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A PDE approach for risk measures for derivatives with regime switching

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  • Robert Elliott
  • Tak Siu
  • Leunglung Chan

Abstract

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Suggested Citation

  • Robert Elliott & Tak Siu & Leunglung Chan, 2008. "A PDE approach for risk measures for derivatives with regime switching," Annals of Finance, Springer, vol. 4(1), pages 55-74, January.
    • Handle: RePEc:kap:annfin:v:4:y:2008:i:1:p:55-74
    DOI: 10.1007/s10436-006-0068-5
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    References listed on IDEAS

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    1. David D. Yao & Qing Zhang & Xun Yu Zhou, 2006. "A Regime-Switching Model for European Options," International Series in Operations Research & Management Science, in: Houmin Yan & George Yin & Qing Zhang (ed.), Stochastic Processes, Optimization, and Control Theory: Applications in Financial Engineering, Queueing Networks, and Manufacturing Systems, chapter 0, pages 281-300, Springer.
    2. Tak Kuen Siu & Howell Tong & Hailiang Yang, 2001. "Bayesian Risk Measures for Derivatives via Random Esscher Transform," North American Actuarial Journal, Taylor & Francis Journals, vol. 5(3), pages 78-91.
    3. Robert J. Elliott & Leunglung Chan & Tak Kuen Siu, 2005. "Option pricing and Esscher transform under regime switching," Annals of Finance, Springer, vol. 1(4), pages 423-432, October.
    4. X. Guo, 2001. "Information and option pricings," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 38-44.
    5. Robert J. Elliott & John van der Hoek, 1997. "An application of hidden Markov models to asset allocation problems (*)," Finance and Stochastics, Springer, vol. 1(3), pages 229-238.
    6. Philippe Artzner & Freddy Delbaen & Jean‐Marc Eber & David Heath, 1999. "Coherent Measures of Risk," Mathematical Finance, Wiley Blackwell, vol. 9(3), pages 203-228, July.
    7. Elliott, R. J. & Malcolm, W. P. & Tsoi, Allanus H., 2003. "Robust parameter estimation for asset price models with Markov modulated volatilities," Journal of Economic Dynamics and Control, Elsevier, vol. 27(8), pages 1391-1409, June.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Date, Paresh & Mamon, Rogemar & Tenyakov, Anton, 2013. "Filtering and forecasting commodity futures prices under an HMM framework," Energy Economics, Elsevier, vol. 40(C), pages 1001-1013.
    2. Mengzhe Zhang & Leunglung Chan, 2016. "Pricing volatility swaps in the Heston’s stochastic volatility model with regime switching: A saddlepoint approximation method," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(04), pages 1-20, December.
    3. Siu, Tak Kuen, 2016. "A functional Itô’s calculus approach to convex risk measures with jump diffusion," European Journal of Operational Research, Elsevier, vol. 250(3), pages 874-883.
    4. Jiao Li, 2016. "Trading VIX futures under mean reversion with regime switching," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 1-20, September.
    5. Siu, Tak Kuen, 2008. "A game theoretic approach to option valuation under Markovian regime-switching models," Insurance: Mathematics and Economics, Elsevier, vol. 42(3), pages 1146-1158, June.
    6. Robert Elliott & Leunglung Chan & Tak Siu, 2006. "Risk measures for derivatives with Markov-modulated pure jump processes," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 13(2), pages 129-149, June.
    7. Fei Lung Yuen & Hailiang Yang, 2012. "Optimal Asset Allocation: A Worst Scenario Expectation Approach," Journal of Optimization Theory and Applications, Springer, vol. 153(3), pages 794-811, June.
    8. Jiao Li, 2016. "Trading VIX Futures under Mean Reversion with Regime Switching," Papers 1605.07945, arXiv.org, revised Jun 2016.

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    More about this item

    Keywords

    Risk measures; Regime-switching PDE; Regime-switching HJB equation; Stochastic optimal control; Esscher transform; Delta-neutral hedging; Jump risk; American options; Exotic options; G32; G13;
    All these keywords.

    JEL classification:

    • G32 - Financial Economics - - Corporate Finance and Governance - - - Financing Policy; Financial Risk and Risk Management; Capital and Ownership Structure; Value of Firms; Goodwill
    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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