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Sensitivity analysis of long-term cash flows

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  • Hyungbin Park

    (Seoul National University)

Abstract

This paper conducts a sensitivity analysis of long-term cash flows. The price of the cash flow at time zero is given by the pricing operator of a Markov diffusion acting on the cash flow function. We study the extent to which the price of the cash flow is affected by small perturbations of the underlying Markov diffusion. The main tool is the Hansen–Scheinkman decomposition, which is a method to express the cash flow in terms of eigenvalues and eigenfunctions of the pricing operator. By incorporating techniques developed by Fournié et al. (Finance Stoch. 3:391–412, 1999), the sensitivities of long-term cash flows can be represented via simple expressions in terms of eigenvalues and eigenfunctions.

Suggested Citation

  • Hyungbin Park, 2018. "Sensitivity analysis of long-term cash flows," Finance and Stochastics, Springer, vol. 22(4), pages 773-825, October.
    • Handle: RePEc:spr:finsto:v:22:y:2018:i:4:d:10.1007_s00780-018-0370-x
    DOI: 10.1007/s00780-018-0370-x
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    References listed on IDEAS

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    1. Jaroslav Borovička & Lars P. Hansen & Jose A. Scheinkman, 2014. "Shock Elasticities and Impulse Responses," NBER Working Papers 20104, National Bureau of Economic Research, Inc.
    2. Youssef El-Khatib & Nicolas Privault, 2004. "Computations of Greeks in a market with jumps via the Malliavin calculus," Finance and Stochastics, Springer, vol. 8(2), pages 161-179, May.
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    4. Davis, Mark H.A. & Johansson, Martin P., 2006. "Malliavin Monte Carlo Greeks for jump diffusions," Stochastic Processes and their Applications, Elsevier, vol. 116(1), pages 101-129, January.
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    6. Tim Leung & Ronnie Sircar, 2015. "Implied Volatility of Leveraged ETF Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 22(2), pages 162-188, April.
    7. Eric Fournié & Jean-Michel Lasry & Pierre-Louis Lions & Jérôme Lebuchoux & Nizar Touzi, 1999. "Applications of Malliavin calculus to Monte Carlo methods in finance," Finance and Stochastics, Springer, vol. 3(4), pages 391-412.
    8. Bernard Wong & C. C. Heyde, 2006. "On changes of measure in stochastic volatility models," International Journal of Stochastic Analysis, Hindawi, vol. 2006, pages 1-13, December.
    9. Eric Benhamou, 2003. "Optimal Malliavin Weighting Function for the Computation of the Greeks," Mathematical Finance, Wiley Blackwell, vol. 13(1), pages 37-53, January.
    10. Likuan Qin & Vadim Linetsky, 2016. "Positive Eigenfunctions of Markovian Pricing Operators: Hansen-Scheinkman Factorization, Ross Recovery, and Long-Term Pricing," Operations Research, INFORMS, vol. 64(1), pages 99-117, February.
    11. Lars Peter Hansen, 2012. "Dynamic Valuation Decomposition Within Stochastic Economies," Econometrica, Econometric Society, vol. 80(3), pages 911-967, May.
    12. Lars Hansen & José Scheinkman, 2012. "Pricing growth-rate risk," Finance and Stochastics, Springer, vol. 16(1), pages 1-15, January.
    13. Chen, Nan & Glasserman, Paul, 2007. "Malliavin Greeks without Malliavin calculus," Stochastic Processes and their Applications, Elsevier, vol. 117(11), pages 1689-1723, November.
    14. Ahn, Dong-Hyun & Gao, Bin, 1999. "A Parametric Nonlinear Model of Term Structure Dynamics," The Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 721-762.
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    Cited by:

    1. Hyungbin Park, 2021. "Influence of risk tolerance on long-term investments: A Malliavin calculus approach," Papers 2104.00911, arXiv.org.
    2. Hyungbin Park & Heejun Yeo, 2022. "Dynamic and static fund separations and their stability for long-term optimal investments," Papers 2212.00391, arXiv.org, revised Mar 2023.
    3. Hyungbin Park, 2019. "Convergence rates of large-time sensitivities with the Hansen--Scheinkman decomposition," Papers 1912.03404, arXiv.org, revised Jan 2021.
    4. Hyungbin Park, 2021. "Modified Mean-Variance Risk Measures for Long-Term Portfolios," Mathematics, MDPI, vol. 9(2), pages 1-23, January.

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    More about this item

    Keywords

    Long-term cash flows; Hansen–Scheinkman decomposition; Sensitivity analysis;
    All these keywords.

    JEL classification:

    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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