Abstract
The Risk Metrics technical document proposes a methodology for Value-at-Risk analysis based on the idea of linearization of the portfolio pricing function leading to a Normal approximation of the profit and loss distribution. In this note we consider the density of the distribution of the change in value of a zero coupon bond. We describe all possible shapes of the density function assuming that log-returns of the risk factor have a normal distribution. In particular, we demonstrate that this density is defined on a finite interval. It has an infinite limit at the right end of this interval. Risk Metrics assumptions are used during our consideration. This theoretical effect becomes detectable if the volatility parameter takes large values.
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© 2001 Springer Science+Business Media Dordrecht
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Kreinin, A. (2001). Non-Linear Risk of Linear Instruments. In: Uryasev, S., Pardalos, P.M. (eds) Stochastic Optimization: Algorithms and Applications. Applied Optimization, vol 54. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-6594-6_9
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DOI: https://doi.org/10.1007/978-1-4757-6594-6_9
Publisher Name: Springer, Boston, MA
Print ISBN: 978-1-4419-4855-7
Online ISBN: 978-1-4757-6594-6
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