IDEAS home Printed from https://ideas.repec.org/a/eee/ecofin/v26y2013icp339-354.html
   My bibliography  Save this article

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

Author

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

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.

Suggested Citation

  • Ng, Andrew C.Y. & Li, Johnny Siu-Hang & Chan, Wai-Sum, 2013. "Pricing options on stocks denominated in different currencies: Theory and illustrations," The North American Journal of Economics and Finance, Elsevier, vol. 26(C), pages 339-354.
    • Handle: RePEc:eee:ecofin:v:26:y:2013:i:c:p:339-354
    DOI: 10.1016/j.najef.2013.02.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S1062940813000247
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.najef.2013.02.009?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Engle, Robert F. & Kroner, Kenneth F., 1995. "Multivariate Simultaneous Generalized ARCH," Econometric Theory, Cambridge University Press, vol. 11(1), pages 122-150, February.
    2. P. Pellizzari, 2001. "Efficient Monte Carlo pricing of European options¶using mean value control variates," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 24(2), pages 107-126, November.
    3. Mary Hardy, 2001. "A Regime-Switching Model of Long-Term Stock Returns," North American Actuarial Journal, Taylor & Francis Journals, vol. 5(2), pages 41-53.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Jean-Yves Datey & Genevieve Gauthier & Jean-Guy Simonato, 2003. "The Performance of Analytical Approximations for the Computation of Asian Quanto-Basket Option Prices," Multinational Finance Journal, Multinational Finance Journal, vol. 7(1-2), pages 55-82, March-Jun.
    9. 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 116-131, February.
    10. 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.
    11. 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.
    12. Mark Rubinstein., 1994. "Implied Binomial Trees," Research Program in Finance Working Papers RPF-232, University of California at Berkeley.
    13. 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.
    14. 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.
    15. 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.
    16. Griselda Deelstra & Jan Liinev & Michèle Vanmaele, 2004. "Pricing of arithmetic basket options by conditioning," ULB Institutional Repository 2013/7600, ULB -- Universite Libre de Bruxelles.
    17. Pelletier, Denis, 2006. "Regime switching for dynamic correlations," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 445-473.
    18. Mathieu Boudreault & Christian-Marc Panneton, 2009. "Multivariate Models of Equity Returns for Investment Guarantees Valuation," North American Actuarial Journal, Taylor & Francis Journals, vol. 13(1), pages 36-53.
    19. 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 339-350, July.
    20. 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.
    21. P. Pellizzari, 1998. "Efficient Monte Carlo Pricing of Basket Options," Finance 9801001, University Library of Munich, Germany.
    22. 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.
    23. 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.
    24. Rubinstein, Mark, 1994. "Implied Binomial Trees," Journal of Finance, American Finance Association, vol. 49(3), pages 771-818, July.
    25. Barraquand, Jérôme & Martineau, Didier, 1995. "Numerical Valuation of High Dimensional Multivariate American Securities," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 30(3), pages 383-405, September.
    26. Jèôme Barraquand, 1995. "Numerical Valuation of High Dimensional Multivariate European Securities," Management Science, INFORMS, vol. 41(12), pages 1882-1891, December.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Lee, Hangsuck & Ha, Hongjun & Lee, Minha, 2023. "Partial quanto lookback options," The North American Journal of Economics and Finance, Elsevier, vol. 64(C).
    2. Chia-Lin Chang & Allen, David & McAleer, Michael, 2013. "Recent developments in financial economics and econometrics: An overview," The North American Journal of Economics and Finance, Elsevier, vol. 26(C), pages 217-226.
    3. Battauz, Anna & De Donno, Marzia & Sbuelz, Alessandro, 2022. "On the exercise of American quanto options," The North American Journal of Economics and Finance, Elsevier, vol. 62(C).
    4. Li, Johnny Siu-Hang & Ng, Andrew C.Y. & Chan, Wai-Sum, 2015. "Managing financial risk in Chinese stock markets: Option pricing and modeling under a multivariate threshold autoregression," International Review of Economics & Finance, Elsevier, vol. 40(C), pages 217-230.
    5. Li, Zhe & Zhang, Wei-Guo & Liu, Yong-Jun, 2018. "European quanto option pricing in presence of liquidity risk," The North American Journal of Economics and Finance, Elsevier, vol. 45(C), pages 230-244.
    6. Atilgan, Yigit & Demirtas, K. Ozgur & Simsek, Koray D., 2016. "Derivative markets in emerging economies: A survey," International Review of Economics & Finance, Elsevier, vol. 42(C), pages 88-102.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Georges Dionne & Geneviève Gauthier & Nadia Ouertani, 2009. "Basket Options on Heterogeneous Underlying Assets," Cahiers de recherche 0918, CIRPEE.
    3. Yijuan Liang & Xiuchuan Xu, 2019. "Variance and Dimension Reduction Monte Carlo Method for Pricing European Multi-Asset Options with Stochastic Volatilities," Sustainability, MDPI, vol. 11(3), pages 1-21, February.
    4. Otranto, Edoardo, 2010. "Identifying financial time series with similar dynamic conditional correlation," Computational Statistics & Data Analysis, Elsevier, vol. 54(1), pages 1-15, January.
    5. Matthias R. Fengler & Helmut Herwartz & Christian Werner, 2012. "A Dynamic Copula Approach to Recovering the Index Implied Volatility Skew," Journal of Financial Econometrics, Oxford University Press, vol. 10(3), pages 457-493, June.
    6. Paolella, Marc S. & Polak, Paweł & Walker, Patrick S., 2021. "A non-elliptical orthogonal GARCH model for portfolio selection under transaction costs," Journal of Banking & Finance, Elsevier, vol. 125(C).
    7. Paul Catani & Timo Teräsvirta & Meiqun Yin, 2017. "A Lagrange multiplier test for testing the adequacy of constant conditional correlation GARCH model," Econometric Reviews, Taylor & Francis Journals, vol. 36(6-9), pages 599-621, October.
    8. Leccadito, Arturo & Paletta, Tommaso & Tunaru, Radu, 2016. "Pricing and hedging basket options with exact moment matching," Insurance: Mathematics and Economics, Elsevier, vol. 69(C), pages 59-69.
    9. Xu, Guoping & Zheng, Harry, 2009. "Approximate basket options valuation for a jump-diffusion model," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 188-194, October.
    10. Silvennoinen, Annastiina & Teräsvirta, Timo, 2007. "Multivariate GARCH models," SSE/EFI Working Paper Series in Economics and Finance 669, Stockholm School of Economics, revised 18 Jan 2008.
    11. Annastiina Silvennoinen & Timo Teräsvirta, 2017. "Consistency and asymptotic normality of maximum likelihood estimators of a multiplicative time-varying smooth transition correlation GARCH model," CREATES Research Papers 2017-28, Department of Economics and Business Economics, Aarhus University.
    12. Long, Xiangdong & Su, Liangjun & Ullah, Aman, 2011. "Estimation and Forecasting of Dynamic Conditional Covariance: A Semiparametric Multivariate Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(1), pages 109-125.
    13. Engle, Robert, 2001. "Financial econometrics - A new discipline with new methods," Journal of Econometrics, Elsevier, vol. 100(1), pages 53-56, January.
    14. Mauro Bernardi & Leopoldo Catania, 2015. "Switching-GAS Copula Models With Application to Systemic Risk," Papers 1504.03733, arXiv.org, revised Jan 2016.
    15. Rotta, Pedro Nielsen & Pereira, Pedro L. Valls, 2013. "Analysis of contagion from the constant conditional correlation model with Markov regime switching," Textos para discussão 340, FGV EESP - Escola de Economia de São Paulo, Fundação Getulio Vargas (Brazil).
    16. Grzegorz Darkiewicz & Griselda Deelstra & Jan Dhaene & Tom Hoedemakers & Michèle Vanmaele, 2009. "Bounds for Right Tails of Deterministic and Stochastic Sums of Random Variables," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 76(4), pages 847-866, December.
    17. Takashi Isogai, 2015. "An Empirical Study of the Dynamic Correlation of Japanese Stock Returns," Bank of Japan Working Paper Series 15-E-7, Bank of Japan.
    18. Ruggero Caldana & Gianluca Fusai & Alessandro Gnoatto & Martino Grasselli, 2016. "General closed-form basket option pricing bounds," Quantitative Finance, Taylor & Francis Journals, vol. 16(4), pages 535-554, April.
    19. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
    20. Xiangdong Long & Liangjun Su & Aman Ullah, 2009. "Estimation and Forecasting of Dynamic Conditional Covariance: A Semiparametric Multivariate Model Variables with Econometric Applications," Working Papers 200908, University of California at Riverside, Department of Economics, revised Jul 2009.

    More about this item

    Keywords

    Conditional Esscher transform; Quantos; Regime-switching lognormal models;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • F31 - International Economics - - International Finance - - - Foreign Exchange

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ecofin:v:26:y:2013:i:c:p:339-354. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/620163 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.