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Lee, Y. S. and Lin, T. K. (1992). Higher-order Cornish Fisher expansion, Applied Statistics 41: 233–240. Lee, Y. S. and Lin, T. K. (1993). Correction to algorithm AS269 : Higher-order Cornish Fisher expansion, Applied Statistics 42: 268–269. Li, D. (1999). pdf. RiskMetrics Group. Longerstaey, J. (1996). Morgan. com. McKay, M. , Beckman, R. J. and Conover, W. J. (1979). A comparison of three methods for selecting values of input variables in the analysis of output from a computer code, Technometrics 21(2): 239–245.

Math. ps. Engle, R. (2000). edu/~mbacci/engle/. Fallon, W. (1996). wharton. pdf. Wharton Financial Institutions Center Working Paper 96-49. , Heidelberger, P. and Shahabuddin, P. (2000). pdf. IBM Research Paper RC21723. Hill, G. W. and Davis, A. W. (1968). Generalized asymptotic expansions of Cornish-Fisher type, Ann. Math. Statist. 39: 1264–1273. Jaschke, S. (2001). pdf. Discussion Paper 54, Sonderforschungsbereich 373, HumboldtUniversit¨at zu Berlin. 5 Variance Reduction Techniques in Monte-Carlo Simulation 33 Jorion, P.

33) (for |t| → ∞). 35) i=1 def x∗ = θ − 1 2 m i=1 δi2 . 36) x∗ is the location and w∗ the “weight” of the singularity. The multivariate delta-gamma-distribution is C ∞ except at x∗ , where the highest continuous derivative of the cdf is of order [(m − 1)/2]. 1. ; µ, σ) is the normal cdf with mean µ and standard deviation 2 2 σ and eiµt−σ t /2 its characteristic function. t. ) Applying the Fourier inversion to F (x) − Φ(x; µ, σ) instead of F (x) solves the (numerical) problem that ti φ(t) has a pole at 0.

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