IDEAS home Printed from https://ideas.repec.org/a/eee/ecofin/v64y2023ics1062940822002066.html
   My bibliography  Save this article

Partial quanto lookback options

Author

Listed:
  • Lee, Hangsuck
  • Ha, Hongjun
  • Lee, Minha

Abstract

Financial instruments for hedging and speculating on the foreign exchange rate and equity risks draw the attention of market participants as financial transactions increase across multiple jurisdictions. Notably, a quanto lookback option has been actively traded because it successfully meets market demands. Although the quanto lookback option provides numerous benefits, a high premium due to the lookback feature is the primary culprit that hinders investors from purchasing it. This paper proposes partial quanto lookback options and provides the closed-form pricing formulas when the lookback feature is applied to the exchange rate or equity value, and the extremes are determined by observing them for a shorter period than the life of the option. Because pricing the options is challenging due to their partial path-dependence, we develop the quanto extreme expectation that facilitates deriving the option prices. Extensive numerical examples demonstrate the efficacy of the partial quanto lookback options in lowering the premiums.

Suggested Citation

  • Lee, Hangsuck & Ha, Hongjun & Lee, Minha, 2023. "Partial quanto lookback options," The North American Journal of Economics and Finance, Elsevier, vol. 64(C).
    • Handle: RePEc:eee:ecofin:v:64:y:2023:i:c:s1062940822002066
    DOI: 10.1016/j.najef.2022.101871
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S1062940822002066
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.najef.2022.101871?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. Gerber, Hans U. & Shiu, Elias S. W., 1996. "Actuarial bridges to dynamic hedging and option pricing," Insurance: Mathematics and Economics, Elsevier, vol. 18(3), pages 183-218, November.
    2. Caporale, Guglielmo Maria & Hunter, John & Menla Ali, Faek, 2014. "On the linkages between stock prices and exchange rates: Evidence from the banking crisis of 2007–2010," International Review of Financial Analysis, Elsevier, vol. 33(C), pages 87-103.
    3. Goldman, M Barry & Sosin, Howard B & Gatto, Mary Ann, 1979. "Path Dependent Options: "Buy at the Low, Sell at the High"," Journal of Finance, American Finance Association, vol. 34(5), pages 1111-1127, December.
    4. 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.
    5. Ho, Tuan & Nguyen, Yen & Parikh, Bhavik & Vo, Dinh-Tri, 2020. "Does foreign exchange risk matter to equity research analysts when forecasting stock prices? Evidence from U.S. firms," International Review of Financial Analysis, Elsevier, vol. 72(C).
    6. Peter Buchen & Otto Konstandatos, 2005. "A New Method Of Pricing Lookback Options," Mathematical Finance, Wiley Blackwell, vol. 15(2), pages 245-259, April.
    7. Min Dai & Hoi Ying Wong & Yue Kuen Kwok, 2004. "Quanto Lookback Options," Mathematical Finance, Wiley Blackwell, vol. 14(3), pages 445-467, July.
    8. Conze, Antoine & Viswanathan, 1991. "Path Dependent Options: The Case of Lookback Options," Journal of Finance, American Finance Association, vol. 46(5), pages 1893-1907, December.
    9. Lee, Hangsuck & Ha, Hongjun & Lee, Minha, 2022. "Foreign equity lookback options with guarantees," Finance Research Letters, Elsevier, vol. 48(C).
    10. Hans Gerber & Elias Shiu, 2003. "Pricing Lookback Options and Dynamic Guarantees," North American Actuarial Journal, Taylor & Francis Journals, vol. 7(1), pages 48-66.
    11. Paul Glasserman & Jeremy Staum, 2001. "Conditioning on One-Step Survival for Barrier Option Simulations," Operations Research, INFORMS, vol. 49(6), pages 923-937, December.
    12. Lee, Hangsuck, 2003. "Pricing equity-indexed annuities with path-dependent options," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 677-690, December.
    13. George Andrew Karolyi & Ying Wu, 2021. "Is Currency Risk Priced in Global Equity Markets? [Exposure to currency risk: definition and measurement]," Review of Finance, European Finance Association, vol. 25(3), pages 863-902.
    14. Liming Feng & Vadim Linetsky, 2009. "Computing exponential moments of the discrete maximum of a Lévy process and lookback options," Finance and Stochastics, Springer, vol. 13(4), pages 501-529, September.
    15. Ya-Chun Huang & Elias Shiu, 2001. "“Pricing Dynamic Investment Fund Protection,” Hans U. Gerber and Gérard Pafumi, April 2000," North American Actuarial Journal, Taylor & Francis Journals, vol. 5(1), pages 153-157.
    16. 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).
    Full references (including those not matched with items on IDEAS)

    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. Lee, Hangsuck & Kim, Eunchae & Ko, Bangwon, 2022. "Valuing lookback options with barrier," The North American Journal of Economics and Finance, Elsevier, vol. 60(C).
    2. Lee, Hangsuck & Ha, Hongjun & Lee, Minha, 2022. "Foreign equity lookback options with guarantees," Finance Research Letters, Elsevier, vol. 48(C).
    3. Kim, Geonwoo & Jeon, Junkee, 2018. "Closed-form solutions for valuing partial lookback options with random initiation," Finance Research Letters, Elsevier, vol. 24(C), pages 321-327.
    4. Sun-Yong Choi & Ji-Hun Yoon & Junkee Jeon, 2019. "Pricing of Fixed-Strike Lookback Options on Assets with Default Risk," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-10, January.
    5. Wong, Hoi Ying & Chan, Chun Man, 2007. "Lookback options and dynamic fund protection under multiscale stochastic volatility," Insurance: Mathematics and Economics, Elsevier, vol. 40(3), pages 357-385, May.
    6. Gerber, Hans U. & Shiu, Elias S.W. & Yang, Hailiang, 2012. "Valuing equity-linked death benefits and other contingent options: A discounted density approach," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 73-92.
    7. Yang, Zhaoqiang, 2020. "Default probability of American lookback option in a mixed jump-diffusion model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    8. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    9. Ha, Mijin & Kim, Donghyun & Yoon, Ji-Hun, 2024. "Valuing of timer path-dependent options," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 208-227.
    10. Hans-Peter Bermin & Peter Buchen & Otto Konstandatos, 2008. "Two Exotic Lookback Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(4), pages 387-402.
    11. Gongqiu Zhang & Lingfei Li, 2021. "A General Approach for Lookback Option Pricing under Markov Models," Papers 2112.00439, arXiv.org.
    12. Peter Buchen & Hamish Malloch, 2014. "CLA's, PLA's and a new method for pricing general passport options," Quantitative Finance, Taylor & Francis Journals, vol. 14(7), pages 1201-1209, July.
    13. Orozco-Garcia, Carolina & Schmeiser, Hato, 2015. "How sensitive is the pricing of lookback and interest rate guarantees when changing the modelling assumptions?," Insurance: Mathematics and Economics, Elsevier, vol. 65(C), pages 77-93.
    14. Detlef Seese & Christof Weinhardt & Frank Schlottmann (ed.), 2008. "Handbook on Information Technology in Finance," International Handbooks on Information Systems, Springer, number 978-3-540-49487-4, November.
    15. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
    16. Benjamin Marcus & Chris K. Anderson, 2006. "Online Low-Price Guarantees---A Real Options Analysis," Operations Research, INFORMS, vol. 54(6), pages 1041-1050, December.
    17. Hans-Peter Bermin, 2000. "Hedging lookback and partial lookback options using Malliavin calculus," Applied Mathematical Finance, Taylor & Francis Journals, vol. 7(2), pages 75-100.
    18. Peter Buchen & Otto Konstandatos, 2009. "A New Approach to Pricing Double-Barrier Options with Arbitrary Payoffs and Exponential Boundaries," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(6), pages 497-515.
    19. Qian, Linyi & Wang, Wei & Wang, Rongming & Tang, Yincai, 2010. "Valuation of equity-indexed annuity under stochastic mortality and interest rate," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 123-129, October.
    20. Ko, Bangwon & Shiu, Elias S.W. & Wei, Li, 2010. "Pricing maturity guarantee with dynamic withdrawal benefit," Insurance: Mathematics and Economics, Elsevier, vol. 47(2), pages 216-223, October.

    More about this item

    Keywords

    Quanto lookback option; Partial monitoring; Quanto extreme expectation;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

    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:64:y:2023:i:c:s1062940822002066. 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.