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LSV models with stochastic interest rates and correlated jumps

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  • Andrey Itkin

Abstract

Pricing and hedging exotic options using local stochastic volatility models drew a serious attention within the last decade, and nowadays became almost a standard approach to this problem. In this paper we show how this framework could be extended by adding to the model stochastic interest rates and correlated jumps in all three components. We also propose a new fully implicit modification of the popular Hundsdorfer and Verwer and Modified Craig-Sneyd finite-difference schemes which provides second order approximation in space and time, is unconditionally stable and preserves positivity of the solution, while still has a linear complexity in the number of grid nodes.

Suggested Citation

  • Andrey Itkin, 2015. "LSV models with stochastic interest rates and correlated jumps," Papers 1511.01460, arXiv.org, revised Nov 2016.
  • Handle: RePEc:arx:papers:1511.01460
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    References listed on IDEAS

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    1. Carl Chiarella & Boda Kang & Gunter H. Meyer & Andrew Ziogas, 2009. "The Evaluation Of American Option Prices Under Stochastic Volatility And Jump-Diffusion Dynamics Using The Method Of Lines," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 12(03), pages 393-425.
    2. Ako Doffou & Jimmy E. Hilliard, 2001. "Pricing Currency Options Under Stochastic Interest Rates And Jump-Diffusion Processes," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 24(4), pages 565-585, December.
    3. Carr, Peter & Wu, Liuren, 2004. "Time-changed Levy processes and option pricing," Journal of Financial Economics, Elsevier, vol. 71(1), pages 113-141, January.
    4. Michael Johannes, 2004. "The Statistical and Economic Role of Jumps in Continuous-Time Interest Rate Models," Journal of Finance, American Finance Association, vol. 59(1), pages 227-260, February.
    5. Das, Sanjiv R., 2002. "The surprise element: jumps in interest rates," Journal of Econometrics, Elsevier, vol. 106(1), pages 27-65, January.
    6. Andrey Itkin, 2013. "Efficient Solution of Backward Jump-Diffusion PIDEs with Splitting and Matrix Exponentials," Papers 1304.3159, arXiv.org, revised Apr 2014.
    7. Carl Chiarella & Boda Kang, 2009. "The Evaluation of American Compound Option Prices Under Stochastic Volatility Using the Sparse Grid Approach," Research Paper Series 245, Quantitative Finance Research Centre, University of Technology, Sydney.
    8. Svetlana Boyarchenko & Sergei Levendorskiń¨, 2013. "American Options in the Heston Model with Stochastic Interest Rate and Its Generalizations," Applied Mathematical Finance, Taylor & Francis Journals, vol. 20(1), pages 26-49, March.
    9. repec:wsi:ijtafx:v:18:y:2015:i:05:n:s0219024915500314 is not listed on IDEAS
    10. Grzelak, Lech & Oosterlee, Kees, 2009. "On The Heston Model with Stochastic Interest Rates," MPRA Paper 20620, University Library of Munich, Germany, revised 18 Jan 2010.
    11. Andrey Itkin, 2014. "Splitting and Matrix Exponential approach for jump-diffusion models with Inverse Normal Gaussian, Hyperbolic and Meixner jumps," Papers 1405.6111, arXiv.org, revised May 2014.
    12. Andrey Itkin, 2013. "New solvable stochastic volatility models for pricing volatility derivatives," Review of Derivatives Research, Springer, vol. 16(2), pages 111-134, July.
    13. Andrey Itkin & Alexander Lipton, 2014. "Efficient solution of structural default models with correlated jumps and mutual obligations," Papers 1408.6513, arXiv.org, revised Nov 2014.
    14. Andrey Itkin, 2015. "HIGH ORDER SPLITTING METHODS FOR FORWARD PDEs AND PIDEs," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(05), pages 1-24.
    15. Garland Durham & Yang-Ho Park, 2013. "Beyond Stochastic Volatility and Jumps in Returns and Volatility," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(1), pages 107-121, January.
    16. Medvedev, Alexey & Scaillet, Olivier, 2010. "Pricing American options under stochastic volatility and stochastic interest rates," Journal of Financial Economics, Elsevier, vol. 98(1), pages 145-159, October.
    17. Doffou, Ako & Hilliard, Jimmy E, 2001. "Pricing Currency Options under Stochastic Interest Rates and Jump-Diffusion Processes," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 24(4), pages 565-585, Winter.
    18. Igor Halperin & Andrey Itkin, 2013. "USLV: Unspanned Stochastic Local Volatility Model," Papers 1301.4442, arXiv.org, revised Mar 2013.
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    Cited by:

    1. Maria Cristina Recchioni & Yu Sun & Gabriele Tedeschi, 2016. "Can negative interest rates really affect option pricing? Empirical evidence from an explicitly solvable stochastic volatility model," Working Papers 2016/23, Economics Department, Universitat Jaume I, Castellón (Spain).
    2. Andrey Itkin, 2017. "Modeling stochastic skew of FX options using SLV models with stochastic spot/vol correlation and correlated jumps," Papers 1701.02821, arXiv.org, revised Jan 2017.
    3. Blessing Taruvinga & Boda Kang & Christina Sklibosios Nikitopoulos, 2018. "Pricing American Options with Jumps in Asset and Volatility," Research Paper Series 394, Quantitative Finance Research Centre, University of Technology, Sydney.

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