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Moment based approaches to value the risk of contingent claim portfolios

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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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References

  • 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.

    Article  Google Scholar 

  • 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.

    Chapter  Google Scholar 

  • Crowder, M. (1986). On consistency and inconsistency of estimating equations. Econometric Theory, 2, 305–330.

    Google Scholar 

  • Duffie, D., & Pan, J. (1997). An overview of value at risk. Journal of Derivatives, 4, 7–49.

    Google Scholar 

  • Durbin, J. (1960). Estimation of parameters in time series regression models. Journal of the Royal Statistical Society Series B, 22, 139–153.

    Google Scholar 

  • Fama, E. (1965). The behavior of stock market prices. Journal of Business, 38, 34, 105.

    Google Scholar 

  • Godambe, V. P. (1960). An optimum property of regular maximum likelihood estimation. The Annals of Mathematical Statistics, 31, 1208–1212.

    Article  Google Scholar 

  • Godambe, V. P. (1976). Conditional likelihood and unconditional optimum estimating equations. Biometrika, 63, 277–284.

    Article  Google Scholar 

  • Godambe, V. P. (1985). The foundation of finite sample estimation in stochastic processes. Biometrika, 72, 419–428.

    Article  Google Scholar 

  • Godambe, V. P. (1991). Estimating functions. London: Oxford University Press.

    Google Scholar 

  • Godambe, V. P., & Heyde, C. C. (1987). Quasi-likelihood and optimal estimation. International Statistical Review, 55, 231–244.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • Godambe, V. P., & Thompson, M. (1984). Robust estimation through estimating equation. Biometrika, 71, 115–125.

    Article  Google Scholar 

  • Godambe, V. P., & Thompson, M. (1989). An extension of quasi-likelihood estimation (with discussion). Journal of Statistical Planning and Inference, 22, 137–172.

    Article  Google Scholar 

  • Heyde, C. C. (1997). Quasi-likelihood and its applications. New York: Springer.

    Google Scholar 

  • Hutton, J. E., & Nelson, P. I. (1986). Quasi-likelihood estimation for semi-martingale. Stochastic Processes and Their Applications, 22, 245–257.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • Kupiec, P. (1995). Techniques for verifying the accuracy of risk measurement models. Journal of Derivatives, 3, 73–84.

    Article  Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Google Scholar 

  • 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.

    Article  Google Scholar 

  • Longerstaey, J., & Zangari, P. (1996). RiskMetrics-technical document (4th ed.). New York: J.P. Morgan.

    Google Scholar 

  • Mandelbrot, B. (1963a). New methods in statistical economics. Journal of Political Economy, 71, 421–440.

    Article  Google Scholar 

  • Mandelbrot, B. (1963b). The variation of certain speculative prices. Journal of Business, 26, 394–419.

    Google Scholar 

  • Rachev, S., & Mittnik, S. (2000). Stable paretian models in finance. New York: Wiley.

    Google Scholar 

  • Wedderburn, R. W. M. (1974). Quasi-likelihood functions, generalized linear models and Gauss-Newton method. Biometrika, 61, 439–447.

    Google Scholar 

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Correspondence to Sergio Ortobelli.

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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

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