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The Variance Gamma Scaled Self-Decomposable Process in Actuarial Modelling

Author

Listed:
  • Conall O'Sullivan

    (University College Dublin)

  • Michael Moloney

    (Mercer IC)

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.

Suggested Citation

  • Conall O'Sullivan & Michael Moloney, 2010. "The Variance Gamma Scaled Self-Decomposable Process in Actuarial Modelling," Working Papers 201030, Geary Institute, University College Dublin.
    • Handle: RePEc:ucd:wpaper:201030
    as

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    File URL: http://www.ucd.ie/geary/static/publications/workingpapers/gearywp201030.pdf
    File Function: First version, 2010
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    References listed on IDEAS

    as
    1. X. Guo, 2001. "Information and option pricings," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 38-44.
    Full references (including those not matched with items on IDEAS)

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    Cited by:

    1. Mosiño, Alejandro & Salomón-Núñez, Laura A. & Moreno-Okuno, Alejandro T., 2017. "Estudio empírico sobre el tipo de cambio MXN/USD: Movimiento Browniano Geométrico vs. Proceso Varianza-Gamma [Empirical analysis of the MXN/USD exchange rate: geometric Brownian motion vs. variance," MPRA Paper 78961, University Library of Munich, Germany.
    2. Forsyth, Peter & Vetzal, Kenneth, 2014. "An optimal stochastic control framework for determining the cost of hedging of variable annuities," Journal of Economic Dynamics and Control, Elsevier, vol. 44(C), pages 29-53.
    3. Alejandro Mosiño & Alejandro Tatsuo Moreno-Okuno, 2018. "On modeling fossil fuel prices: geometric Brownian motion vs. variance-gamma process," Economics Bulletin, AccessEcon, vol. 38(1), pages 509-519.

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    More about this item

    Keywords

    Variance gamma; regime switching lognormal; long term equity returns.;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G23 - Financial Economics - - Financial Institutions and Services - - - Non-bank Financial Institutions; Financial Instruments; Institutional Investors

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