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Bridge Copula Model for Option Pricing

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  • Giuseppe Campolieti
  • Roman N. Makarov
  • Andrey Vasiliev
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    Abstract

    In this paper we present a new multi-asset pricing model, which is built upon newly developed families of solvable multi-parameter single-asset diffusions with a nonlinear smile-shaped volatility and an affine drift. Our multi-asset pricing model arises by employing copula methods. In particular, all discounted single-asset price processes are modeled as martingale diffusions under a risk-neutral measure. The price processes are so-called UOU diffusions and they are each generated by combining a variable (Ito) transformation with a measure change performed on an underlying Ornstein-Uhlenbeck (Gaussian) process. Consequently, we exploit the use of a normal bridge copula for coupling the single-asset dynamics while reducing the distribution of the multi-asset price process to a multivariate normal distribution. Such an approach allows us to simulate multidimensional price paths in a precise and fast manner and hence to price path-dependent financial derivatives such as Asian-style and Bermudan options using the Monte Carlo method. We also demonstrate how to successfully calibrate our multi-asset pricing model by fitting respective equity option and asset market prices to the single-asset models and their return correlations (i.e. the copula function) using the least-square and maximum-likelihood estimation methods.

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    File URL: http://arxiv.org/pdf/1110.4669
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number 1110.4669.

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    Date of creation: Oct 2011
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    Handle: RePEc:arx:papers:1110.4669

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    Web page: http://arxiv.org/

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    1. Giuseppe Campolieti & Roman Makarov, 2008. "Path integral pricing of Asian options on state-dependent volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 8(2), pages 147-161.
    2. Giuseppe Campolieti & Roman Makarov, 2007. "Pricing Path-Dependent Options On State Dependent Volatility Models With A Bessel Bridge," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 10(01), pages 51-88.
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