Pricing options on stocks denominated in different currencies: Theory and illustrations
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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Volume (Year): 26 (2013)
Issue (Month): C ()
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- Deelstra, G. & Liinev, J. & Vanmaele, M., 2004. "Pricing of arithmetic basket options by conditioning," Insurance: Mathematics and Economics, Elsevier, vol. 34(1), pages 55-77, February.
- P. Pellizzari, 2001. "Efficient Monte Carlo pricing of European options¶using mean value control variates," Decisions in Economics and Finance, Springer, vol. 24(2), pages 107-126, November.
- Siu, Tak Kuen, 2005. "Fair valuation of participating policies with surrender options and regime switching," Insurance: Mathematics and Economics, Elsevier, vol. 37(3), pages 533-552, December.
- Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
- Georges Dionne & Genevieve Gauthier & Nadia Ouertani & Nabil Tahani, 2011.
"Heterogeneous Basket Options Pricing Using Analytical Approximations,"
Multinational Finance Journal,
Multinational Finance Journal, vol. 15(1-2), pages 47-85, March - J.
- Georges Dionne & Geneviève Gauthier & Nadia Ouertani & Nabil Tahani, 2006. "Heterogeneous Basket Options Pricing Using Analytical Approximations," Cahiers de recherche 0605, CIRPEE.
- Michael Curran, 1994. "Valuing Asian and Portfolio Options by Conditioning on the Geometric Mean Price," Management Science, INFORMS, vol. 40(12), pages 1705-1711, December.
- Bollerslev, Tim & Engle, Robert F & Wooldridge, Jeffrey M, 1988. "A Capital Asset Pricing Model with Time-Varying Covariances," Journal of Political Economy, University of Chicago Press, vol. 96(1), pages 116-31, February.
- Yuan, Chunming, 2011.
"The exchange rate and macroeconomic determinants: Time-varying transitional dynamics,"
The North American Journal of Economics and Finance,
Elsevier, vol. 22(2), pages 197-220, August.
- Chunming Yuan, 2008. "The Exchange Rate and Macroeconomic Determinants: Time-Varying Transitional Dynamics," UMBC Economics Department Working Papers 09-114, UMBC Department of Economics, revised 01 Nov 2009.
- Wang, Shen & Mayes, David G., 2012. "Monetary policy announcements and stock reactions: An international comparison," The North American Journal of Economics and Finance, Elsevier, vol. 23(2), pages 145-164.
- Rubinstein, Mark, 1994. " Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
- Denis Pelletier, 2004.
"Regime Switching for Dynamic Correlations,"
Econometric Society 2004 North American Summer Meetings
230, Econometric Society.
- Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(01), pages 122-150, February.
- Jèôme Barraquand, 1995. "Numerical Valuation of High Dimensional Multivariate European Securities," Management Science, INFORMS, vol. 41(12), pages 1882-1891, December.
- 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.
- 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.
- Ng, Andrew Cheuk-Yin & Li, Johnny Siu-Hang, 2011. "Valuing variable annuity guarantees with the multivariate Esscher transform," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 393-400.
- de Jesús, Raúl & Ortiz, Edgar & Cabello, Alejandra, 2013. "Long run peso/dollar exchange rates and extreme value behavior: Value at Risk modeling," The North American Journal of Economics and Finance, Elsevier, vol. 24(C), pages 139-152.
- Vanmaele, Michele & Deelstra, Griselda & Liinev, Jan, 2004. "Approximation of stop-loss premiums involving sums of lognormals by conditioning on two variables," Insurance: Mathematics and Economics, Elsevier, vol. 35(2), pages 343-367, October.
- Griselda Deelstra & Jan Liinev & Michèle Vanmaele, 2004. "Pricing of arithmetic basket options by conditioning," ULB Institutional Repository 2013/7600, ULB -- Universite Libre de Bruxelles.
- Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-50, July.
- Robert J. Elliott & Leunglung Chan & Tak Kuen Siu, 2005. "Option pricing and Esscher transform under regime switching," Annals of Finance, Springer, vol. 1(4), pages 423-432, October.
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