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

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.