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Jump-Diffusion Processes: Volatility Smile Fitting and Numerical Methods for Option Pricing

Citations

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Cited by:

  1. Y. Wang & H. Yin & L. Qi, 2004. "No-Arbitrage Interpolation of the Option Price Function and Its Reformulation," Journal of Optimization Theory and Applications, Springer, vol. 120(3), pages 627-649, March.
  2. Agnieszka Janek & Tino Kluge & Rafal Weron & Uwe Wystup, 2010. "FX Smile in the Heston Model," HSC Research Reports HSC/10/02, Hugo Steinhaus Center, Wroclaw University of Technology.
  3. Georgiev, Slavi G. & Vulkov, Lubin G., 2021. "Computation of the unknown volatility from integral option price observations in jump–diffusion models," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 188(C), pages 591-608.
  4. N. Hilber & N. Reich & C. Schwab & C. Winter, 2009. "Numerical methods for Lévy processes," Finance and Stochastics, Springer, vol. 13(4), pages 471-500, September.
  5. Leila Khodayari & Mojtaba Ranjbar, 2017. "A Numerical Method to Approximate Multi-Asset Option Pricing Under Exponential Lévy Model," Computational Economics, Springer;Society for Computational Economics, vol. 50(2), pages 189-205, August.
  6. Carol Alexander & Leonardo M. Nogueira, 2004. "Hedging with Stochastic and Local Volatility," ICMA Centre Discussion Papers in Finance icma-dp2004-10, Henley Business School, University of Reading, revised Dec 2004.
  7. 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.
  8. Cristian Homescu, 2011. "Implied Volatility Surface: Construction Methodologies and Characteristics," Papers 1107.1834, arXiv.org.
  9. Kuo-Shing Chen & Yu-Chuan Huang, 2021. "Detecting Jump Risk and Jump-Diffusion Model for Bitcoin Options Pricing and Hedging," Mathematics, MDPI, vol. 9(20), pages 1-24, October.
  10. Ke Nian & Thomas F. Coleman & Yuying Li, 2018. "Learning minimum variance discrete hedging directly from the market," Quantitative Finance, Taylor & Francis Journals, vol. 18(7), pages 1115-1128, July.
  11. T. F. Coleman & Y. Kim & Y. Li & M. Patron, 2007. "Robustly Hedging Variable Annuities With Guarantees Under Jump and Volatility Risks," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 74(2), pages 347-376, June.
  12. Ioannis Kyriakou & Panos K. Pouliasis & Nikos C. Papapostolou & Nikos K. Nomikos, 2018. "Income uncertainty and the decision to invest in bulk shipping," European Financial Management, European Financial Management Association, vol. 24(3), pages 387-417, June.
  13. Kuldip Singh Patel & Mani Mehra, 2018. "Fourth-Order Compact Scheme For Option Pricing Under The Merton’S And Kou’S Jump-Diffusion Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(04), pages 1-26, June.
  14. H. A. Windcliff & P. A. Forsyth & K. R. Vetzal, 2006. "Numerical Methods and Volatility Models for Valuing Cliquet Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(4), pages 353-386.
  15. Jean-Pierre Fouque & Ning Ning, 2017. "Uncertain Volatility Models with Stochastic Bounds," Papers 1702.05036, arXiv.org.
  16. Alexander Lipton & Andrey Gal & Andris Lasis, 2013. "Pricing of vanilla and first generation exotic options in the local stochastic volatility framework: survey and new results," Papers 1312.5693, arXiv.org.
  17. Orcan Ogetbil & Bernhard Hientzsch, 2020. "Extensions of Dupire Formula: Stochastic Interest Rates and Stochastic Local Volatility," Papers 2005.05530, arXiv.org, revised Feb 2023.
  18. Andrey Itkin, 2017. "Modelling stochastic skew of FX options using SLV models with stochastic spot/vol correlation and correlated jumps," Applied Mathematical Finance, Taylor & Francis Journals, vol. 24(6), pages 485-519, November.
  19. Campi, L. & Polbennikov, S.Y. & Sbuelz, A., 2005. "Assessing Credit with Equity : A CEV Model with Jump to Default," Other publications TiSEM 21b78fcf-8401-4e4d-8224-7, Tilburg University, School of Economics and Management.
  20. H. Yin & Y. Wang & L. Qi, 2009. "Shape-Preserving Interpolation and Smoothing for Options Market Implied Volatility," Journal of Optimization Theory and Applications, Springer, vol. 142(1), pages 243-266, July.
  21. Emmanuel Hanert & Aanand Venkatramanan, 2008. "Meshfree Approximation for Multi-Asset Options," ICMA Centre Discussion Papers in Finance icma-dp2009-07, Henley Business School, University of Reading, revised Jun 2009.
  22. Karl Friedrich Mina & Gerald H. L. Cheang & Carl Chiarella, 2015. "Approximate Hedging Of Options Under Jump-Diffusion Processes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(04), pages 1-26.
  23. Kai Yin & Anirban Mondal, 2023. "Bayesian uncertainty quantification of local volatility model," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 290-324, May.
  24. J. K. Hoogland & C. D. D. Neumann & M. H. Vellekoop, 2003. "Symmetries In Jump-Diffusion Models With Applications In Option Pricing And Credit Risk," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 6(02), pages 135-172.
  25. Dan Pirjol & Lingjiong Zhu, 2023. "Asymptotics for Short Maturity Asian Options in Jump-Diffusion models with Local Volatility," Papers 2308.15672, arXiv.org, revised Feb 2024.
  26. Kozarski, R., 2013. "Pricing and hedging in the VIX derivative market," Other publications TiSEM 221fefe0-241e-4914-b6bd-c, Tilburg University, School of Economics and Management.
  27. Tim Leung & Marco Santoli, 2014. "Accounting for earnings announcements in the pricing of equity options," Journal of Financial Engineering (JFE), World Scientific Publishing Co. Pte. Ltd., vol. 1(04), pages 1-46.
  28. Zhang, Le & Schmidt, Wolfgang M., 2016. "An approximation of small-time probability density functions in a general jump diffusion model," Applied Mathematics and Computation, Elsevier, vol. 273(C), pages 741-758.
  29. Antonie Kotzé & Rudolf Oosthuizen & Edson Pindza, 2015. "Implied and Local Volatility Surfaces for South African Index and Foreign Exchange Options," JRFM, MDPI, vol. 8(1), pages 1-40, January.
  30. Carl Chiarella & Andrew Ziogas, 2009. "American Call Options Under Jump-Diffusion Processes - A Fourier Transform Approach," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(1), pages 37-79.
  31. Windcliff, H. & Forsyth, P.A. & Vetzal, K.R., 2006. "Pricing methods and hedging strategies for volatility derivatives," Journal of Banking & Finance, Elsevier, vol. 30(2), pages 409-431, February.
  32. Hilliard, Jimmy E. & Hilliard, Jitka, 2019. "A jump-diffusion model for pricing and hedging with margined options: An application to Brent crude oil contracts," Journal of Banking & Finance, Elsevier, vol. 98(C), pages 137-155.
  33. Pierre Collin-Dufresne & Robert S. Goldstein & Fan Yang, 2010. "On the Relative Pricing of long Maturity S&P 500 Index Options and CDX Tranches," NBER Working Papers 15734, National Bureau of Economic Research, Inc.
  34. Jérôme Detemple, 2014. "Optimal Exercise for Derivative Securities," Annual Review of Financial Economics, Annual Reviews, vol. 6(1), pages 459-487, December.
  35. Christara, Christina C. & Leung, Nat Chun-Ho, 2016. "Option pricing in jump diffusion models with quadratic spline collocation," Applied Mathematics and Computation, Elsevier, vol. 279(C), pages 28-42.
  36. Recchioni, Maria Cristina & Tedeschi, Gabriele & Gallegati, Mauro, 2015. "A calibration procedure for analyzing stock price dynamics in an agent-based framework," Journal of Economic Dynamics and Control, Elsevier, vol. 60(C), pages 1-25.
  37. Andrey Itkin & Peter Carr, 2012. "Using Pseudo-Parabolic and Fractional Equations for Option Pricing in Jump Diffusion Models," Computational Economics, Springer;Society for Computational Economics, vol. 40(1), pages 63-104, June.
  38. Ron Tat Lung Chan, 2016. "Adaptive Radial Basis Function Methods for Pricing Options Under Jump-Diffusion Models," Computational Economics, Springer;Society for Computational Economics, vol. 47(4), pages 623-643, April.
  39. Stefano Galluccio & Yann Le Cam, 2005. "Implied Calibration of Stochastic Volatility Jump Diffusion Models," Finance 0510028, University Library of Munich, Germany.
  40. Company, Rafael & Egorova, Vera N. & Jódar, Lucas, 2021. "A front-fixing ETD numerical method for solving jump–diffusion American option pricing problems," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 189(C), pages 69-84.
  41. 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.
  42. Bakshi, Gurdip & Panayotov, George, 2010. "First-passage probability, jump models, and intra-horizon risk," Journal of Financial Economics, Elsevier, vol. 95(1), pages 20-40, January.
  43. Yulian Fan & Huadong Zhang, 2017. "The pricing of average options with jump diffusion processes in the uncertain volatility model," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 1-31, March.
  44. Cerrato, Mario & Lo, Chia Chun & Skindilias, Konstantinos, 2011. "Adaptive Continuous time Markov Chain Approximation Model to General Jump-Diusions," SIRE Discussion Papers 2011-53, Scottish Institute for Research in Economics (SIRE).
  45. Luciano Campi & Simon Polbennikov & Sbuelz, 2005. "Assessing Credit with Equity: A CEV Model with Jump to Default," Working Papers 24/2005, University of Verona, Department of Economics.
  46. Bilel Jarraya & Abdelfettah Bouri, 2013. "A Theoretical Assessment on Optimal Asset Allocations in Insurance Industry," International Journal of Finance & Banking Studies, Center for the Strategic Studies in Business and Finance, vol. 2(4), pages 30-44, October.
  47. Kuldip Singh Patel & Mani Mehra, 2018. "Fourth order compact scheme for option pricing under Merton and Kou jump-diffusion models," Papers 1804.07534, arXiv.org.
  48. Nomikos, Nikos K. & Kyriakou, Ioannis & Papapostolou, Nikos C. & Pouliasis, Panos K., 2013. "Freight options: Price modelling and empirical analysis," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 51(C), pages 82-94.
  49. Feunou Bruno & Tafolong Ernest, 2015. "Fourier inversion formulas for multiple-asset option pricing," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 19(5), pages 531-559, December.
  50. Gabriel Drimus & Walter Farkas, 2013. "Local volatility of volatility for the VIX market," Review of Derivatives Research, Springer, vol. 16(3), pages 267-293, October.
  51. Simonato, Jean-Guy, 2011. "Computing American option prices in the lognormal jump–diffusion framework with a Markov chain," Finance Research Letters, Elsevier, vol. 8(4), pages 220-226.
  52. Cyrus Ramezani & Yong Zeng, 2007. "Maximum likelihood estimation of the double exponential jump-diffusion process," Annals of Finance, Springer, vol. 3(4), pages 487-507, October.
  53. Chen, Z. & Vetzal, K. & Forsyth, P.A., 2008. "The effect of modelling parameters on the value of GMWB guarantees," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 165-173, August.
  54. Alexander Lipton & Artur Sepp, 2022. "Toward an efficient hybrid method for pricing barrier options on assets with stochastic volatility," Papers 2202.07849, arXiv.org.
  55. Farzad Alavi Fard & Firmin Doko Tchatoka & Sivagowry Sriananthakumar, 2021. "Maximum Entropy Evaluation of Asymptotic Hedging Error under a Generalised Jump-Diffusion Model," JRFM, MDPI, vol. 14(3), pages 1-19, February.
  56. Hatem Ben-Ameur & Rim Chérif & Bruno Rémillard, 2016. "American-style options in jump-diffusion models: estimation and evaluation," Quantitative Finance, Taylor & Francis Journals, vol. 16(8), pages 1313-1324, August.
  57. Vinicius Albani & Jorge Zubelli, 2018. "A Splitting Strategy for the Calibration of Jump-Diffusion Models," Papers 1811.02028, arXiv.org.
  58. Kyungsub Lee & Byoung Ki Seo, 2017. "Performance of Tail Hedged Portfolio with Third Moment Variation Swap," Computational Economics, Springer;Society for Computational Economics, vol. 50(3), pages 447-471, October.
  59. Itkin, Andrey, 2014. "Splitting and matrix exponential approach for jump-diffusion models with Inverse Normal Gaussian, Hyperbolic and Meixner jumps," Algorithmic Finance, IOS Press, vol. 3(3-4), pages 233-250.
  60. Xun Li & Ping Lin & Xue-Cheng Tai & Jinghui Zhou, 2015. "Pricing Two-asset Options under Exponential L\'evy Model Using a Finite Element Method," Papers 1511.04950, arXiv.org.
  61. Rehez Ahlip & Laurence A. F. Park & Ante Prodan, 2017. "Pricing currency options in the Heston/CIR double exponential jump-diffusion model," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 4(01), pages 1-30, March.
  62. Chan, Tat Lung (Ron), 2019. "Efficient computation of european option prices and their sensitivities with the complex fourier series method," The North American Journal of Economics and Finance, Elsevier, vol. 50(C).
  63. Nicola Bruti-Liberati, 2007. "Numerical Solution of Stochastic Differential Equations with Jumps in Finance," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2007.
  64. Farshid Jamshidian, 2004. "Numeraire-invariant option pricing and american, bermudan, trigger stream rollover (v1.6)," Finance 0407015, University Library of Munich, Germany.
  65. Kuldip Singh Patel & Mani Mehra, 2018. "Compact finite difference method for pricing European and American options under jump-diffusion models," Papers 1804.09043, arXiv.org.
  66. Konstantinos Skindilias & Chia Lo, 2015. "Local volatility calibration during turbulent periods," Review of Quantitative Finance and Accounting, Springer, vol. 44(3), pages 425-444, April.
  67. Vadim Kaushansky & Alexander Lipton & Christoph Reisinger, 2016. "Numerical analysis of an extended structural default model with mutual liabilities and jump risk," Papers 1701.00030, arXiv.org.
  68. K. Borovkov & G. Decrouez & J. Hinz, 2010. "Jump-diffusion modeling in emission markets," Papers 1001.3728, arXiv.org.
  69. Zheng Gong & Wojciech Frys & Renzo Tiranti & Carmine Ventre & John O'Hara & Yingbo Bai, 2022. "A new encoding of implied volatility surfaces for their synthetic generation," Papers 2211.12892, arXiv.org, revised Jun 2023.
  70. Vinicius V. L. Albani & Jorge P. Zubelli, 2020. "A splitting strategy for the calibration of jump-diffusion models," Finance and Stochastics, Springer, vol. 24(3), pages 677-722, July.
  71. Nicola Bruti-Liberati, 2007. "Numerical Solution of Stochastic Differential Equations with Jumps in Finance," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1, July-Dece.
  72. Volk-Makarewicz, Warren & Borovkova, Svetlana & Heidergott, Bernd, 2022. "Assessing the impact of jumps in an option pricing model: A gradient estimation approach," European Journal of Operational Research, Elsevier, vol. 298(2), pages 740-751.
  73. Karel in 't Hout & Jari Toivanen, 2015. "Application of Operator Splitting Methods in Finance," Papers 1504.01022, arXiv.org.
  74. Mario Cerrato & Chia Chun Lo & Konstantinos Skindilias, 2011. "Adaptive continuous time Markov chain approximation model to general jump-diffusions," Working Papers 2011_16, Business School - Economics, University of Glasgow.
  75. Yingzi Chen & Wansheng Wang & Aiguo Xiao, 2019. "An Efficient Algorithm for Options Under Merton’s Jump-Diffusion Model on Nonuniform Grids," Computational Economics, Springer;Society for Computational Economics, vol. 53(4), pages 1565-1591, April.
  76. Campi, Luciano & Polbennikov, Simon & Sbuelz, Alessandro, 2009. "Systematic equity-based credit risk: A CEV model with jump to default," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 93-108, January.
  77. S. Kindermann & P. Mayer, 2011. "On the calibration of local jump-diffusion asset price models," Finance and Stochastics, Springer, vol. 15(4), pages 685-724, December.
  78. C. He & J. Kennedy & T. Coleman & P. Forsyth & Y. Li & K. Vetzal, 2006. "Calibration and hedging under jump diffusion," Review of Derivatives Research, Springer, vol. 9(1), pages 1-35, January.
  79. Abdulwahab Animoku & Ömür Uğur & Yeliz Yolcu-Okur, 2018. "Modeling and implementation of local volatility surfaces in Bayesian framework," Computational Management Science, Springer, vol. 15(2), pages 239-258, June.
  80. Tinne Haentjens & Karel J. in 't Hout, 2011. "ADI finite difference schemes for the Heston-Hull-White PDE," Papers 1111.4087, arXiv.org.
  81. Eduardo Abi Jaber & Louis-Amand G'erard, 2024. "Signature volatility models: pricing and hedging with Fourier," Papers 2402.01820, arXiv.org.
  82. Erhan Bayraktar & Hao Xing, 2009. "Pricing American options for jump diffusions by iterating optimal stopping problems for diffusions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 70(3), pages 505-525, December.
  83. Hilmar Gudmundsson & David Vyncke, 2021. "A Generalized Weighted Monte Carlo Calibration Method for Derivative Pricing," Mathematics, MDPI, vol. 9(7), pages 1-22, March.
  84. Matthew Lorig & Stefano Pagliarani & Andrea Pascucci, 2013. "A family of density expansions for L\'evy-type processes," Papers 1312.7328, arXiv.org.
  85. Campi, L. & Sbuelz, A., 2005. "Close-Form Pricing of Benchmark Equity Default Swaps Under the CEV Assumption," Other publications TiSEM f10edfa3-d4c3-489b-bffe-4, Tilburg University, School of Economics and Management.
  86. Karel in 't Hout & Pieter Lamotte, 2022. "Efficient numerical valuation of European options under the two-asset Kou jump-diffusion model," Papers 2207.10060, arXiv.org, revised May 2023.
  87. Campi, L. & Polbennikov, S.Y. & Sbuelz, A., 2005. "Assessing Credit with Equity : A CEV Model with Jump to Default," Discussion Paper 2005-27, Tilburg University, Center for Economic Research.
  88. Xu, Guoping & Zheng, Harry, 2010. "Basket options valuation for a local volatility jump-diffusion model with the asymptotic expansion method," Insurance: Mathematics and Economics, Elsevier, vol. 47(3), pages 415-422, December.
  89. J. S. Kennedy & P. A. Forsyth & K. R. Vetzal, 2009. "Dynamic Hedging Under Jump Diffusion with Transaction Costs," Operations Research, INFORMS, vol. 57(3), pages 541-559, June.
  90. Jamal Amani Rad & Kourosh Parand, 2014. "Numerical pricing of American options under two stochastic factor models with jumps using a meshless local Petrov-Galerkin method," Papers 1412.6064, arXiv.org.
  91. Mark Broadie & Jerome B. Detemple, 2004. "ANNIVERSARY ARTICLE: Option Pricing: Valuation Models and Applications," Management Science, INFORMS, vol. 50(9), pages 1145-1177, September.
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  93. Yijuan Liang & Xiuchuan Xu, 2019. "Variance and Dimension Reduction Monte Carlo Method for Pricing European Multi-Asset Options with Stochastic Volatilities," Sustainability, MDPI, vol. 11(3), pages 1-21, February.
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  95. Finbarr Murphy & Ehud Ronn, 2015. "The valuation and information content of options on crude-oil futures contracts," Review of Derivatives Research, Springer, vol. 18(2), pages 95-106, July.
  96. Stefano, Pagliarani & Pascucci, Andrea & Candia, Riga, 2011. "Expansion formulae for local Lévy models," MPRA Paper 34571, University Library of Munich, Germany.
  97. Leif Andersen & Alexander Lipton, 2012. "Asymptotics for Exponential Levy Processes and their Volatility Smile: Survey and New Results," Papers 1206.6787, arXiv.org.
  98. Liming Feng & Vadim Linetsky, 2008. "Pricing Options in Jump-Diffusion Models: An Extrapolation Approach," Operations Research, INFORMS, vol. 56(2), pages 304-325, April.
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