Value at Risk For Derivatives

Asia-Pacific Finan Markets

Tong

Yang

2004

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. Copyright Springer Science+Business Media, Inc. 2004subjective VaR, Bayesian method, Gerber-Shiu's model, leptokurtic effect, non-linear portfolios, model risk,

Section: Bayesian Var For Non-linear Portfoliosmentioning

confidence: 99%

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

Asia-Pacific Finan Markets

Tong

Yang

2004

“…Another shortcoming of VaR is that it may lead to some bizarre and suboptimal decisions if it is used as a binding constraint in portfolio selection (see [2]). VaR has been considered by both academia and practitioners as a measure for derivative risks, see, for example, Morgans Risk Metrics-Technical document [3,4]. However, due to the nonlinearity of derivative risks, the loss distribution of a derivative position may not be elliptical, and it is reasonable to question if VaR is appropriate as a measure for derivative risks.…”

Section: Introductionmentioning

confidence: 98%

A BSDE Approach to Convex Risk Measures for Derivative Securities

Elliott

Stochastic Analysis and Applications

2012

A backward stochastic differential equation (BSDE) approach is used to evaluate convex risk measures for unhedged positions of derivative securities in a continuoustime economy. The convex risk measure is represented as the solution of a BSDE. We use the Clark-Ocone representation result together with Malliavin calculus to identify the integrand in the martingale representation associated with the BSDE. In the Markov case, we relate the BSDE solution to a partial differential equation solution for convex risk measure evaluation.

“…Since the introduction of VaR, much effort has been placed on investigating VaR for derivatives. See, for example, J. P. Morgan (1996), Duffie andPan (1997), andEl-Jahel, Perraudin, andSellin (1999).…”

Section: Introductionmentioning

confidence: 98%

Bayesian Risk Measures for Derivatives via Random Esscher Transform

North American Actuarial Journal

Tong

Yang

2001

This paper proposes a model for measuring risks for derivatives that is easy to implement and satisfies a set of four coherent properties introduced in Artzner et al. (1999). We construct our model within the context of Gerber-Shiu's option-pricing framework. A new concept, namely Bayesian Esscher scenarios, which extends the concept of generalized scenarios, is introduced via a random Esscher transform. Our risk measure involves the use of the risk-neutral Bayesian Esscher scenario for pricing and a family of real-world Bayesian Esscher scenarios for risk measurement. Closed-form expressions for our risk measure can be obtained in some special cases.