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Laplacian risk management

Author

Listed:
  • Madan, Dilip B.
  • Smith, Robert H.
  • Wang, King

Abstract

Risk management is developed by using implied volatilities associated with a Laplacian base density as opposed to the normal distribution. Expressions are derived for all the Laplacian greeks. The Laplacian implied volatilities and greeks are compared with their Gaussian counterparts. Differences in hedges are illustrated by hedging long dated straddles using short maturity options. The Laplacian hedge delivers cash flows with a lower final variability in the case presented. The computation speed of Laplacian entities is also observed to be substantially faster as there are no calls to the cumnorm function.

Suggested Citation

  • Madan, Dilip B. & Smith, Robert H. & Wang, King, 2017. "Laplacian risk management," Finance Research Letters, Elsevier, vol. 22(C), pages 202-210.
    • Handle: RePEc:eee:finlet:v:22:y:2017:i:c:p:202-210
    DOI: 10.1016/j.frl.2016.12.013
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    References listed on IDEAS

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    1. Dilip B. Madan, 2016. "Adapted hedging," Annals of Finance, Springer, vol. 12(3), pages 305-334, December.
    2. 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..
    3. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Madan, Dilip B. & Wang, King, 2018. "Strike asymptotics for Laplace implied volatilities," Finance Research Letters, Elsevier, vol. 25(C), pages 183-189.
    2. Dilip B. Madan & Sofie Reyners & Wim Schoutens, 2019. "Advanced model calibration on bitcoin options," Digital Finance, Springer, vol. 1(1), pages 117-137, November.
    3. Tobias Behrens & Gero Junike, 2023. "Greeks' pitfalls for the COS method in the Laplace model," Papers 2306.08421, arXiv.org, revised Jul 2023.
    4. Christian Gouriéroux & Yang Lu, 2023. "Noncausal affine processes with applications to derivative pricing," Mathematical Finance, Wiley Blackwell, vol. 33(3), pages 766-796, July.

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    More about this item

    Keywords

    Local volatility; Compound Poisson; Theta; Gamma; Vega; Volga and vanna;
    All these keywords.

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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