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Strike asymptotics for Laplace implied volatilities

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  • Madan, Dilip B.
  • Wang, King

Abstract

Laplace implied volatilities unlike their Black Merton Scholes counterparts are bounded above by the square root of 2. In the extremes they are proportional to the square root of one minus the negative exponential of absolute log moneyness. Extreme strike estimates of proportionality for the S&P 500 index indicate an increase in the number of finite positive moments with the set of finite negative moments remaining unchanged. More moments are finite on both sides at the longer maturities.

Suggested Citation

  • Madan, Dilip B. & Wang, King, 2018. "Strike asymptotics for Laplace implied volatilities," Finance Research Letters, Elsevier, vol. 25(C), pages 183-189.
    • Handle: RePEc:eee:finlet:v:25:y:2018:i:c:p:183-189
    DOI: 10.1016/j.frl.2017.10.015
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    1. Todorov, Viktor & Tauchen, George & Grynkiv, Iaryna, 2011. "Realized Laplace transforms for estimation of jump diffusive volatility models," Journal of Econometrics, Elsevier, vol. 164(2), pages 367-381, October.
    2. Curato, Imma Valentina & Mancino, Maria Elvira & Recchioni, Maria Cristina, 2018. "Spot volatility estimation using the Laplace transform," Econometrics and Statistics, Elsevier, vol. 6(C), pages 22-43.
    3. 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..
    4. 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.
    5. Viktor Todorov & George Tauchen, 2011. "Inverse Realized Laplace Transforms for Nonparametric Volatility Estimation in Jump-Diffusions," Working Papers 11-21, Duke University, Department of Economics.
    6. Madan, Dilip B. & Smith, Robert H. & Wang, King, 2017. "Laplacian risk management," Finance Research Letters, Elsevier, vol. 22(C), pages 202-210.
    7. Roger W. Lee, 2004. "The Moment Formula For Implied Volatility At Extreme Strikes," Mathematical Finance, Wiley Blackwell, vol. 14(3), pages 469-480, July.
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