Asia-Pacific Financial Markets

, Volume 11, Issue 2, pp 161-184

First online:

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

  • Tak Kuen SiuAffiliated withDepartment of Actuarial Mathematics and Statistics, Heriot-Watt University Email author 
  • , Howell TongAffiliated withDepartment of Statistics, London School of Economics
  • , Hailiang YangAffiliated withDepartment of Statistics and Actuarial Science, The University of Hong Kong

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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