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Worst-Of Options And Correlation Skew Under A Stochastic Correlation Framework

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  • JACINTO MARABEL ROMO

    (BBVA, Vía de los Poblados s/n, 28033, Madrid, Spain;
    University Institute for Economic and Social Analysis, University of Alcalá, Plaza de la Victoria 2, 28802, Alcalá de Henares, Spain)

Abstract

This article considers a multi-asset model based on Wishart processes that accounts for stochastic volatility and for stochastic correlations between the underlying assets, as well as between their volatilities. The model accounts for the existence of correlation term structure and correlation skew. The article shows that the Wishart specification can generate different patterns corresponding to the correlation skew for a wide range of correlation term structures.Another advantage of the model is that it is analytically tractable and, hence, it is possible to obtain semi-closed-form solutions for the prices of plain vanilla options, as well as for the price of exotic derivatives. In this sense, this article develops semi-closed-form formulas for the price of European worst-of options with barriers and/or forward-start features. To motivate the introduction of the Wishart volatility model, the article compares the prices obtained under this model and under a multi-asset stochastic volatility model with constant instantaneous correlations. The results reveal the existence of a stochastic correlation premium and show that the consideration of stochastic correlation is a key element for the valuation of these structures.

Suggested Citation

  • Jacinto Marabel Romo, 2012. "Worst-Of Options And Correlation Skew Under A Stochastic Correlation Framework," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 15(07), pages 1-32.
    • Handle: RePEc:wsi:ijtafx:v:15:y:2012:i:07:n:s0219024912500513
    DOI: 10.1142/S0219024912500513
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    References listed on IDEAS

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    1. Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv, December.
    2. Alex Langnau, 2009. "Introduction into "Local Correlation Modelling"," Papers 0909.3441, arXiv.org, revised Sep 2009.
    3. Christian Gourieroux & Razvan Sufana, 2004. "Derivative Pricing with Multivariate Stochastic Volatility : Application to Credit Risk," Working Papers 2004-31, Center for Research in Economics and Statistics.
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    Cited by:

    1. Monfort, Alain & Renne, Jean-Paul & Roussellet, Guillaume, 2015. "A Quadratic Kalman Filter," Journal of Econometrics, Elsevier, vol. 187(1), pages 43-56.
    2. Jacinto Marabel Romo, 2016. "Is the information obtained from European options on equally weighted baskets enough to determine the prices of exotic derivatives such as worst-of options?," Review of Derivatives Research, Springer, vol. 19(1), pages 65-83, April.

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