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Simple Binomial Processes as Diffusion Approximations in Financial Models

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Cited by:

  1. Beliaeva, Natalia & Nawalkha, Sanjay, 2012. "Pricing American interest rate options under the jump-extended constant-elasticity-of-variance short rate models," Journal of Banking & Finance, Elsevier, vol. 36(1), pages 151-163.
  2. Weihan Li & Jin E. Zhang & Xinfeng Ruan & Pakorn Aschakulporn, 2024. "An empirical study on the early exercise premium of American options: Evidence from OEX and XEO options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 44(7), pages 1117-1153, July.
  3. Dietmar Leisen, 2004. "Mixed Lognormal Distributions for Derivatives Pricing and Risk-Management," Computing in Economics and Finance 2004 48, Society for Computational Economics.
  4. Ludovic Goudenège & Andrea Molent & Antonino Zanette, 2021. "Gaussian process regression for pricing variable annuities with stochastic volatility and interest rate," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 44(1), pages 57-72, June.
  5. Dietmar P.J. Leisen, 1997. "The Random-Time Binomial Model," Finance 9711005, University Library of Munich, Germany, revised 29 Nov 1998.
  6. Wenbin Wang & Mark E. Ferguson & Shanshan Hu & Gilvan C. Souza, 2013. "Dynamic Capacity Investment with Two Competing Technologies," Manufacturing & Service Operations Management, INFORMS, vol. 15(4), pages 616-629, October.
  7. David S. Bates, 1995. "Testing Option Pricing Models," NBER Working Papers 5129, National Bureau of Economic Research, Inc.
  8. Babbs, Simon, 2000. "Binomial valuation of lookback options," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1499-1525, October.
  9. Anlong Li, 1992. "Binomial approximation in financial models: computational simplicity and convergence," Working Papers (Old Series) 9201, Federal Reserve Bank of Cleveland.
  10. Damiano Brigo, 2008. "The general mixture-diffusion SDE and its relationship with an uncertain-volatility option model with volatility-asset decorrelation," Papers 0812.4052, arXiv.org.
  11. Chung-Lun Li & Panos Kouvelis, 1999. "Flexible and Risk-Sharing Supply Contracts Under Price Uncertainty," Management Science, INFORMS, vol. 45(10), pages 1378-1398, October.
  12. Hi Jun Choe & Jeong Ho Chu & So Jeong Shin, 2014. "Recombining binomial tree for constant elasticity of variance process," Papers 1410.5955, arXiv.org.
  13. Jerzy Filar & Boda Kang & Malgorzata Korolkiewicz, 2008. "Pricing Financial Derivatives on Weather Sensitive Assets," Research Paper Series 223, Quantitative Finance Research Centre, University of Technology, Sydney.
  14. David C. Ling, 1993. "Mortgage‐Backed Futures and Options," Real Estate Economics, American Real Estate and Urban Economics Association, vol. 21(1), pages 47-67, March.
  15. Peterson, Sandra & Stapleton, Richard C. & Subrahmanyam, Marti G., 2003. "A Multifactor Spot Rate Model for the Pricing of Interest Rate Derivatives," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 38(4), pages 847-880, December.
  16. Jimmy E. Hilliard & Adam L. Schwartz & Alan L. Tucker, 1996. "Bivariate Binomial Options Pricing With Generalized Interest Rate Processes," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 19(4), pages 585-602, December.
  17. Viral V. Acharya & Jennifer N. Carpenter, 2002. "Corporate Bond Valuation and Hedging with Stochastic Interest Rates and Endogenous Bankruptcy," The Review of Financial Studies, Society for Financial Studies, vol. 15(5), pages 1355-1383.
  18. Rosa Ferrentino & Luca Vota, 2022. "A Mathematical Model for the Pricing of Derivative Financial Products: the Role of the Banking Supervision and of the Model Risk," Journal of Finance and Investment Analysis, SCIENPRESS Ltd, vol. 11(1), pages 1-2.
  19. Chuang-Chang Chang & Jun-Biao Lin & Wei-Che Tsai & Yaw-Huei Wang, 2012. "Using Richardson extrapolation techniques to price American options with alternative stochastic processes," Review of Quantitative Finance and Accounting, Springer, vol. 39(3), pages 383-406, October.
  20. Warren J. Hahn & James S. Dyer, 2011. "A Discrete Time Approach for Modeling Two-Factor Mean-Reverting Stochastic Processes," Decision Analysis, INFORMS, vol. 8(3), pages 220-232, September.
  21. Lei Shi, 2010. "Portfolio Analysis and Equilibrium Asset Pricing with Heterogeneous Beliefs," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2-2010, January-A.
  22. Wael Bahsoun & Pawel Góra & Silvia Mayoral & Manuel Morales, 2006. "Random Dynamics and Finance: Constructing Implied Binomial Trees from a Predetermined Stationary Den," Faculty Working Papers 13/06, School of Economics and Business Administration, University of Navarra.
  23. Hahn, Warren J. & Dyer, James S., 2008. "Discrete time modeling of mean-reverting stochastic processes for real option valuation," European Journal of Operational Research, Elsevier, vol. 184(2), pages 534-548, January.
  24. Kumar Muthuraman & Tarik Aouam & Ronald Rardin, 2008. "Regulation of Natural Gas Distribution Using Policy Benchmarks," Operations Research, INFORMS, vol. 56(5), pages 1131-1145, October.
  25. Bastian-Pinto, Carlos & Brando, Luiz & Hahn, Warren J., 2009. "Flexibility as a source of value in the production of alternative fuels: The ethanol case," Energy Economics, Elsevier, vol. 31(3), pages 411-422, May.
  26. Ludovic Gouden`ege & Andrea Molent & Xiao Wei & Antonino Zanette, 2024. "Enhancing Valuation of Variable Annuities in L\'evy Models with Stochastic Interest Rate," Papers 2404.07658, arXiv.org.
  27. Maya Briani & Lucia Caramellino & Giulia Terenzi & Antonino Zanette, 2016. "Numerical stability of a hybrid method for pricing options," Papers 1603.07225, arXiv.org, revised Dec 2019.
  28. Detemple, Jerome & Kitapbayev, Yerkin, 2022. "Optimal technology adoption for power generation," Energy Economics, Elsevier, vol. 111(C).
  29. Oliver Musshoff & Norbert Hirschauer, 2008. "Investment planning under uncertainty and flexibility: the case of a purchasable sales contract ," Australian Journal of Agricultural and Resource Economics, Australian Agricultural and Resource Economics Society, vol. 52(1), pages 17-36, March.
  30. Hibiki Ichiue & Yoichi Ueno, 2007. "Equilibrium Interest Rate and the Yield Curve in a Low Interest Rate Environment," Bank of Japan Working Paper Series 07-E-18, Bank of Japan.
  31. Brian A. Maris & Jo‐Mae Maris & Tyler T. Yang, 2003. "The Effect of Exercise Date Uncertainty on Employee Stock Option Value," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 30(5‐6), pages 669-698, June.
  32. Maria B. Chiarolla & Tiziano Angelis & Gabriele Stabile, 2022. "An analytical study of participating policies with minimum rate guarantee and surrender option," Finance and Stochastics, Springer, vol. 26(2), pages 173-216, April.
  33. Xu, Ruxing, 2011. "A lattice approach for pricing convertible bond asset swaps with market risk and counterparty risk," Economic Modelling, Elsevier, vol. 28(5), pages 2143-2153, September.
  34. Pascal François & Sophie Pardo, 2015. "Prepayment risk on callable bonds: theory and test," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 38(2), pages 147-176, October.
  35. Ariste, Ruolz & Lasserre, Pierre, 2001. "La gestion optimale d’une forêt exploitée pour son potentiel de diminution des gaz à effet de serre et son bois," L'Actualité Economique, Société Canadienne de Science Economique, vol. 77(1), pages 27-51, mars.
  36. Jung Ho Park & Kwangsoo Shin, 2018. "R&D Project Valuation Considering Changes of Economic Environment: A Case of a Pharmaceutical R&D Project," Sustainability, MDPI, vol. 10(4), pages 1-15, March.
  37. Bowei Chen & Jun Wang, 2014. "A lattice framework for pricing display advertisement options with the stochastic volatility underlying model," Papers 1409.0697, arXiv.org, revised Dec 2015.
  38. Lingfei Li & Vadim Linetsky, 2013. "Optimal Stopping and Early Exercise: An Eigenfunction Expansion Approach," Operations Research, INFORMS, vol. 61(3), pages 625-643, June.
  39. Maya Briani & Lucia Caramellino & Antonino Zanette, 2017. "A hybrid approach for the implementation of the Heston model," Post-Print hal-00916440, HAL.
  40. Ma, Jingtang & Yang, Wensheng & Cui, Zhenyu, 2021. "CTMC integral equation method for American options under stochastic local volatility models," Journal of Economic Dynamics and Control, Elsevier, vol. 128(C).
  41. Raimbourg, Philippe & Zimmermann, Paul, 2022. "Is normal backwardation normal? Valuing financial futures with a local index-rate covariance," European Journal of Operational Research, Elsevier, vol. 298(1), pages 351-367.
  42. Carol Alexander & Xi Chen, 2021. "Model risk in real option valuation," Annals of Operations Research, Springer, vol. 299(1), pages 1025-1056, April.
  43. Aouam, Tarik & Rardin, Ronald & Abrache, Jawad, 2010. "Robust strategies for natural gas procurement," European Journal of Operational Research, Elsevier, vol. 205(1), pages 151-158, August.
  44. T. S. Ho & Richard C. Stapleton & Marti G. Subrahmanyam, 1995. "Correlation risk, cross‐market derivative products and portfolio performance," European Financial Management, European Financial Management Association, vol. 1(2), pages 105-124, July.
  45. Ludovic Gouden`ege & Andrea Molent & Antonino Zanette, 2016. "Pricing and Hedging GMWB in the Heston and in the Black-Scholes with Stochastic Interest Rate Models," Papers 1602.09078, arXiv.org, revised Mar 2016.
  46. Werner Hürlimann, 2012. "Valuation of fixed and variable rate mortgages: binomial tree versus analytical approximations," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 35(2), pages 171-202, November.
  47. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
  48. Li, Chenxu & Ye, Yongxin, 2019. "Pricing and Exercising American Options: an Asymptotic Expansion Approach," Journal of Economic Dynamics and Control, Elsevier, vol. 107(C), pages 1-1.
  49. Maya Briani & Lucia Caramellino & Giulia Terenzi & Antonino Zanette, 2019. "Numerical Stability Of A Hybrid Method For Pricing Options," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(07), pages 1-46, November.
  50. Jin-Yu Zhang & Wen-Bo Wu & Yong Li & Zhu-Sheng Lou, 2021. "Pricing Exotic Option Under Jump-Diffusion Models by the Quadrature Method," Computational Economics, Springer;Society for Computational Economics, vol. 58(3), pages 867-884, October.
  51. Sandra Peterson & Richard C. Stapleton & Marti G. Subrahmanyam, 1999. "The Valuation of American-Style Swaptions in a Two-factor Spot-Futures Model," New York University, Leonard N. Stern School Finance Department Working Paper Seires 99-078, New York University, Leonard N. Stern School of Business-.
  52. Buttimer, Richard Jr. & Lin, Che-Chun, 2005. "Valuing US and Canadian mortgage servicing rights with default and prepayment," Journal of Housing Economics, Elsevier, vol. 14(3), pages 194-211, September.
  53. Xue-Zhong He & Lei Shi, 2016. "A Binomial Model of Asset and Option Pricing with Heterogeneous Beliefs," Published Paper Series 2016-4, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
  54. Fontana, Claudio & Rotondi, Francesco, 2023. "Valuation of general GMWB annuities in a low interest rate environment," Insurance: Mathematics and Economics, Elsevier, vol. 112(C), pages 142-167.
  55. Paolo Angelis & Roberto Marchis & Antonio L. Martire & Emilio Russo, 2022. "A flexible lattice framework for valuing options on assets paying discrete dividends and variable annuities embedding GMWB riders," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 45(1), pages 415-446, June.
  56. Harding, John P., 2000. "Mortgage Valuation with Optimal Intertemporal Refinancing Strategies," Journal of Housing Economics, Elsevier, vol. 9(4), pages 233-266, December.
  57. Andrea Beltratti & Paolo Colla, 2007. "A portfolio-based evaluation of affine term structure models," Annals of Operations Research, Springer, vol. 151(1), pages 193-222, April.
  58. Giulia De Rossi & Tiziano Vargiolu, 2010. "Optimal prepayment and default rules for mortgage-backed securities," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 33(1), pages 23-47, May.
  59. Mark Broadie & Jérôme Detemple, 1996. "Recent Advances in Numerical Methods for Pricing Derivative Securities," CIRANO Working Papers 96s-17, CIRANO.
  60. Marat Kramin & Timur Kramin & Stephen Young & Venkat Dharan, 2005. "A Simple Induction Approach and an Efficient Trinomial Lattice for Multi-State Variable Interest Rate Derivatives Models," Review of Quantitative Finance and Accounting, Springer, vol. 24(2), pages 199-226, January.
  61. Kathrin Glau & Mirco Mahlstedt & Christian Potz, 2018. "A new approach for American option pricing: The Dynamic Chebyshev method," Papers 1806.05579, arXiv.org.
  62. Jimmy E. Hilliard, 2014. "Robust binomial lattices for univariate and multivariate applications: choosing probabilities to match local densities," Quantitative Finance, Taylor & Francis Journals, vol. 14(1), pages 101-110, January.
  63. Andrea Gamba & Lenos Trigeorgis, 2007. "An Improved Binomial Lattice Method for Multi-Dimensional Options," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(5), pages 453-475.
  64. Dong Zou & Pu Gong, 2017. "A Lattice Framework with Smooth Convergence for Pricing Real Estate Derivatives with Stochastic Interest Rate," The Journal of Real Estate Finance and Economics, Springer, vol. 55(2), pages 242-263, August.
  65. Lander, Diane M. & Pinches, George E., 1998. "Challenges to the Practical Implementation of Modeling and Valuing Real Options," The Quarterly Review of Economics and Finance, Elsevier, vol. 38(3, Part 2), pages 537-567.
  66. Ruxing Xu & Dan Wu & Ronghua Yi, 2016. "Pricing Cdss And Cds Options Under A Regime-Switching Cev Process With Jump To Default," ECONOMIC COMPUTATION AND ECONOMIC CYBERNETICS STUDIES AND RESEARCH, Faculty of Economic Cybernetics, Statistics and Informatics, vol. 50(1), pages 253-271.
  67. Costabile, Massimo & Gaudenzi, Marcellino & Massabò, Ivar & Zanette, Antonino, 2009. "Evaluating fair premiums of equity-linked policies with surrender option in a bivariate model," Insurance: Mathematics and Economics, Elsevier, vol. 45(2), pages 286-295, October.
  68. Massimo Costabile & Arturo Leccadito & Ivar Massabó, 2009. "Computationally simple lattice methods for option and bond pricing," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 32(2), pages 161-181, November.
  69. Ho, T. S. & Stapleton, Richard C. & Subrahmanyam, Marti G., 1997. "The valuation of American options on bonds1," Journal of Banking & Finance, Elsevier, vol. 21(11-12), pages 1487-1513, December.
  70. Philip Brown & Alex Szimayer, 2008. "Valuing executive stock options: performance hurdles, early exercise and stochastic volatility," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 48(3), pages 363-389, September.
  71. Yuh-Dauh Lyuu & Chi-Ning Wu, 2005. "On accurate and provably efficient GARCH option pricing algorithms," Quantitative Finance, Taylor & Francis Journals, vol. 5(2), pages 181-198.
  72. Vincenzina Messina & Valentina Bosetti, 2006. "Integrating stochastic programming and decision tree techniques in land conversion problems," Annals of Operations Research, Springer, vol. 142(1), pages 243-258, February.
  73. Massimo Costabile & Ivar Massabó & Emilio Russo, 2011. "A binomial approximation for two-state Markovian HJM models," Review of Derivatives Research, Springer, vol. 14(1), pages 37-65, April.
  74. U Hou Lok & Yuh-Dauh Lyuu, 2022. "A Valid and Efficient Trinomial Tree for General Local-Volatility Models," Computational Economics, Springer;Society for Computational Economics, vol. 60(3), pages 817-832, October.
  75. U Hou Lok & Yuh‐Dauh Lyuu, 2020. "Efficient trinomial trees for local‐volatility models in pricing double‐barrier options," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(4), pages 556-574, April.
  76. Carlos Andrés Zapata Quimbayo, 2020. "OPCIONES REALES Una guía teórico-práctica para la valoración de inversiones bajo incertidumbre mediante modelos en tiempo discreto y simulación de Monte Carlo," Books, Universidad Externado de Colombia, Facultad de Finanzas, Gobierno y Relaciones Internacionales, number 138.
  77. Aricson Cruz & José Carlos Dias, 2020. "Valuing American-style options under the CEV model: an integral representation based method," Review of Derivatives Research, Springer, vol. 23(1), pages 63-83, April.
  78. Sandra Peterson & Richard Stapleton, 2002. "The pricing of Bermudan-style options on correlated assets," Review of Derivatives Research, Springer, vol. 5(2), pages 127-151, May.
  79. Xiaotong Lian & Yingda Song, 2021. "Pricing and calibration of the futures options market: A unified approximation," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 41(7), pages 1074-1091, July.
  80. Nobuhiro Nakamura, 2004. "Numerical Approach to Asset Pricing Models with Stochastic Differential Utility," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 11(3), pages 267-300, September.
  81. Xu, Wei & Šević, Aleksandar & Šević, Željko, 2022. "Implied volatility surface construction for commodity futures options traded in China," Research in International Business and Finance, Elsevier, vol. 61(C).
  82. M. Briani & L. Caramellino & A. Zanette, 2015. "A hybrid tree/finite-difference approach for Heston-Hull-White type models," Papers 1503.03705, arXiv.org, revised Dec 2017.
  83. J. X. Jiang & R. H. Liu & D. Nguyen, 2016. "A Recombining Tree Method For Option Pricing With State-Dependent Switching Rates," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(02), pages 1-26, March.
  84. Claudio Fontana & Francesco Rotondi, 2022. "Valuation of general GMWB annuities in a low interest rate environment," Papers 2208.10183, arXiv.org, revised Aug 2023.
  85. Slade, Margaret E., 2001. "Valuing Managerial Flexibility: An Application of Real-Option Theory to Mining Investments," Journal of Environmental Economics and Management, Elsevier, vol. 41(2), pages 193-233, March.
  86. Das Gupta, Supratim, 2021. "Using real options to value capacity additions and investment expenditures in renewable energies in India," Energy Policy, Elsevier, vol. 148(PA).
  87. Ren-Raw Chen & Tyler Yang, 1999. "A universal lattice," Review of Derivatives Research, Springer, vol. 3(2), pages 115-133, May.
  88. Dietmar Leisen & Matthias Reimer, 1996. "Binomial models for option valuation - examining and improving convergence," Applied Mathematical Finance, Taylor & Francis Journals, vol. 3(4), pages 319-346.
  89. Chung, San-Lin & Shih, Pai-Ta, 2009. "Static hedging and pricing American options," Journal of Banking & Finance, Elsevier, vol. 33(11), pages 2140-2149, November.
  90. Hibiki Ichiue & Yoichi Ueno, 2006. "Monetary Policy and the Yield Curve at Zero Interest: The Macro-Finance Model of Interest Rates as Options," Bank of Japan Working Paper Series 06-E-16, Bank of Japan.
  91. Yi-Ping Chang & Ming-Chin Hung & Yi-Chen Ko, 2011. "A multinomial tree model for pricing credit default swap options," Computational Statistics, Springer, vol. 26(1), pages 95-120, March.
  92. Leisen, Dietmar P. J., 1999. "The random-time binomial model," Journal of Economic Dynamics and Control, Elsevier, vol. 23(9-10), pages 1355-1386, September.
  93. Feyza G. Sahinyazan & Marie‐Ève Rancourt & Vedat Verter, 2021. "Improving Transportation Procurement in the Humanitarian Sector: A Data‐driven Approach for Abnormally Low Bid Detection," Production and Operations Management, Production and Operations Management Society, vol. 30(4), pages 1082-1109, April.
  94. Anna Battauz & Francesco Rotondi, 2022. "American options and stochastic interest rates," Computational Management Science, Springer, vol. 19(4), pages 567-604, October.
  95. Jing Zhao & Hoi Ying Wong, 2012. "A closed-form solution to American options under general diffusion processes," Quantitative Finance, Taylor & Francis Journals, vol. 12(5), pages 725-737, July.
  96. Carlos de Lamare Bastian-Pinto & Alexandre Paula Silva Ramos & Luiz de Magalhães Ozorio & Luiz Eduardo Teixeira Brandão, 2015. "Uncertainty and Flexibility in the Brazilian Beef Livestock Sector: the Value of the Confinement Option," Brazilian Business Review, Fucape Business School, vol. 12(6), pages 100-120, November.
  97. Chuang-Chang Chang & Jun-Biao Lin, 2010. "The valuation of multivariate contingent claims under transformed trinomial approaches," Review of Quantitative Finance and Accounting, Springer, vol. 34(1), pages 23-36, January.
  98. Das Gupta, Supratim, 2018. "Using real options to study the impact of capacity additions and investment expenditures in renewable energies in India," MPRA Paper 90441, University Library of Munich, Germany.
  99. Chuang-Chang Chang & Jun-Biao Lin & Chun-Chieh Yang, 2015. "The effect of stochastic interest rates on a firm’s capital structure under a generalized model," Review of Quantitative Finance and Accounting, Springer, vol. 45(4), pages 695-719, November.
  100. Yuan Hu & W. Brent Lindquist & Svetlozar T. Rachev & Frank J. Fabozzi, 2024. "Option Pricing Using a Skew Random Walk Binary Tree," JRFM, MDPI, vol. 17(4), pages 1-29, March.
  101. Massimo Costabile, 2006. "On pricing lookback options under the CEV process," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 29(2), pages 139-153, November.
  102. Yuan Hu & W. Brent Lindquist & Svetlozar T. Rachev & Frank J. Fabozzi, 2023. "Option pricing using a skew random walk pricing tree," Papers 2303.17014, arXiv.org.
  103. Goudenège, Ludovic & Molent, Andrea & Zanette, Antonino, 2016. "Pricing and hedging GLWB in the Heston and in the Black–Scholes with stochastic interest rate models," Insurance: Mathematics and Economics, Elsevier, vol. 70(C), pages 38-57.
  104. Ait-Sahalia, Yacine, 1996. "Testing Continuous-Time Models of the Spot Interest Rate," The Review of Financial Studies, Society for Financial Studies, vol. 9(2), pages 385-426.
  105. Ludovic Goudenege & Andrea Molent & Antonino Zanette, 2015. "Pricing and Hedging GLWB in the Heston and in the Black-Scholes with Stochastic Interest Rate Models," Papers 1509.02686, arXiv.org.
  106. Sanjiv R. Das & Rangarajan K. Sundaram, 2007. "An Integrated Model for Hybrid Securities," Management Science, INFORMS, vol. 53(9), pages 1439-1451, September.
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