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Digital Contracts: Simple Tools for Pricing Complex Derivatives

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  • Ingersoll, Jonathan E, Jr

Abstract

This article presents a simple, unified approach for valuing a variety of financial assets using digital contracts. Three types of digitals are used: a digital option paying either one dollar or nothing, a digital share paying nothing or converting into one share of the underlying asset; and a first-touch digital paying one dollar the first time that the price of the underlying stock moves into some specified region. It is shown how the values of these three types of digitals can be determined for a wide variety of payoff events and how they can be combined to price complex contracts. Copyright 2000 by University of Chicago Press.

Suggested Citation

  • Ingersoll, Jonathan E, Jr, 2000. "Digital Contracts: Simple Tools for Pricing Complex Derivatives," The Journal of Business, University of Chicago Press, vol. 73(1), pages 67-88, January.
    • Handle: RePEc:ucp:jnlbus:v:73:y:2000:i:1:p:67-88
    DOI: 10.1086/209632
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    Citations

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    Cited by:

    1. Jun Lu & Hiroshi Ohta, 2003. "A data and digital-contracts driven method for pricing complex derivatives," Quantitative Finance, Taylor & Francis Journals, vol. 3(3), pages 212-219.
    2. Lee, Hangsuck & Ha, Hongjun & Kong, Byungdoo, 2024. "Pricing first-touch digitals with a multi-step double boundary and American barrier options," Finance Research Letters, Elsevier, vol. 59(C).
    3. Moraux, Franck, 2004. "A closed form solution for pricing defaultable bonds," Finance Research Letters, Elsevier, vol. 1(2), pages 135-142, June.
    4. Hardy Hulley & Shane Miller & Eckhard Platen, 2005. "Benchmarking and Fair Pricing Applied to Two Market Models," Research Paper Series 155, Quantitative Finance Research Centre, University of Technology, Sydney.
    5. William N. Goetzmann & Jonathan E. Ingersoll & Stephen A. Ross, 2003. "High‐Water Marks and Hedge Fund Management Contracts," Journal of Finance, American Finance Association, vol. 58(4), pages 1685-1718, August.
    6. Kasprowicz Tomasz & Bednorz Andrzej, 2017. "Threshold Theory – modelling risk attitude," Financial Internet Quarterly (formerly e-Finanse), Sciendo, vol. 13(4), pages 97-109, December.
    7. Evan Gatev & Stephen Ross, 2000. "Rebels, Conformists, Contrarians And Momentum Traders," Yale School of Management Working Papers ysm137, Yale School of Management, revised 01 Jan 2003.
    8. Peter Buchen, 2004. "The pricing of dual-expiry exotics," Quantitative Finance, Taylor & Francis Journals, vol. 4(1), pages 101-108.
    9. Ravi Kashyap, 2022. "Options as Silver Bullets: Valuation of Term Loans, Inventory Management, Emissions Trading and Insurance Risk Mitigation using Option Theory," Annals of Operations Research, Springer, vol. 315(2), pages 1175-1215, August.
    10. Bakshi, Gurdip & Madan, Dilip & Panayotov, George, 2010. "Returns of claims on the upside and the viability of U-shaped pricing kernels," Journal of Financial Economics, Elsevier, vol. 97(1), pages 130-154, July.
    11. Hyong-Chol O & Mun-Chol KiM, 2013. "The Pricing of Multiple-Expiry Exotics," Papers 1302.3319, arXiv.org, revised Aug 2013.
    12. Ally Quan Zhang & Matthias Thul, 2017. "How much is the gap?—Efficient jump risk-adjusted valuation of leveraged certificates," Quantitative Finance, Taylor & Francis Journals, vol. 17(9), pages 1387-1401, September.
    13. Ravi Kashyap, 2016. "Options as Silver Bullets: Valuation of Term Loans, Inventory Management, Emissions Trading and Insurance Risk Mitigation using Option Theory," Papers 1609.01274, arXiv.org, revised Mar 2022.
    14. Hyong-Chol O & Dae-Sung Choe, 2019. "Pricing Formulae of Power Binary and Normal Distribution Standard Options and Applications," Papers 1903.04106, arXiv.org.
    15. Jonathan Ingersoll, 2002. "The Subjective and Objective Evaluation of Incentive Stock Options," Yale School of Management Working Papers ysm276, Yale School of Management, revised 01 Jul 2003.
    16. Jonathan Ingersoll, 2002. "The Subjective and Objective Evaluation of Incentive Stock Options," Yale School of Management Working Papers ysm276, Yale School of Management, revised 01 Jul 2003.
    17. Doobae Jun & Hyejin Ku, 2013. "Valuation of American partial barrier options," Review of Derivatives Research, Springer, vol. 16(2), pages 167-191, July.
    18. J Lu & H Ohta, 2003. "Digital contracts-driven method for pricing complex derivatives," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 54(9), pages 1002-1010, September.

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