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Options and the Gamma Knife

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  • Martin, Ian

Abstract

I survey work of Steve Ross (1976) and of Douglas Breeden and Robert Litzenberger (1978) that first showed how to use options to synthesize more complex securities. Their results made it possible to infer the risk-neutral measure associated with a traded asset, and underpinned the development of the VIX index. The other main result of Ross (1976), which shows how to infer joint risk-neutral distributions from option prices, has been much less influential. I explain why, and propose an alternative approach to the problem. This paper is dedicated to Steve Ross, and was written for a special issue of the Journal of Portfolio Management in memory of him.

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  • Martin, Ian, 2018. "Options and the Gamma Knife," CEPR Discussion Papers 12883, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:12883
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    1. Ian W. R. Martin & Christian Wagner, 2019. "What Is the Expected Return on a Stock?," Journal of Finance, American Finance Association, vol. 74(4), pages 1887-1929, August.
    2. David Backus & Mikhail Chernov & Ian Martin, 2011. "Disasters Implied by Equity Index Options," Journal of Finance, American Finance Association, vol. 66(6), pages 1969-2012, December.
    3. Martin, Ian W. R. & Ross, Stephen A., 2019. "Notes on the yield curve," Journal of Financial Economics, Elsevier, vol. 134(3), pages 689-702.
    4. 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..
    5. Arditti, Fred D. & John, Kose, 1980. "Spanning the State Space with Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 15(1), pages 1-9, March.
    6. Fernando Alvarez & Urban J. Jermann, 2005. "Using Asset Prices to Measure the Persistence of the Marginal Utility of Wealth," Econometrica, Econometric Society, vol. 73(6), pages 1977-2016, November.
    7. Breeden, Douglas T & Litzenberger, Robert H, 1978. "Prices of State-contingent Claims Implicit in Option Prices," The Journal of Business, University of Chicago Press, vol. 51(4), pages 621-651, October.
    8. Ian Martin, 2017. "What is the Expected Return on the Market?," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 132(1), pages 367-433.
    9. Lukas Kremens & Ian Martin, 2019. "The Quanto Theory of Exchange Rates," American Economic Review, American Economic Association, vol. 109(3), pages 810-843, March.
    10. Stephen A. Ross, 1976. "Options and Efficiency," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 90(1), pages 75-89.
    11. Steve Ross, 2015. "The Recovery Theorem," Journal of Finance, American Finance Association, vol. 70(2), pages 615-648, April.
    12. Jouini,E. & Cvitanic,J. & Musiela,Marek (ed.), 2001. "Handbooks in Mathematical Finance," Cambridge Books, Cambridge University Press, number 9780521792370, October.
    13. 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.
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    Cited by:

    1. Lukas Kremens & Ian Martin, 2019. "The Quanto Theory of Exchange Rates," American Economic Review, American Economic Association, vol. 109(3), pages 810-843, March.
    2. Jianlei Han & Martina Linnenluecke & Zhangxin Liu & Zheyao Pan & Tom Smith, 2019. "A general equilibrium approach to pricing volatility risk," PLOS ONE, Public Library of Science, vol. 14(4), pages 1-18, April.

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    More about this item

    Keywords

    Option prices; Gamma knife; Arrow-debreu securities; Risk-neutral distribution; Vix; Svix; Radon transform; Derivatives;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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