A Quantile‐Fitting Approach to Value at Risk for Options

Abstract

The curvilinear shape of a bond price‐yield curve implies that risk management based on a linear approximation using duration is only viable for very small changes in interest rates. Not accounting for convexity when there are large yield changes can result in critical errors in measuring or hedging interest rate risk. The linear approximations will under‐or overestimate the value at risk (VaR) for non‐linear financial instruments. Nonlinearity can be particularly problematic if there are large changes in market risk factors. The large changes are more likely to occur when VaR is computed for high confidence levels and/or longer time horizons. Even if the movements in risk factors are small, estimation errors in VaR would get larger as the degree of non‐linearity in financial instruments increases.

Citation

NAM, D. and GUP, B.E. (2003), "A Quantile‐Fitting Approach to Value at Risk for Options", Journal of Risk Finance, Vol. 5 No. 1, pp. 40-50. https://doi.org/10.1108/eb022978