IDEAS home Printed from https://ideas.repec.org/a/sae/ausman/v22y1997i1p1-20.html
   My bibliography  Save this article

The Pricing of Marked†to†Market Contingent Claims in a No†Arbitrage Economy

Author

Listed:
  • Stephen E. Satchell

    (Trinity College, Trinity Street, Cambridge CB2 1TQ, UK.)

  • Richard C. Stapleton

    (The Management School, Lancaster University, Bailrigg, Lancaster, LA1 4YW, UK.)

  • Marti G. Subrahmanyam

    (Stern School of Business, New York University, Salomon Center, 40th West Fourth Street, New York NY 10012–1118, USA; E†mail: msubrahm@stern.nyu.edu)

Abstract

This paper assumes that the underlying asset prices are lognormally distributed, and derives necessary and sufficient conditions for the valuation of options using a Black†Scholes type methodology. It is shown that the price of a futures†style, marked†to†market option is given by Black's for Mula if the pricing kernel is lognormally distributed. Assuming that this condition is fulfilled, it is then shown that the Black†Scholes for Mula prices a spot†settled contingent claim, if the interest†rate accumulation factor is lognormally distributed. Otherwise, the Black†Scholes for Mula holds if the product of the pricing kernel and the interest†rate accumulation factor is lognormally distributed.

Suggested Citation

  • Stephen E. Satchell & Richard C. Stapleton & Marti G. Subrahmanyam, 1997. "The Pricing of Marked†to†Market Contingent Claims in a No†Arbitrage Economy," Australian Journal of Management, Australian School of Business, vol. 22(1), pages 1-20, June.
    • Handle: RePEc:sae:ausman:v:22:y:1997:i:1:p:1-20
    DOI: 10.1177/031289629702200101
    as

    Download full text from publisher

    File URL: https://journals.sagepub.com/doi/10.1177/031289629702200101
    Download Restriction: no
    File URL: https://libkey.io/10.1177/031289629702200101?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
    ---><---

    References listed on IDEAS

    as
    1. Brenner, Menachem & Courtadon, Georges & Subrahmanyam, Marti, 1985. "Options on the Spot and Options on Futures," Journal of Finance, American Finance Association, vol. 40(5), pages 1303-1317, December.
    2. Ho, T S & Stapleton, Richard C & Subrahmanyam, Marti G, 1997. "The Valuation of American Options with Stochastic Interest Rates: A Generalization of the Geske-Johnson Technique," Journal of Finance, American Finance Association, vol. 52(2), pages 827-840, June.
    3. Derming Lieu, 1990. "Option pricing with futures‐style margining," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 10(4), pages 327-338, August.
    4. Jamshidian, Farshid, 1989. " An Exact Bond Option Formula," Journal of Finance, American Finance Association, vol. 44(1), pages 205-209, March.
    5. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    6. Ramaswamy, Krishna & Sundaresan, Suresh M, 1985. "The Valuation of Options on Futures Contracts," Journal of Finance, American Finance Association, vol. 40(5), pages 1319-1340, December.
    7. Hodrick, Robert J. & Srivastava, Sanjay, 1987. "Foreign currency futures," Journal of International Economics, Elsevier, vol. 22(1-2), pages 1-24, February.
    8. Chen, Ren-Raw, 1992. "Exact Solutions for Futures and European Futures Options on Pure Discount Bonds," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 27(1), pages 97-107, March.
    9. Mark Rubinstein, 1976. "The Valuation of Uncertain Income Streams and the Pricing of Options," Bell Journal of Economics, The RAND Corporation, vol. 7(2), pages 407-425, Autumn.
    10. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "An Intertemporal General Equilibrium Model of Asset Prices," Econometrica, Econometric Society, vol. 53(2), pages 363-384, March.
    11. Duffie, Darrell & Stanton, Richard, 1992. "Pricing continuously resettled contingent claims," Journal of Economic Dynamics and Control, Elsevier, vol. 16(3-4), pages 561-573.
    12. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    13. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    14. French, Kenneth R., 1983. "A comparison of futures and forward prices," Journal of Financial Economics, Elsevier, vol. 12(3), pages 311-342, November.
    15. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    16. Brennan, M J, 1979. "The Pricing of Contingent Claims in Discrete Time Models," Journal of Finance, American Finance Association, vol. 34(1), pages 53-68, March.
    17. Cox, John C. & Ingersoll, Jonathan Jr. & Ross, Stephen A., 1981. "The relation between forward prices and futures prices," Journal of Financial Economics, Elsevier, vol. 9(4), pages 321-346, December.
    18. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
    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. Ho, T. S. & Stapleton, Richard C. & Subrahmanyam, Marti G., 1997. "The valuation of American options on bonds1," Journal of Banking & Finance, Elsevier, vol. 21(11-12), pages 1487-1513, December.

    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. 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.
    2. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    3. repec:dau:papers:123456789/5374 is not listed on IDEAS
    4. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.
    5. Mondher Bellalah, 2009. "Derivatives, Risk Management & Value," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 7175, December.
    6. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742, Decembrie.
    7. Munk, Claus, 2015. "Financial Asset Pricing Theory," OUP Catalogue, Oxford University Press, number 9780198716457, Decembrie.
    8. Raimbourg, Philippe & Zimmermann, Paul, 2022. "Is normal backwardation normal? Valuing financial futures with a local index-rate covariance," European Journal of Operational Research, Elsevier, vol. 298(1), pages 351-367.
    9. 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.
    10. repec:uts:finphd:40 is not listed on IDEAS
    11. Ke Du, 2013. "Commodity Derivative Pricing Under the Benchmark Approach," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2013.
    12. David S. Bates, 1995. "Testing Option Pricing Models," NBER Working Papers 5129, National Bureau of Economic Research, Inc.
    13. Jean-Paul Décamps, 1993. "Valorisation de produits obligataires dans un modéle d'équilibre général en temps discret," Annals of Economics and Statistics, GENES, issue 31, pages 73-100.
    14. Sercu, P., 1991. "Bond options and bond portfolio insurance," Insurance: Mathematics and Economics, Elsevier, vol. 10(3), pages 203-230, December.
    15. David Babbel & Craig Merrill, 1998. "Economic Valuation Models for Insurers," North American Actuarial Journal, Taylor & Francis Journals, vol. 2(3), pages 1-15.
    16. 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.
    17. John Crosby, 2008. "A multi-factor jump-diffusion model for commodities," Quantitative Finance, Taylor & Francis Journals, vol. 8(2), pages 181-200.
    18. Constantin Mellios, 2001. "Valuation of Interest Rate Options in a Two-Factor Model of the Term Structure of Interest Rate," Working Papers 2001-1, Laboratoire Orléanais de Gestion - université d'Orléans.
    19. Ke Du, 2013. "Commodity Derivative Pricing Under the Benchmark Approach," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2, July-Dece.
    20. Carl Chiarella & Xue-Zhong He & Christina Sklibosios Nikitopoulos, 2015. "Derivative Security Pricing," Dynamic Modeling and Econometrics in Economics and Finance, Springer, edition 127, number 978-3-662-45906-5, July-Dece.
    21. Robert A. Jarrow, 2009. "The Term Structure of Interest Rates," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 69-96, November.
    22. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.

    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:sae:ausman:v:22:y:1997:i:1:p:1-20. 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: SAGE Publications (email available below). General contact details of provider: http://www.agsm.edu.au .

    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.