The Variance Gamma Scaled Self-Decomposable Process in Actuarial Modelling

Conall O'Sullivan and Michael Moloney
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Conall O'Sullivan: University College Dublin
Michael Moloney: Mercer IC

No 201030, Working Papers from Geary Institute, University College Dublin

Abstract: A scaled self-decomposable stochastic process put forward by Carr, Geman, Madan and Yor (2007) is used to model long term equity returns and options prices. This parsimonious model is compared to a number of other one-dimensional continuous time stochastic processes (models) that are commonly used in finance and the actuarial sciences. The comparisons are conducted along three dimensions: the models ability to fit monthly time series data on a number of different equity indices; the models ability to fit the tails of the times series and the models ability to calibrate to index option prices across strike price and maturities. The last criteria is becoming increasingly important given the popularity of capital gauranteed products that contain long term imbedded options that can be (at least partially) hedged by purchasing short term index options and rolling them over or purchasing longer term index options. Thus we test if the models can reproduce a typical implied volatility surface seen in the market.

Keywords: Variance gamma; regime switching lognormal; long term equity returns. (search for similar items in EconPapers)
JEL-codes: G13 G23 (search for similar items in EconPapers)
Pages: 31 pages
Date: 2010-06-29
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (3)

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