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Pricing options on stocks denominated in different currencies: Theory and illustrations

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  • Ng, Andrew C.Y.
  • Li, Johnny Siu-Hang
  • Chan, Wai-Sum
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    Abstract

    Basket options have long been an important structured product. One can write a basket option on assets denominated in different currencies, but settle the option in one single currency at some fixed exchange rate. This special type of basket options can be found in many life insurance products that encompass an investment component. In order to value such options, we need to consider not only the joint dynamics of the returns on the underlying assets but also the quanto feature involved. In this paper, we use a regime-switching multivariate lognormal model for modeling returns on various assets and exchange rates. As the parameters of the model can change according to the state of a Markov chain, the model allows for stochastic volatility and correlations. We then demonstrate how domestic investors can choose a risk-neutral probability measure by the multivariate Esscher transform. This valuation methodology is illustrated with an hypothetical investment guarantee that is sold with a life insurance contract.

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    Bibliographic Info

    Article provided by Elsevier in its journal The North American Journal of Economics and Finance.

    Volume (Year): 26 (2013)
    Issue (Month): C ()
    Pages: 339-354

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    Handle: RePEc:eee:ecofin:v:26:y:2013:i:c:p:339-354

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    Web page: http://www.elsevier.com/locate/inca/620163

    Related research

    Keywords: Conditional Esscher transform; Quantos; Regime-switching lognormal models;

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    References

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    1. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
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    3. Michèle Vanmaele & Griselda Deelstra & Jan Liinev, 2004. "Approximation of stop-loss premiums involving sums of lognormals by conditioning on two variables," ULB Institutional Repository 2013/7604, ULB -- Universite Libre de Bruxelles.
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    16. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
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    Cited by:
    1. Chia-Lin Chang & David Allen & Michael McAleer, 2013. "Recent Developments in Financial Economics and Econometrics: An Overview," Documentos del Instituto Complutense de Análisis Económico 2013-03, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales.
    2. Chia-Lin Chang & David Allen & Michael McAleer, 2013. "Recent Developments in Financial Economics and Econometrics: An Overview," Tinbergen Institute Discussion Papers 13-021/III, Tinbergen Institute.

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