Abstract
In this paper we describe and apply the estimating function methodology to value the risk of asset derivative portfolios. We first implement the Li’s model based on the first four moments and then we show the limits of this model in forecasting the maximum loss of contingent claims. In addition, we show that four moments are not enough to describe the behavior of the lower percentiles of derivatives. Finally, we propose a model that considers the first six moments and we compare the performances of these models proposing a backtest analysis on several historical and truncated asset derivative portfolios.
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Chen, Y. (1993). Asymptotic theory of optimal estimating functions (Technical Report Series STAT-93-01). University of Waterloo.
Christoffersen, P. (1998). Evaluating interval forecasts. International Economic Review, 39, 841–862.
Consiglio, A., Massabò, I., & Ortobelli, S. (2003). Non-Gaussian distribution for VaR calculation: an assessment for the Italian market. In R. Neck (Ed.), Modeling and control of economic system 2001 (pp. 213–218). New York: Elsevier.
Crowder, M. (1986). On consistency and inconsistency of estimating equations. Econometric Theory, 2, 305–330.
Duffie, D., & Pan, J. (1997). An overview of value at risk. Journal of Derivatives, 4, 7–49.
Durbin, J. (1960). Estimation of parameters in time series regression models. Journal of the Royal Statistical Society Series B, 22, 139–153.
Fama, E. (1965). The behavior of stock market prices. Journal of Business, 38, 34, 105.
Godambe, V. P. (1960). An optimum property of regular maximum likelihood estimation. The Annals of Mathematical Statistics, 31, 1208–1212.
Godambe, V. P. (1976). Conditional likelihood and unconditional optimum estimating equations. Biometrika, 63, 277–284.
Godambe, V. P. (1985). The foundation of finite sample estimation in stochastic processes. Biometrika, 72, 419–428.
Godambe, V. P. (1991). Estimating functions. London: Oxford University Press.
Godambe, V. P., & Heyde, C. C. (1987). Quasi-likelihood and optimal estimation. International Statistical Review, 55, 231–244.
Godambe, V. P., & Kale, B. K. (1991). Estimating functions: an overview. In V. P. Godambe (Ed.), Estimating functions (pp. 3–20). London: Oxford University Press.
Godambe, V. P., & Thompson, M. (1984). Robust estimation through estimating equation. Biometrika, 71, 115–125.
Godambe, V. P., & Thompson, M. (1989). An extension of quasi-likelihood estimation (with discussion). Journal of Statistical Planning and Inference, 22, 137–172.
Heyde, C. C. (1997). Quasi-likelihood and its applications. New York: Springer.
Hutton, J. E., & Nelson, P. I. (1986). Quasi-likelihood estimation for semi-martingale. Stochastic Processes and Their Applications, 22, 245–257.
Iaquinta, G., Lamantia, F., Massabò, I., & Ortobelli, S. (2003). A semi-parametric approach to value the risk of asset derivative portfolios (Technical Report 15). University of Bergamo.
Kale, B. K. (1962). An extension of the Cramer-Rao inequality for statistical estimating functions. Scandinavian Actuarial Journal, 45, 60–89.
Kupiec, P. (1995). Techniques for verifying the accuracy of risk measurement models. Journal of Derivatives, 3, 73–84.
Lamantia, F., Ortobelli, S., & Rachev, S. T. (2006a). VaR, CVaR and time rules with elliptical and asymmetric stable distributed returns. Investment Management and Financial Innovations, 4, 19–39.
Lamantia, F., Ortobelli, S., & Rachev, S. T. (2006b). An empirical comparison among VaR models and time rules with elliptical and stable distributed returns. Investment Management and Financial Innovations, 3, 8–29.
Li, D. X. (1999). Value at risk based on the volatility, skewness and kurtosis (Working Paper). RiskMetrics Group.
Li, D. X., & Turtle, H. J. (2000). Semiparametric ARCH models: An estimating function approach. Journal of Business & Economic Statistics, 18, 174–186.
Longerstaey, J., & Zangari, P. (1996). RiskMetrics-technical document (4th ed.). New York: J.P. Morgan.
Mandelbrot, B. (1963a). New methods in statistical economics. Journal of Political Economy, 71, 421–440.
Mandelbrot, B. (1963b). The variation of certain speculative prices. Journal of Business, 26, 394–419.
Rachev, S., & Mittnik, S. (2000). Stable paretian models in finance. New York: Wiley.
Wedderburn, R. W. M. (1974). Quasi-likelihood functions, generalized linear models and Gauss-Newton method. Biometrika, 61, 439–447.
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Iaquinta, G., Lamantia, F., Massabò, I. et al. Moment based approaches to value the risk of contingent claim portfolios. Ann Oper Res 165, 97–121 (2009). https://doi.org/10.1007/s10479-007-0306-x
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DOI: https://doi.org/10.1007/s10479-007-0306-x