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The pricing of dual-expiry exotics

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  • Peter Buchen

Abstract

This paper develops a new technique for pricing a class of exotic options that are characterized by two expiry dates. Examples of such exotics include compound options, chooser options, extendable options, shout options, partial barrier options and others. The method, based on the partial differential equation approach to option pricing, however requires no formal solution of such equations. Instead, the method exploits the observation that dual expiry options have payoffs that can be perfectly replicated by a particular set of first and second order binary options. Hence, in order to avoid arbitrage, the exotic option prices are obtained by static replication with respect to this family of binaries. The representation of prices in terms of these binaries is also quite general and does not depend on any particular underlying asset price dynamics. Closed form expressions agreeing with published results are given for the case of log-normal asset price dynamics and standard Black-Scholes assumptions.

Suggested Citation

  • Peter Buchen, 2004. "The pricing of dual-expiry exotics," Quantitative Finance, Taylor & Francis Journals, vol. 4(1), pages 101-108.
    • Handle: RePEc:taf:quantf:v:4:y:2004:i:1:p:101-108
    DOI: 10.1088/1469-7688/4/1/009
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    References listed on IDEAS

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    1. Geske, Robert, 1979. "The valuation of compound options," Journal of Financial Economics, Elsevier, vol. 7(1), pages 63-81, March.
    2. Geske, Robert, 1979. "A note on an analytical valuation formula for unprotected American call options on stocks with known dividends," Journal of Financial Economics, Elsevier, vol. 7(4), pages 375-380, December.
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    Citations

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    Cited by:

    1. Kyng, T. & Konstandatos, O. & Bienek, T., 2016. "Valuation of employee stock options using the exercise multiple approach and life tables," Insurance: Mathematics and Economics, Elsevier, vol. 68(C), pages 17-26.
    2. Konstandatos, Otto, 2020. "Fair-value analytical valuation of reset executive stock options consistent with IFRS9 requirements," Annals of Actuarial Science, Cambridge University Press, vol. 14(1), pages 188-218, March.
    3. 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.
    4. Hyong-Chol O & Dong-Hyok Kim & Jong-Jun Jo & Song-Hun Ri, 2013. "Integrals of Higher Binary Options and Defaultable Bond with Discrete Default Information," Papers 1305.6988, arXiv.org, revised Oct 2013.
    5. Lian, Yu-Min & Chen, Jun-Home, 2023. "Valuation of chooser options with state-dependent risks," Finance Research Letters, Elsevier, vol. 52(C).
    6. Otto Konstandatos & Timothy J Kyng, 2012. "Real Options Analysis for Commodity Based Mining Enterprises with Compound and Barrier Features," Published Paper Series 2012-3, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    7. Hans-Peter Bermin & Peter Buchen & Otto Konstandatos, 2008. "Two Exotic Lookback Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(4), pages 387-402.
    8. Hyong-chol O, 2013. "The Pricing of A Moving Barrier Option," Papers 1303.1296, arXiv.org.
    9. Otto Konstandatos & Timothy Kyng, 2012. "Real Options Analysis for Commodity Based Mining Enterprises with Compound and Barrier Features," Accounting and Finance Research, Sciedu Press, vol. 1(2), pages 216-216, November.
    10. Fergusson, Kevin, 2020. "Less-Expensive Valuation And Reserving Of Long-Dated Variable Annuities When Interest Rates And Mortality Rates Are Stochastic," ASTIN Bulletin, Cambridge University Press, vol. 50(2), pages 381-417, May.
    11. Hyong-Chol O & Ji-Sok Kim, 2013. "General Properties of Solutions to Inhomogeneous Black-Scholes Equations with Discontinuous Maturity Payoffs and Application," Papers 1309.6505, arXiv.org, revised Sep 2013.
    12. Hyong-Chol O & Tae-Song Kim & Tae-Song Choe, 2021. "Solution Representations of Solving Problems for the Black-Scholes equations and Application to the Pricing Options on Bond with Credit Risk," Papers 2109.10818, arXiv.org, revised Nov 2021.
    13. Hyong-Chol O & Song-Yon Kim & Dong-Hyok Kim & Chol-Hyok Pak, 2013. "Comprehensive Unified Models of Structural and Reduced Form Models for Defaultable Fixed Income Bonds (Part 1: One factor-model, Part 2:Two factors-model)," Papers 1309.1647, arXiv.org, revised Sep 2013.
    14. Hyong Chol O & Tae Song Kim, 2020. "Analysis on the Pricing model for a Discrete Coupon Bond with Early redemption provision by the Structural Approach," Papers 2007.01511, arXiv.org.
    15. repec:uts:finphd:40 is not listed on IDEAS
    16. Hyong-Chol O & Tae-Song Choe, 2022. "General properties of the Solutions to Moving Boundary Problems for Black-Sholes Equations," Papers 2203.05726, arXiv.org.
    17. Hyong-Chol O & Mun-Chol KiM, 2013. "The Pricing of Multiple-Expiry Exotics," Papers 1302.3319, arXiv.org, revised Aug 2013.
    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. Chudjakow, Tatjana & Vorbrink, Jörg, 2011. "Exercise strategies for American exotic options under ambiguity," Center for Mathematical Economics Working Papers 421, Center for Mathematical Economics, Bielefeld University.
    20. 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.
    21. Hyong-Chol O & Dae-Sung Choe, 2019. "Pricing Formulae of Power Binary and Normal Distribution Standard Options and Applications," Papers 1903.04106, arXiv.org.
    22. Kevin John Fergusson, 2018. "Less-Expensive Pricing and Hedging of Extreme-Maturity Interest Rate Derivatives and Equity Index Options Under the Real-World Measure," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 3-2018.

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