View Item 

Show simple item record

Valuation Of Continuously Monitored Double Barrier Options And Related Securities
dc.contributor.authorBoyarchenko, Mityaen_US
dc.contributor.authorLevendorskiĭ, Sergeien_US
dc.date.accessioned2012-07-12T17:23:54Z
dc.date.available2013-09-03T15:38:27Zen_US
dc.date.issued2012-07en_US
dc.identifier.citationBoyarchenko, Mitya; Levendorskiĭ, Sergei (2012). "Valuation Of Continuously Monitored Double Barrier Options And Related Securities." Mathematical Finance 22(3). <http://hdl.handle.net/2027.42/92059>en_US
dc.identifier.issn0960-1627en_US
dc.identifier.issn1467-9965en_US
dc.identifier.urihttps://hdl.handle.net/2027.42/92059
dc.publisherWiley Periodicals, Inc.en_US
dc.publisherBlackwell Publishing Incen_US
dc.subject.otherCGMY Modelen_US
dc.subject.otherFast Fourier Transformen_US
dc.subject.otherCarr's Randomizationen_US
dc.subject.otherLaplace Transformen_US
dc.subject.otherWiener‐Hopf Factorizationen_US
dc.subject.otherOption Pricingen_US
dc.subject.otherDouble Barrier Optionsen_US
dc.subject.otherDouble‐No‐Touch Optionsen_US
dc.subject.otherLéVy Processesen_US
dc.subject.otherVariance Gamma Processesen_US
dc.subject.otherNormal Inverse Gaussian Processesen_US
dc.subject.otherKuznetsov's β‐Processesen_US
dc.subject.otherKoBoL Processesen_US
dc.titleValuation Of Continuously Monitored Double Barrier Options And Related Securitiesen_US
dc.typeArticleen_US
dc.rights.robotsIndexNoFollowen_US
dc.subject.hlbsecondlevelMathematicsen_US
dc.subject.hlbsecondlevelFinanceen_US
dc.subject.hlbsecondlevelEconomicsen_US
dc.subject.hlbtoplevelBusinessen_US
dc.subject.hlbtoplevelScienceen_US
dc.description.peerreviewedPeer Revieweden_US
dc.contributor.affiliationumUniversity of Michiganen_US
dc.contributor.affiliationotherThe University of Leicesteren_US
dc.description.bitstreamurlhttp://deepblue.lib.umich.edu/bitstream/2027.42/92059/1/j.1467-9965.2010.00469.x.pdf
dc.identifier.doi10.1111/j.1467-9965.2010.00469.xen_US
dc.identifier.sourceMathematical Financeen_US
dc.identifier.citedreferenceLi, A. ( 1999 ): The Pricing of Double Barrier Options and Their Variations, Adv. Futures Options Res. 10, 17 – 41.en_US
dc.identifier.citedreferenceGeman, H. ( 2001 ): Time Changes, Laplace Transforms and Path‐dependent Options, Computat. Economics 17 ( 1 ), 81 – 92.en_US
dc.identifier.citedreferenceGeman, H., and M. Yor ( 1996 ): Pricing and Hedging Double‐barrier Options: A Probabilistic Approach, Math. Finance 6 ( 4 ), 365 – 378.en_US
dc.identifier.citedreferenceHui, C. ( 1996 ): One‐touch Double Barrier Binary Option Values, Appl. Finan. Econ. 6 ( 4 ), 343 – 346.en_US
dc.identifier.citedreferenceHui, C., C. Lo, and P. Yuen ( 2000 ): Comment on “Pricing Double Barrier Options Using Laplace Transforms” by Antoon Pelsser, Finance Stoch. 4 ( 1 ), 105 – 107.en_US
dc.identifier.citedreferenceJeannin, M., and M. Pistorius ( 2007 ): A Transform Approach to Calculate Prices and Greeks of Barrier Options Driven by a Class of Lévy Processes, King's College London and Nomura Models and Methodology Group Preprint. Available at: http://arxiv.org/abs/0812.3128.en_US
dc.identifier.citedreferenceKadankova, T., and N. Veraverbeke ( 2007 ): On Several Two‐boundary Problems for a Particular Class of Lévy Processes, J. Theor. Prob. 20 ( 4 ), 1073.en_US
dc.identifier.citedreferenceKolkiewicz, A. ( 2002 ): Pricing and Hedging More General Double‐barrier Options, J. Computat. Finance 5 ( 3 ), 1 – 26.en_US
dc.identifier.citedreferenceKoponen, I. ( 1995 ): Analytic Approach to the Problem of Convergence of Truncated Lévy Flights towards the Gaussian Stochastic Process, Phys. Rev. E 52, 1197 – 1199.en_US
dc.identifier.citedreferenceKou, S. ( 2002 ): A Jump‐diffusion Model for Option Pricing, Manage. Sci. 48 ( 8 ), 1086 – 1101.en_US
dc.identifier.citedreferenceKou, S., and H. Wang ( 2003 ): First Passage Times of a Jump Diffusion Process, Adv. Appl. Prob. 35 ( 2 ), 504 – 531.en_US
dc.identifier.citedreferenceKou, S., and H. Wang ( 2004 ): Option Pricing under a Double Exponential Jump Diffusion Model, Manage. Sci. 50 ( 9 ), 1178 – 1192.en_US
dc.identifier.citedreferenceKudryavtsev, O., and S. Levendorskiĭ ( 2006 ): Pricing of First Touch Digitals under Normal Inverse Gaussian Processes, Int. J. Theor. Appl. Finance 9 ( 6 ), 915 – 950.en_US
dc.identifier.citedreferenceKudryavtsev, O., and S. Levendorskiĭ ( 2009 ): Fast and Accurate Pricing of Barrier Options under Lévy Processes, Finance Stoch. 13 ( 4 ), 531 – 562.en_US
dc.identifier.citedreferenceKunimoto, N., and M. Ikeda ( 1992 ): Pricing Options with Curved Boundaries, Math. Finance 2 ( 4 ), 275 – 298.en_US
dc.identifier.citedreferenceKuznetsov, A. ( 2010 ): Wiener‐Hopf Factorization and Distribution of Extrema for a Family of Lévy Processes, Ann. Appl. Prob. 20 ( 5 ), 1801 – 1830.en_US
dc.identifier.citedreferenceLevendorskiĭ, S. ( 2004 ): Pricing of the American Put under Lévy Processes, Int. J. Theor. Appl. Finance 7 ( 3 ), 303 – 335.en_US
dc.identifier.citedreferenceLewis, A., and E. Mordecki ( 2008 ): Wiener‐Hopf Factorization and Distribution of Extrema for a Family of Lévy Processes, Ann. Appl. Prob. 45, 118 – 134.en_US
dc.identifier.citedreferenceLipton, A. ( 2002a ): Assets with Jumps, Risk, 149 – 153.en_US
dc.identifier.citedreferenceLipton, A. ( 2002b ): Path‐dependent Options on Assets with Jumps, 5 th Columbia‐Jaffe Conference. Available at http://www.math.columbia.edu/~lrb/columbia2002.pdf.en_US
dc.identifier.citedreferenceLuo, L. ( 2001 ): Various Types of Double‐barrier Options, J. Computat. Finance 4 ( 3 ), 125 – 138.en_US
dc.identifier.citedreferenceMadan, D., P. Carr, and E. Chang ( 1998 ): The Variance Gamma Process and Option Pricing, Eur. Finance Rev. 2, 79 – 105.en_US
dc.identifier.citedreferenceMadan, D., and F. Milne ( 1991 ): Option Pricing with V.G. Martingale Components, Math. Finance 1 ( 4 ), 39 – 55.en_US
dc.identifier.citedreferenceMadan, D., and E. Seneta ( 1990 ): The Variance Gamma (V.G.) Model for Share Market Returns, J. Business 63, 511 – 524.en_US
dc.identifier.citedreferenceMerton, R. ( 1976 ): Option Pricing When Underlying Stock Returns Are Discontinuous, J. Finan. Econ. 3, 125 – 144.en_US
dc.identifier.citedreferencePelsser, A. ( 2000 ): Pricing Double Barrier Options Using Laplace Transforms, Finance Stoch. 4 ( 1 ), 95 – 104.en_US
dc.identifier.citedreferenceRogers, L., and D. Williams ( 1994 ): Diffusions, Markov Processes, and Martingales. Vol. 1: Foundations, 2nd ed., Chichester: John Wiley & Sons, Ltd.en_US
dc.identifier.citedreferenceRogozin, B. ( 1972 ): The Distribution of the First Hit for Stable and Asymptotically Stable Walks on an Interval, Theor. Probab. Appl. 17, 332 – 338.en_US
dc.identifier.citedreferenceSato, K. ( 1999 ): Lévy Processes and Infinitely Divisible Distributions, Cambridge Stud. Adv. Math., Vol. 68, Cambridge: Cambridge University Press.en_US
dc.identifier.citedreferenceSchröder, M. ( 2000 ): On the Valuation of Double‐barrier Options: Computational Aspects, J. Computat. Finance 3 ( 4 ), 5 – 33.en_US
dc.identifier.citedreferenceSepp, A. ( 2004 ): Analytical Pricing of Double‐barrier Options under a Double‐exponential Jump Diffusion Process: Applications of Laplace Transform, Int. J. Theor. Appl. Finance 7 ( 2 ), 151 – 175.en_US
dc.identifier.citedreferenceSidenius, J. ( 1998 ): Double Barrier Options: Valuation by Path Counting, J. Comput. Finance 1 ( 3 ), 63 – 79.en_US
dc.identifier.citedreferenceAsmussen, S., F. Avram, and M. Pistorius ( 2004 ): Russian and American Put Options under Exponential Phase‐type Lévy Models, Stoch. Process. Appl. 109 ( 1 ), 79 – 111.en_US
dc.identifier.citedreferenceBarndorff‐Nielsen, O. ( 1998 ): Processes of Normal Inverse Gaussian Type, Finance Stoch. 2, 41 – 68.en_US
dc.identifier.citedreferenceBarndorff‐Nielsen, O., and S. Levendorskiǐ ( 2001 ): Feller Processes of Normal Inverse Gaussian Type, Quantit. Finance 1, 318 – 331.en_US
dc.identifier.citedreferenceBertoin, J. ( 1996 ): Lévy Processes, Cambridge Tracts in Mathematics, Vol. 121, Cambridge, UK: Cambridge University Press.en_US
dc.identifier.citedreferenceBoyarchenko, M. ( 2008 ): Carr's Randomization for Finite‐Lived Barrier Options: Proof of Convergence, Working Paper. Available at SSRN: http://papers.ssrn.com/abstract=1275666.en_US
dc.identifier.citedreferenceBoyarchenko, M., and S. Levendorskiĭ ( 2009a ): Prices and Sensitivities of Barrier and First‐touch Digital Options in Lévy‐driven Models, Int. J. Theor. Appl. Finance 12 ( 8 ), 1125 – 1170.en_US
dc.identifier.citedreferenceBoyarchenko, M., and S. Levendorskiĭ ( 2009b ): Refined and Enhanced Fast Fourier Transform Techniques, with an Application to the Pricing of Barrier Options, Working Paper. Available at SSRN: http://papers.ssrn.com/abstract=1142833.en_US
dc.identifier.citedreferenceBoyarchenko, S. ( 2006 ): Two‐point Boundary Problems and Perpetual American Strangles in Jump‐diffusion Models, Working Paper. Available at SSRN: http://ssrn.com/abstract=896260.en_US
dc.identifier.citedreferenceBoyarchenko, S., and S. Levendorskiĭ ( 2000 ): Option Pricing for Truncated Lévy Processes, Int. J. Theor. Appl. Finance 3 ( 3 ), 549 – 552.en_US
dc.identifier.citedreferenceBoyarchenko, S., and S. Levendorskiĭ ( 2002 ): Non‐Gaussian Merton‐Black‐Scholes Theory, Adv. Ser. Stat. Sci. Appl. Probab., Vol. 9, River Edge, NJ: World Scientific Publishing Co.en_US
dc.identifier.citedreferenceCarr, P. ( 1998 ): Randomization and the American Put, Rev. Finan. Stud. 11 ( 3 ), 597 – 626.en_US
dc.identifier.citedreferenceCarr, P., and J. Crosby ( 2008 ): A Class of Lévy Process Models with Almost Exact Calibration to Both Barrier and Vanilla FX Options, Working Paper. Available at: http://www.john‐crosby.co.uk/.en_US
dc.identifier.citedreferenceCarr, P., and D. Faguet ( 1996 ): Valuing Finite‐Lived Options as Perpetual, Working Paper. Available at SSRN: http://ssrn.com/abstract=706 or DOI: http://dx.doi.org/10.2139/ssrn.706.en_US
dc.identifier.citedreferenceCarr, P., H. Geman, D. Madan, and M. Yor ( 2002 ): The Fine Structure of Asset Returns: An Empirical Investigation, J. Business 75, 305 – 332.en_US
dc.identifier.citedreferenceCarr, P., and D. Madan ( 1999 ): Option Valuation Using the Fast Fourier Transform, J. Computat. Finance 2 ( 4 ), 61 – 73.en_US
dc.identifier.citedreferenceDouady, R. ( 1999 ): Closed Form Formulas for Exotic Options and Their Lifetime Distribution, Int. J. Theor. Appl. Finance 2 ( 1 ), 17 – 42.en_US
dc.identifier.citedreferenceEskin, G. ( 1981 ): Boundary Value Problems for Elliptic Pseudodifferential Equations, Transl. Math. Monogr., Vol. 9, Providence, RI: American Mathematical Society.en_US
dc.identifier.citedreferenceEydeland, A. ( 1994 ): A Fast Algorithm for Computing Integrals in Function Spaces: Financial Applications, Computat. Econ. 7, 277 – 285.en_US
dc.identifier.citedreferenceEydeland, A., and D. Mahoney ( 2001 ): The Grid Model for Derivative Pricing, Mirant Technical Report.en_US
dc.identifier.citedreferenceFeng, L., and V. Linetsky ( 2008 ): Pricing Discretely Monitored Barrier Options and Defaultable Bonds in Lévy Process Models: A Fast Hilbert Transform Approach, Math. Finance 18 ( 3 ), 337 – 384.en_US
dc.owningcollnameInterdisciplinary and Peer-Reviewed


Files in this item

Name:
j.1467-9965.2010.00469.x.pdf
Size:
709.1KB
Format:
PDF
View/Open

Show simple item record

Remediation of Harmful Language

The University of Michigan Library aims to describe library materials in a way that respects the people and communities who create, use, and are represented in our collections. Report harmful or offensive language in catalog records, finding aids, or elsewhere in our collections anonymously through our metadata feedback form. More information at Remediation of Harmful Language.

Accessibility

If you are unable to use this file in its current format, please select the Contact Us link and we can modify it to make it more accessible to you.