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Asia-Pacific Financial Markets

, Volume 11, Issue 2, pp 161–184 | Cite as

On Bayesian Value at Risk: From Linear to Non-Linear Portfolios

  • Tak Kuen Siu
  • Howell Tong
  • Hailiang Yang
Article

Abstract

This paper proposes the use of Bayesian approach to implement Value at Risk (VaR) model for both linear and non-linear portfolios. The Bayesian approach provides risk traders with the flexibility of adjusting their VaR models according to their subjective views. First, we deal with the case of linear portfolios. By imposing the conjugate-prior assumptions, a closed-form expression for the Bayesian VaR is obtained. The Bayesian VaR model can also be adjusted in order to deal with the ageing effect of the past data. By adopting Gerber-Shiu's option-pricing model, our Bayesian VaR model can also be applied to deal with non-linear portfolios of derivatives. We obtain an exact formula for the Bayesian VaR in the case of a single European call option. We adopt the method of back-testing to compare the non-adjusted and adjusted Bayesian VaR models with their corresponding classical counterparts in both linear and non-linear cases.

Key words

subjective VaR Bayesian method Gerber-Shiu's model leptokurtic effect non-linear portfolios model risk 

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Copyright information

© Springer Science+Business Media, Inc. 2006

Authors and Affiliations

  1. 1.Department of Actuarial Mathematics and StatisticsHeriot-Watt UniversityEdinburghUnited Kingdom
  2. 2.Department of StatisticsLondon School of EconomicsLondonUK
  3. 3.Department of Statistics and Actuarial ScienceThe University of Hong KongHong KongChina

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