Distribution-free option pricing

Schepper, Ann De; Heijnen, B.

doi:10.1016/j.insmatheco.2006.04.002

Cited by 18 publications

(14 citation statements)

References 28 publications

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“…In fact, this upper bound is tight under mean and variance information (see De Schepper and Heijnen [34]). …”

Section: Mean-variance (Mv) Modelmentioning

confidence: 94%

“…However, these models do not include information about the asymmetry of the distribution. Recent literature attempts to address this by assuming knowledge of higher moments, such as skewness or kurtosis (Jansen et al [23]; De Schepper and Heijnen [34]; He et al [21]; Zuluaga et al [38]). Since the higher moments result in a problem with third and fourth order constraints, it is usually not easy to find a closed-form expression for the optimal bounds.…”

Section: Introductionmentioning

confidence: 99%

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Asymmetry and Ambiguity in Newsvendor Models

2018

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The traditional decision-making framework for newsvendor models is to assume a distribution of the underlying demand. However, the resulting optimal policy is typically sensitive to the choice of the distribution. A more conservative approach is to assume that the distribution belongs to a set parameterized by a few known moments. An ambiguity-averse newsvendor would choose to maximize the worst-case profit. Most models of this type assume that only the mean and the variance are known, but do not attempt to include asymmetry properties of the distribution. Other recent models address asymmetry by including skewness and kurtosis. However, closed-form expressions on the optimal bounds are difficult to find for such models. In this paper, we propose a framework under which the expectation of a piecewise linear objective function is optimized over a set of distributions with known asymmetry properties. This asymmetry is represented by the first two moments of multiple random variables that result from partitioning the original distribution. In the simplest case, this reduces to semivariance. The optimal bounds can be solved through a second-order cone programming (SOCP) problem. This framework can be applied to the risk-averse and risk-neutral newsvendor problems and option pricing. We provide a closed-form expression for the worst-case newsvendor profit with only mean, variance and semivariance information.

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“…In fact, this upper bound is tight under mean and variance information (see De Schepper and Heijnen [34]). …”

Section: Mean-variance (Mv) Modelmentioning

confidence: 94%

Section: Introductionmentioning

confidence: 99%

Asymmetry and Ambiguity in Newsvendor Models

2018

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“…This setting is related to, but different from, the setting that is assumed in the literature on the so‐called moment bounds for VaR (as well as related risk characteristics such as survival probabilities and stop‐loss premiums). In this stream of the literature, the bounds are derived under the assumption that some of the moments of the portfolio sum are known; see Kaas and Goovaerts (, ), Hürlimann , and De Schepper and Heijnen for treatments in the context of actuarial science, and Grundy , De Schepper and Heijnen , and Lo for related results in finance. The main difference between our approach and that of these articles is thus that we assume that the marginal distributions as primary source of portfolio information are available, whereas this information is not used in the literature on moment bounds.…”

Section: Introductionmentioning

confidence: 99%

Value‐at‐Risk Bounds With Variance Constraints

Bernard¹,

Rüschendorf²,

Vanduffel³

2015

J of Risk & Insurance

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We study bounds on the Value-at-Risk (VaR) of a portfolio when besides the marginal distributions of the components its variance is also known, a situation that is of considerable interest in risk management. We discuss when the bounds are sharp (attainable) and also point out a new connection between the study of VaR bounds and the convex ordering of aggregate risk. This connection leads to the construction of an algorithm, called Extended Rearrangement Algorithm (ERA), that makes it possible to approximate sharp VaR bounds. We test the stability and the quality of the algorithm in several numerical examples. We apply the results to the case of credit risk portfolio models and verify that adding the variance constraint gives rise to significantly tighter bounds in all situations of interest. IntroductionIn this article, we study bounds on the Value-at-Risk (VaR) of sums of risks with known marginal distributions (describing the stand-alone risks) under the additional constraint that a bound on the variance of the sum is known. The variance of the sum partially describes the dependence among the risks, as it involves their correlations. This setting is of significant interest as in many practical situations it corresponds closely to the maximum information at hand when assessing the VaR of a portfolio. For example, in the context of credit risk portfolio models, one typically has knowledge regarding the marginal risks (through the so-called PD, EAD, and LGD models), and the variance of the aggregate risk (sum of the individual losses) is also often available, as obtained from default correlation models or through statistical analysis of observed

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“…This has been pointed out by several authors in actuarial and financial research, see e.g. Schepper and Heijnen (2007), Gerber and Smith (2008), De Schepper and Heijnen (2010), Wong and Zhang (2013), and references therein.…”

Section: Introductionmentioning

confidence: 69%

Optimal retention for a stop-loss reinsurance with incomplete information

Yang

Zhang

2015

Insurance: Mathematics and Economics

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This paper considers the determination of optimal retention in a stop-loss reinsurance. Assume that we only have incomplete information on a risk X for an insurer, we calculate an upper bound for the value at risk (VaR) of the total loss of an insurer after stop-loss reinsurance arrangement. The adopted method is a distribution-free approximation which allows to construct the extremal random variables with respect to the stochastic dominance order and the stop-loss order. We develop an optimization criterion for deriving the optimal retention such that the obtained upper bound of the VaR attains the minimum. We formally establish the sufficient and necessary conditions for the existence of the nontrivial optimal stop-loss reinsurance. For illustration purpose, some numerical examples are included and compared with the results yielded in Theorem 2.1 of Cai and Tan (2007).

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Distribution-free option pricing

Cited by 18 publications

References 28 publications

Asymmetry and Ambiguity in Newsvendor Models

Asymmetry and Ambiguity in Newsvendor Models

Value‐at‐Risk Bounds With Variance Constraints

Optimal retention for a stop-loss reinsurance with incomplete information

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