Time consistency of multi-period distortion measures

Fasen, Vicky; Svejda, Adela

doi:10.1524/strm.2012.1115

Cited by 7 publications

(6 citation statements)

References 29 publications

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“…A similar result was obtained by Fasen and Svejda (2010) for Choquet risk measures in a finite setting. For a comprehensive discussion of Choquet risk measures we refer to Carlier and Dana (2003) and Tsanakas (2004).…”

Section: The New Risk Measure Does Not Present the Rejection Inconsissupporting

confidence: 84%

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Characterization and Construction of Sequentially Consistent Risk Measures

Bignozzi

Tsanakas

2012

SSRN Journal

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In dynamic risk measurement the problem emerges of assessing the risk of a financial position at different times. Sufficient conditions are provided for conditional coherent risk measures, in order that the requirements of acceptance-, rejection-and sequential consistency are satisfied. It is shown that these conditions are often violated for standard methods of updating. A method is consequently proposed for constructing a sequentially consistent risk measure, which entails the modification of the set of probability measures used to obtain the risk assessment at an initial time. This is demonstrated for the coherent entropic risk measure and for the class of Choquet risk measures, which generalizes the well-known TVaR. Finally we consider the situation where the term of risk exposures is longer than the time horizon used in solvency assessment. Then, regulation such as Solvency II requires replacing the financial position itself with its fair value at the time horizon. We show that in this setting acceptance consistency can be preserved, though the same is not true about rejection consistency.

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Section: The New Risk Measure Does Not Present the Rejection Inconsissupporting

confidence: 84%

“…When Ω is finite, the set Q ′ is a polytope and P satisfies condition (14), so, using Fasen and Svejda (2010) to construct a sequentially consistent version of distortion risk measures in a finite framework.…”

Section: Remark 3 Conditional Risk Measures With the Additional Propmentioning

confidence: 99%

Characterization and Construction of Sequentially Consistent Risk Measures

Bignozzi

Tsanakas

2012

SSRN Journal

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“…To price American options with early execution characteristics, a multinomial, dynamic concave distortion measure must be used. Taking into account the temporal consistency of prices, the multiperiod dynamic uniform concave distortion measure given by Fasen and Svejda [4] is used to obtain the price of American options.…”

Section: Distort Expectations Pricing and Discretizationmentioning

confidence: 99%

“…Dilip Madan and Wim Schoutens [3] solved the parameter correction problem of distortion risk measures by using the bid-ask transaction history data in the options market. Fasen and Svejda [4] gave a dynamic consistency version to ensure that acceptability decisions are consistent over time. One of the static risk measures is the so-called distortion measure.…”

Section: Introductionmentioning

confidence: 99%

Pricing American Options by a Fourier Transform Multinomial Tree in a Conic Market

Wang

2022

Discrete Dynamics in Nature and Society

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Based on FFT, a high-order multinomial tree is constructed, and the method to obtain the price of American style options in the Lévy conic market is studied. Firstly, the nature of the Lévy process and the pricing principle of European-style options are introduced. Secondly, the method to construct a high-order multinomial tree based on Fourier transform is presented. It can be proved by theoretical derivation that the multinomial tree can converge to the Lévy process. Thirdly, we introduce the conic market theory based on the concave distortion function and give the discretization method of the concave distortion expectation. Then, the American option pricing method based on reverse iteration is given. Finally, the CGMY process is used to demonstrate how to price the American put option in the Lévy conic market. We can draw conclusions that the Fourier transform multinomial tree can avoid the difficulty of parameter estimation when using traditional moment matching methods to construct multinomial trees. Because the Lévy process has the analytic form characteristic function, this method is a promising method to calculate the prices of options in the Lévy conic market.

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“…Exemplos envolvendo distribuições invariantes a localização, escala e formato são apresentadas para ilustrar a abordagem. Fasen & Svejda (2012) estendem o conceito de medidas de risco de distorção para o campo dinâmico. Para tanto, os autores utilizam os conceitos de Roorda & Schumacher (2007) para definições de Consistência Sequencial, Condicional e Dinâmica para medidas de risco de distorção dinâmicas, as utilizando em resultados que ligam axiomas e representação dual.…”

Section: Medidas De Risco De Distorçãounclassified

Teoria de Medidas de Risco: uma revisão abrangente

Righi

Ceretta

2014

Braz. Rev. Fin.

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A fundamental aspect of proper risk management is the measurement, especially forecasting of risk measures. Measures such as variance, volatility and Value at Risk had been considered valid because of their practical intuition. However, a solid theoretical framework it is important to ensure better properties for risk measures. Such background is the risk measures theory. This paper presents a comprehensive literature review on risk measures theory, focusing in basic theory and extensions to this fundamental outline. The paper is structured in order to cover the main risk measures classes from literature, which are coherent risk measures, convex risk measures, spectral and distortion risk measures and generalized deviation measures.

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Time consistency of multi-period distortion measures

Cited by 7 publications

References 29 publications

Characterization and Construction of Sequentially Consistent Risk Measures

Characterization and Construction of Sequentially Consistent Risk Measures

Pricing American Options by a Fourier Transform Multinomial Tree in a Conic Market

Teoria de Medidas de Risco: uma revisão abrangente

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