NDLI: Capturing parameter risk with convex risk measures

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Approximations for quantiles of life expectancy and annuity values using the parametric improvement rate approach to modelling and projecting mortality

Return distributions of equity-linked retirement plans under jump and interest rate risk

A Joint Stock and Bond Market based on the Hyperbolic Gaussian Model

The finite-time ruin probability under the compound binomial risk model

On the analysis of a class of loss models incorporating time dependence

European Actuarial Journal : Volume 2

European Actuarial Journal : Volume 1

Capturing parameter risk with convex risk measures

Content Provider	Springer Nature Link
Author	Bannör, Karl F. Scherer, Matthias
Copyright Year	2013
Abstract	Adequately specifying the parameters of a financial or actuarial model is challenging. In case of historical estimation, uncertainty arises through the estimator’s volatility and possible bias. In case of market implied parameters, the solution of a calibration to market data might not be unique or the numerical routine returns a local instead of a global minimum. This paper provides a new method based on convex risk measures to quantify parameter risk and to translate it into prices, extending results in Cont (Math Finance 16(3):519–547, 2006) and Lindström (Adv Decision Sci, 2010). We introduce the notion of risk-capturing functionals and prices, provided a distribution on the parameter (or model) set is available, and present explicit examples where the Average-Value-at-Risk and the entropic risk measure are used. For some classes of risk-capturing functionals, the risk-captured price preserves weak convergence of the distributions. In particular, the risk-captured price generated by the distributions of a consistent sequence of estimators converges to the true price. For asymptotically normally distributed estimators we provide large sample approximations for risk-captured prices. Following Bion-Nadal (J Math Econ 45(11):738–750, 2009); Carr et al. (J Financ Econ 62:131–167, 2001); Cherny and Madan (Int J Theor Appl Finance 13(8):1149–1177, 2010); Xu (Ann Finance 2:51–71, 2006), we interpret the risk-captured price as an ask price, reflecting aversion towards parameter risk. To acknowledge parameter risk in case of calibration to market prices, we create a parameter distribution from the pricing error function, allowing us to compare the intrinsic parameter risk of the stochastic volatility models of Heston and Barndorff-Nielsen and Shephard as well as the Variance Gamma option pricing model by pricing different exotics.
Starting Page	97
Ending Page	132
Page Count	36
File Format	PDF
ISSN	21909733
Journal	European Actuarial Journal
Volume Number	3
Issue Number	1
e-ISSN	21909741
Language	English
Publisher	Springer-Verlag
Publisher Date	2013-05-08
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Parameter risk Convex risk measure Risk-capturing functional Risk-captured price Bid-ask spread Calibration risk Quantitative Finance Finance/Investment/Banking Applications of Mathematics Game Theory, Economics, Social and Behav. Sciences
Content Type	Text
Resource Type	Article
Subject	Statistics and Probability Economics and Econometrics Statistics, Probability and Uncertainty

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