IDEAS home Printed from https://ideas.repec.org/a/wsi/ijtafx/v17y2014i04ns0219024914500265.html
   My bibliography  Save this article

Closed-Form Approximation Of Perpetual Timer Option Prices

Author

Listed:
  • MINQIANG LI

    (Derivatives Research, Bloomberg LP. 731 Lexington Avenue, New York City, New York, 10022, USA)

  • FABIO MERCURIO

    (Derivatives Research, Bloomberg LP. 731 Lexington Avenue, New York City, New York, 10022, USA)

Abstract

We develop an asymptotic expansion technique for pricing timer options in stochastic volatility models when the effect of volatility of variance is small. Based on the pricing PDE, closed-form approximation formulas have been obtained. The approximation has an easy-to-understand Black–Scholes-like form and many other attractive properties. Numerical analysis shows that the approximation formulas are very fast and accurate, especially when the volatility of variance is not large.

Suggested Citation

  • Minqiang Li & Fabio Mercurio, 2014. "Closed-Form Approximation Of Perpetual Timer Option Prices," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(04), pages 1-34.
    • Handle: RePEc:wsi:ijtafx:v:17:y:2014:i:04:n:s0219024914500265
    DOI: 10.1142/S0219024914500265
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219024914500265
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219024914500265?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. Minqiang Li & Fabio Mercurio, 2015. "Analytic Approximation of Finite‐Maturity Timer Option Prices," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 35(3), pages 245-273, March.
    2. Alan L. Lewis, 2000. "Option Valuation under Stochastic Volatility," Option Valuation under Stochastic Volatility, Finance Press, number ovsv, December.
    3. Minqiang Li, 2015. "Derivatives Pricing on Integrated Diffusion Processes: A General Perturbation Approach," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 35(6), pages 582-595, June.
    4. Alexander Lipton, 2001. "Mathematical Methods for Foreign Exchange:A Financial Engineer's Approach," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 4694, February.
    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. Zhenyu Cui & J. Lars Kirkby & Guanghua Lian & Duy Nguyen, 2017. "Integral Representation Of Probability Density Of Stochastic Volatility Models And Timer Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(08), pages 1-32, December.
    2. Pingping Zeng & Yue Kuen Kwok & Wendong Zheng, 2015. "Fast Hilbert Transform Algorithms For Pricing Discrete Timer Options Under Stochastic Volatility Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(07), pages 1-26, November.
    3. Wendong Zheng & Pingping Zeng, 2016. "Pricing timer options and variance derivatives with closed-form partial transform under the 3/2 model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 23(5), pages 344-373, September.

    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. Zhenyu Cui & J. Lars Kirkby & Guanghua Lian & Duy Nguyen, 2017. "Integral Representation Of Probability Density Of Stochastic Volatility Models And Timer Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(08), pages 1-32, December.
    2. Fazlollah Soleymani & Andrey Itkin, 2019. "Pricing foreign exchange options under stochastic volatility and interest rates using an RBF--FD method," Papers 1903.00937, arXiv.org.
    3. Andrey Itkin, 2023. "The ATM implied skew in the ADO-Heston model," Papers 2309.15044, arXiv.org.
    4. Viatcheslav Gorovoi & Vadim Linetsky, 2004. "Black's Model of Interest Rates as Options, Eigenfunction Expansions and Japanese Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 14(1), pages 49-78, January.
    5. Vadim Linetsky, 2004. "The Spectral Decomposition Of The Option Value," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 7(03), pages 337-384.
    6. Andrey Itkin, 2015. "HIGH ORDER SPLITTING METHODS FOR FORWARD PDEs AND PIDEs," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(05), pages 1-24.
    7. Alexander Lipton & Andrey Gal & Andris Lasis, 2014. "Pricing of vanilla and first-generation exotic options in the local stochastic volatility framework: survey and new results," Quantitative Finance, Taylor & Francis Journals, vol. 14(11), pages 1899-1922, November.
    8. Alexander Lipton, 2023. "Kelvin Waves, Klein-Kramers and Kolmogorov Equations, Path-Dependent Financial Instruments: Survey and New Results," Papers 2309.04547, arXiv.org.
    9. Li, Minqiang & Mercurio, Fabio, 2013. "Closed-Form Approximation of Timer Option Prices under General Stochastic Volatility Models," MPRA Paper 47465, University Library of Munich, Germany.
    10. Leif Andersen & Alexander Lipton, 2013. "Asymptotics For Exponential Lévy Processes And Their Volatility Smile: Survey And New Results," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(01), pages 1-98.
    11. Likuan Qin & Vadim Linetsky, 2016. "Positive Eigenfunctions of Markovian Pricing Operators: Hansen-Scheinkman Factorization, Ross Recovery, and Long-Term Pricing," Operations Research, INFORMS, vol. 64(1), pages 99-117, February.
    12. Wendong Zheng & Pingping Zeng, 2016. "Pricing timer options and variance derivatives with closed-form partial transform under the 3/2 model," Applied Mathematical Finance, Taylor & Francis Journals, vol. 23(5), pages 344-373, September.
    13. Minqiang Li & Fabio Mercurio, 2015. "Analytic Approximation of Finite‐Maturity Timer Option Prices," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 35(3), pages 245-273, March.
    14. Lorenzo Torricelli, 2013. "Pricing Joint Claims On An Asset And Its Realized Variance In Stochastic Volatility Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(01), pages 1-18.
    15. Pierre Henry-labordere, 2007. "Solvable local and stochastic volatility models: supersymmetric methods in option pricing," Quantitative Finance, Taylor & Francis Journals, vol. 7(5), pages 525-535.
    16. Christoffersen, Peter & Heston, Steven & Jacobs, Kris, 2010. "Option Anomalies and the Pricing Kernel," Working Papers 11-17, University of Pennsylvania, Wharton School, Weiss Center.
    17. Chenxu Li, 2014. "Closed-Form Expansion, Conditional Expectation, and Option Valuation," Mathematics of Operations Research, INFORMS, vol. 39(2), pages 487-516, May.
    18. Fisher, Travis & Pulido, Sergio & Ruf, Johannes, 2019. "Financial models with defaultable numéraires," LSE Research Online Documents on Economics 84973, London School of Economics and Political Science, LSE Library.
    19. Nicolas Langrené & Geoffrey Lee & Zili Zhu, 2016. "Switching To Nonaffine Stochastic Volatility: A Closed-Form Expansion For The Inverse Gamma Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(05), pages 1-37, August.
    20. Peter Carr & Travis Fisher & Johannes Ruf, 2014. "On the hedging of options on exploding exchange rates," Finance and Stochastics, Springer, vol. 18(1), pages 115-144, January.

    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:wsi:ijtafx:v:17:y:2014:i:04:n:s0219024914500265. 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijtaf/ijtaf.shtml .

    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.