Theory of choiceunder risk.Mathematics Subject Classification 91B30.

We investigate multiperiod portfolio selection problems in a Black & Scholes type market where a basket of 1 riskfree and m risky securities are traded continuously. We look for the optimal allocation of wealth within the class of ’constant mix’ portfolios. First, we consider the portfolio selection problem of a decision maker who invests money at predetermined points in time in order to obtain a target capital at the end of the time period under consideration. A second problem concerns a decision maker who invests some amount of money (the initial wealth or provision) in order to be able to fullfil a series of future consumptions or payment obligations. Several optimality criteria and their interpretation within Yaari’s dual theory of choice under risk are presented. For both selection problems, we propose accurate approximations based on the concept of comonotonicity, as studied in Dhaene, Denuit, Goovaerts, Kaas & Vyncke (2002 a,b). Our analytical approach avoids simulation, and hence reduces the computing effort drastically.

In this paper, the authors consider the present value of a series of fixed cash flows under stochastic interest rates. To model these interest rates, they don’t use the common lognormal model, but stable laws, which better fit in with reality. Their main intention is to derive a result for the distribution function of such a present value. However, due to the dependencies between successive discounted payments, the calculation of an exact analytical distribution is impossible. Therefore, use is made of the methodology of comonotonic random variables and the convex ordering of risks, introduced by the same authors in some previous papers. The present paper starts with a brief overview of properties and features of stable laws, and of the possible application of the concept of convex ordering to sums of risks, which is also the situation for a present value of future payments. Afterwards, the authors show how, for the present value under investigation, an approximation in the form of a convex upper...

n an insurance context, one is often interested in the distribution function of a sum of random variables. Such a sum appears when considering the aggregate claims of an insurance portfolio over a certain reference period. It also appears when considering discounted payments related to a single policy or a portfolio at different future points in time. The assumption of mutual independence between the components of the sum is very convenient from a computational point of view, but sometimes not realistic. We will determine approximations for sums of random variables, when the distributions of the terms are known, but the stochastic dependence structure between them is unknown or too cumbersome to work with. In this paper, the theoretical aspects are considered. Applications of this theory are considered in a subsequent paper. Both papers are to a large extent an overview of recent research results obtained by the authors, but also new theoretical and practical results are presented. ispartof: DTEW Research Report 0216 pages:1-50 status: published

In an insurance context, one is often interested in the distribution function of a sum of random variables (rv’s). Such a sum appears when considering the aggregate claims of an insurance portfolio over a certain reference period. It also appears when considering discounted payments related to a single policy or a portfolio, at different future points in time. The assumption of mutual independence between the components of the sum is very convenient from a computational point of view, but sometimes not a realistic one. In The Concept of Comonotonicity in Actuarial Science and Finance: Theory, we determined approximations for sums of rv’s, when the distributions of the components are known, but the stochastic dependence structure between them is unknown or too cumbersome to work with. Practical applications of this theory will be considered in this paper. Both papers are to a large extent an overview of recent research results obtained by the authors, but also new theoretical and practical results are presented.

The distribution of the present value of a series of cash flows under stochastic interest rates has been investigated by many researchers. One of the main problems in this context is the fact that the calculation of exact analytical results for this type of distributions turns out to be rather complicated, and is known only for special cases. An interesting solution to this difficulty consists of determining computable upper bounds, as close as possible to the real distribution.In the present contribution, we want to show how it is possible to compute such bounds for the present value of cash flows when not only the interest rates but also volatilities are stochastic. We derive results for the stop loss premium and distribution of these bounds. ispartof: DTEW Research Report 0218 pages:1-24 status: published

In the individual risk model, the total claims amount on a portfolio of insurance contracts is the random variable of interest. The total claims is modeled as the sum of all claims on the individual policies, which are assumed independent. We present several techniques, such as convolution and recursions, to obtain results in this model. Keywords: aggregate claims; total claims; convolution; transform; approximation; recursion

In this paper we present an efficient methodology for approximating the distribution function of the net present value of a series of cash-flows, when discounting is presented by a stochastic differential equation as in the Vasicek model and in the Ho–Lee model. Upper and lower bounds in convexity order are obtained. The high accuracy of the method is illustrated for cash-flows for which no analytical results are available. Copyright © 2001 John Wiley & Sons, Ltd.

To evaluate the aggregate risk in a financial or insurance portfolio, a risk analyst has to calculate the distribution function of a sum of random variables. As the individual risk factors are often positively dependent, the classical convolution technique will not be sufficient. On the other hand, assuming a comonotonic dependence structure will likely overrate the real aggregate risk. In order to choose between the two approximations, or perhaps use a weighted average, we should have an indication of the accuracy. Clearly this accuracy will depend on the copula between the individual risk factors, but it is also influenced by the marginal distributions. In this paper we introduce a multivariate dependence measure that takes both aspects into account. This new measure differs from other multivariate dependence measures, as it focuses on the aggregate risk rather than on the copula or the joint distribution function itself. We prove several interesting properties of this new measure and discuss its relation to other dependence measures. We also give some comments on the estimation and conclude with examples and numerical results. © 2013 Elsevier B.V. All rights reserved. publisher: Elsevier articletitle: A multivariate dependence measure for aggregating risks journaltitle: Journal of Computational and Applied Mathematics articlelink: http://dx.doi.org/10.1016/j.cam.2013.12.010 content_type: article copyright: Copyright © 2014 Elsevier B.V. All rights reserved. ispartof: Journal of Computational and Applied Mathematics vol:263 pages:78-87 status: published

The Birmingham hip resurfacing (BHR) arthroplasty has shown good medium-term results in the centres that have been involved in its development. A retrospective cohort study analyzing the clinical and functional outcome of 297 metal-on-metal BHR arthroplasties at an independent hospital was performed. At medium-term follow-up, 4 patients had died, 8 patients were lost to follow-up (2.7%), and 6 hips (2.0%) had undergone revision surgery. The mean Harris hip score (HHS) increased from 56.2 preoperatively to 96.4 at follow-up. The BHR resulted in a very high postoperative HHS and enabled active patients to return to work and engage in sports. With an acceptable revision rate of 2.0% and an overall survival rate of 97.1% at five years, our results were similar to those of the designer centers.

We introduce a new and easy to calculate measure for systemic risk in …nancial markets. This measure is baptized the Herd Behavior Index (HIX). It is modelindependent and forward looking, based on observed option data. In order to determine the degree of systemic risk or herd behavior in a …nancial market one should compare the observed market situation with the extreme (theoretical) situation under which the whole system is driven by a single factor. The Herd Behavior Index (HIX) is de…ned as the ratio of an option-based estimate of the risk-neutral variance of the market index and an option-based estimate of the corresponding variance of this extreme market situation. Using the theory of comonotonicity, the extreme situation can easily be backed out of the observed option quotes. The HIX can be determined for any market index provided an appropriate series of vanilla options is traded on this index as well as on its components. As an illustration, we determine historical values of the 30-days implied Herd Behavior Index for the Dow Jones Industrial Average, covering the period January 2003 to October 2009.

FLWIN, info:eu-repo/semantics/published

This paper investigates whether gender identity, or the extent to which an individual identifies with socially constructed sex roles, moderates the influence of sex on typically male and female ad preferences. We distinguish primary from secondary ad stimuli. Universally, men prefer young women and women prefer babies and children (= primary stimuli). On the other hand, cultural changes might affect sex specific preferences of, for example, leisure activities (= secondary stimuli). Results of our first study partly support this duality. However, gender identity did moderate women's preference of primary stimuli. Study 2 revealed that identification may explain this unexpected result.

In the individual risk model, the total claims amount on a portfolio of insurance contracts is the random variable of interest. The total claims is modeled as the sum of all claims on the individual policies, which are assumed independent. We present several techniques, such as convolution and recursions, to obtain results in this model. Keywords: aggregate claims; total claims; convolution; transform; approximation; recursion

In the recent actuarial literature, several proofs have been given for the fact that if a random vector (X1X2, …, Xn) with given marginals has a comonotonic joint distribution, the sum X1 + X2 + … + Xn is the largest possible in convex order. In this note we give a lucid proof of this fact, based on a geometric interpretation of the support of the comonotonic distribution.

In their seminal paper, Gerber and Shiu (1994) introduced the concept of the Esscher transform for option pricing. As examples they considered the shifted Poisson process, the random walk, a shifted gamma process, and a shifted inverse Gaussian process to describe the logarithm of the stock price. In the present article it is shown how upper and lower bounds in convex order can be obtained when we use these types of models to describe the stochastic accumulation factors for a given cash flow.

International audience; Estimating high level quantiles of aggregated variables (mainly sums or weighted sums) is crucial in risk management for many application fields such as finance, insurance, environment. . . . This question has been widely treated but new efficient methods are always welcome; especially if they apply in relatively) high dimension. We propose an estimation procedure based on the checkerboard copula. It allows to get good estimations from a quite) small sample of the multivariate law and a full knowledge of the marginal laws. This situation is realistic for many applications, mainly in insurance. Moreover, we may also improve the estimations by including in the checkerboard copula some additional information (on the lawof a sub-vector or on extreme probabilities).