Third-Order Moment Closure Through A Mass-Flux Approach

Purpose This paper aims to test three parametric models in pricing and hedging higher-order moment swaps. Using vanilla option prices from the volatility surface of the Euro Stoxx 50 Index, the paper shows that the pricing accuracy of these models is very satisfactory under four different pricing error functions. The result is that taking a position in a third moment swap considerably improves the performance of the standard hedge of a variance swap based on a static position in the log-contract and a dynamic trading strategy. The position in the third moment swap is taken by running a Monte Carlo simulation. Design/methodology/approach This paper undertook empirical tests of three parametric models. The aim of the paper is twofold: assess the pricing accuracy of these models and show how the classical hedge of the variance swap in terms of a position in a log-contract and a dynamic trading strategy can be significantly enhanced by using third-order moment swaps. The pricing accuracy was measured under four different pricing error functions. A Monte Carlo simulation was run to take a position in the third moment swap. Findings The results of the paper are twofold: the pricing accuracy of the Heston (1993) model and that of two Levy models with stochastic time and stochastic volatility are satisfactory; taking a position in third-order moment swaps can significantly improve the performance of the standard hedge of a variance swap. Research limitations/implications The limitation is that these empirical tests are conducted on existing three parametric models. Maybe more critical insights could have been revealed had these tests been conducted in a brand new derivatives pricing model. Originality/value This work is 100 per cent original, and it undertook empirical tests of the pricing and hedging accuracy of existing three parametric models.

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Analogy between predictions of Kolmogorov and Yaglom

Journal of Fluid Mechanics ◽

10.1017/s0022112096004090 ◽

1997 ◽

Vol 332 ◽

pp. 395-409 ◽

Cited By ~ 83

Author(s):

R. A. Antonia ◽

M. Ould-Rouis ◽

F. Anselmet ◽

Y. Zhu

Keyword(s):

Reynolds Number ◽

Prandtl Number ◽

Longitudinal Velocity ◽

Turbulent Wake ◽

Mean Value ◽

Order Moment ◽

Third Order ◽

The Third ◽

Velocity Increments ◽

The Mean

The relation, first written by Kolmogorov, between the third-order moment of the longitudinal velocity increment δu1 and the second-order moment of δu1 is presented in a slightly more general form relating the mean value of the product δu1(δui)2, where (δui)2 is the sum of the square of the three velocity increments, to the secondorder moment of δui. In this form, the relation is similar to that derived by Yaglom for the mean value of the product δu1(δuθ)2 where (δuθ)2 is the square of the temperature increment. Both equations reduce to a ‘four-thirds’ relation for inertialrange separations and differ only through the appearance of the molecular Prandtl number for very small separations. These results are confirmed by experiments in a turbulent wake, albeit at relatively small values of the turbulence Reynolds number.

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