A moment matching market implied calibration

作者：Guillaume Florence^*; Schoutens Wim

来源：Quantitative Finance, 2013, 13(9): 1359-1373.

DOI：10.1080/14697688.2013.794950

• Model calibration
• Financial engineering
• Levy process
• Options applications

This paper provides a new market implied calibration based on a moment matching methodology where the moments of the risk-neutral density function are inferred from at-the-money and out-the-money European vanilla option quotes. In particular, we derive a model-independent risk-neutral formula for the moments of the asset log-return distribution function by expanding power returns as a weighted sum of vanilla option payoffs (based on results of Breeden and Litzenberger and Carr and Madan). For the numerical study, we develop different popular exponential Levy models, namely the VG, NIG and Meixner models. The new calibration methodology rests on closed-form formulae only: it is shown that the moment matching system can be transformed into a system of algebraic equations that computes directly the optimal value of the market standardized moments under the different Levy models under investigation. Hence, the proposed calibration can be performed almost instantaneously. Furthermore, for the models considered in this paper, the method does not require any search algorithm and hence any starting value for the model parameters and avoids the problem of becoming stuck in local minima.

• 出版日期2013-9-1