Early exercise boundary and option prices in Lévy driven models

References

References

• Ahn , D- H , Dittmar , R F and Gallant , A R . 2002 . Quadratic term structure models: theory and evidence . Review of Financial Studies , 15 : 243 – 88 .
   Web of Science ®Google Scholar
• Ahn , D- H , Dittmar , R F , Gallant , A R and Bin , Gao . 2003 . Pure bred or hybrid?: Reproducing the volatility in term structure dynamics . J. Econometrics , 116 : 147 – 80 .
   Web of Science ®Google Scholar
• Ait-Sahalia Y 2003 Disentangling diffusion from jumps Forthcoming in J. Financial Economics
   Google Scholar
• Ait-Sahalia , Y . 2002 . Telling from discrete data whether the underlying continuous-time model is a diffusion . J. Finance , 57 : 2075 – 112 .
   Web of Science ®Google Scholar
• Alili L Kyprianou A E 2004 Some remarks on first passage of Lévy processes, the American put and pasting principles Working Paper
   Google Scholar
• Avram , F , Chan , T and Usabel , M . 2002 . On the valuation of constant barrier options under spectrally one-sided exponential Lévy models and Carr's randomization for American puts . Stochastic Processes and their Applications , 100 : 75 – 107 .
   Web of Science ®Google Scholar
• Barles , G , Burdeau , J , Romano , M and Samsoen , N . 1995 . Critical stock price near expiration . Mathematical Finance , 5 : 77 – 95 .
   Google Scholar
• Barndorff-Nielsen , O E . 1998 . Processes of normal inverse gaussian type . Finance and Stochastics , 2 : 41 – 68 .
   Google Scholar
• Barndorff-Nielsen , O E and Levendorskiǐ , S Z . 2000 . Feller processes of normal inverse Gaussian type . Quantitative Finance , 1 : 318 – 31 .
   Google Scholar
• Barndorff-Nielsen , O E , Nicolato , E and Shephard , N . 2002 . Some recent developments in stochastic volatility modelling . Quantitative Finance , 2 : 11 – 23 .
   Google Scholar
• Bates , D S . 2003 . Empirical option pricing: a retrospection . J. Econometrics , 116 : 387 – 404 .
   Web of Science ®Google Scholar
• Bernanke , B S . 1993 . Irreversibility, uncertainty, and cyclical investment . Quarterly J. Economics , 98 : 85 – 106 .
   Google Scholar
• Bouchaud J P Potters M 1997 Theory of Financial Risk Eurolles, Paris Aléa-Saclay
   Google Scholar
• Boyarchenko S I 2004 Irreversible decisions and record setting news principles American Economic Review
   Google Scholar
• Boyarchenko N Levendorskiǐ S 2004 Eigenfunction expansion method in multi-factor models Working Paper http://ssrn/com/abstract=627642
   Google Scholar
• Boyarchenko S I Levendorskiǐ S Z 1998 On rational pricing of derivative securities for a family of non-Gaussian processes Preprint 98/7, February Universität Potsdam, Institute für Mathematik Potsdam Germany
   Google Scholar
• Boyarchenko S I Levendorskiǐ S Z 1999 Generalizations of the Black–Scholes equation for truncated Lévy processes Working Paper
   Google Scholar
• Boyarchenko , S I and Levendorskiǐ , S Z . 2000 . Option pricing for truncated Lévy processes . Intern. J. Theor. Appl. Finance , 3 : 549 – 52 .
   Google Scholar
• Boyarchenko S I Levendorskiǐ S Z 2001 Option pricing and hedging under Regular Lévy processes of Exponential type Mathematical Finance Workshop of the Mathematical Finance Research project Konstanz, Germany, October 5–7, ed M Kohlmann and S Tang Birkhäuser Basel–Boston–Berlin Birkhäuser pp 121–30
   Google Scholar
• Boyarchenko , S I and Levendorskiǐ , S Z . 2002a . Perpetual American options under Lévy processes . SIAM J. Control and Optimization , 40 : 1663 – 96 .
   Web of Science ®Google Scholar
• Boyarchenko S I Levendorskiǐ S Z 2002b Non-Gaussian Merton–Black–Scholes Theory New Jersey, London, Singapore, Hong Kong World Scientific
   Google Scholar
• Boyarchenko , S I and Levendorskiǐ , S Z . 2002c . Barrier options and touch-and-out options under regular Lévy processes of exponential type . Annals of Applied Probability , 12 : 261 – 98 .
   Web of Science ®Google Scholar
• Boyarchenko , S I and Levendorskiǐ , S Z . 2002d . Pricing of perpetual Bermudan options . Quantitative Finance , 2 : 432 – 42 .
   Google Scholar
• Boyarchenko S I Levendorskiǐ S Z 2004a Practical guide to real options in discrete time Submitted to International Economic Review Working Paper (February 24), http://ssrn/com/abstract=5170324
   Google Scholar
• Boyarchenko S I Levendorskiǐ S Z 2004b American options: the EPV pricing model Submitted to Annals of Finance
   Google Scholar
• Carr , P . 1998 . Randomization and the American put . Review of Financial Studies , 11 : 597 – 626 .
   Web of Science ®Google Scholar
• Carr P Faguet D 1994 Fast accurate valuation of American options Working Paper, Cornell University Ithaca
   Google Scholar
• Carr , P , Geman , H , Madan , D B and Yor , M . 2002 . The fine structure of asset returns: an empirical investigation . J. Business , 75 : 305 – 32 .
   Web of Science ®Google Scholar
• Carr , P and Hirsa , A . 2003 . Why be backward? . Risk , 26 : 103 – 7 .
   Google Scholar
• Carr , P and Wu , L . 2003 . What type of process underlies options? A simple robust test . J. Finance , 57 : 2581 – 610 .
   Google Scholar
• Chacko , G and Das , S . 2002 . Pricing interest rate derivatives: a general approach . Review of Financial Studies , 15 : 195 – 241 .
   Web of Science ®Google Scholar
• Chernov , M , Gallant , E , Chysels , E and Tauchen , G . 2003 . Alternative models for stock price dynamics . Journal of Econometrics , 116 : 225 – 57 .
   Web of Science ®Google Scholar
• Cont R Potters M Bouchaud J- P 1997 Scaling in stock market data: stable laws and beyond Scale Invariance and beyond ed B Dubrulle, F Graner and D Sornette (Proceedings of the CNRS Workshop on Scale Invariance Les Houches, March 1997) Berlin Springer
   Google Scholar
• Cont R Volchkova E 2003 A finite difference scheme for option pricing in jump diffusion and exponential Lévy models Rapport Interne CMAP Numeréro 513, Sept
   Google Scholar
• Darling D A Liggett T Taylor H M 1972 Optimal stopping for partial sums Annals of Mathematical Statistics 43 1363 68
   Google Scholar
• Delbaen , F and Schachermayer , W . 1994 . A general version of the fundamental theorem of asset pricing . Mathematische Annalen , 300 : 463 – 520 .
   Web of Science ®Google Scholar
• Duffie , D , Pan , J and Singleton , K . 2000 . Transform analysis and option pricing for affine jump-diffusions . Econometrica , 68 : 1343 – 76 .
   Web of Science ®Google Scholar
• Eberlein , E and Keller , U . 1995 . Hyperbolic distributions in finance . Bernoulli , 1 : 281 – 99 .
   Google Scholar
• Eberlein , E , Keller , U and Prause , K . 1998 . New insights into smile, mispricing and value at risk: the hyperbolic model . J. Business , 71 : 371 – 406 .
   Web of Science ®Google Scholar
• Heston , S . 1993 . A closed form solution for options with stochastic volatility with applications to bond and currency options . Review of Financial Studies , 6 : 327 – 423 .
   Web of Science ®Google Scholar
• Hirsa , A and Madan , DB . 2003 . Pricing American options under Variance Gamma . Journal of Computational Finance , 7
   Google Scholar
• Koponen , I . 1995 . Analytic approach to the problem of convergence of truncated Lévy flights towards the Gaussian stochastic process . Phys. Rev. E , 52 : 1197 – 99 .
   PubMed Web of Science ®Google Scholar
• Kudryavzev O E Levendorskiǐ S Z 2002 Comparative study of first touch digitals: normal inverse gaussian vs. gaussian modelling MaPhySto research report 33, October Aarhus University (submitted to Int. J. Theoretical and Applied Finance)
   Google Scholar
• Lamberton D 1995 Critical price for an American option near maturity Seminar on Stochastic Analysis, Random Fields and Applications ed E Bolthausen, M Dozzi and F Russo Boston–Basel–Berlin Birkhaüser
   Google Scholar
• Levendorskiǐ S Z 2002 Pseudo-dnffusions and quadratic term structure models MaVhySto research report 43, December 2002, Aarhus University, extended version to appear in Mathematical Finance
   Google Scholar
• Levendorskiǐ , S Z . 2004a . Consistency conditions for affine term structure models . Stochastic Processes and their Applecations , 109 : 225 – 61 .
   Web of Science ®Google Scholar
• Levendorskiǐ , S Z . 2004b . Pricing of the American put under Lévy processes . Int. J. Theoretical and Applied Finance , 7 : 303 – 35 .
   Google Scholar
• Levendorskiǐ S Z 2004c The American put and European options near expiry, under Lévy processes Working Paper http://ssrn/com/abstract=520062
   Google Scholar
• Levendorskiǐ S Kudryavzev O Zherder V 2004d A note on relative efficiency of some numerical methods for pricing of American options under Lévy processes Working Paper (October 27), http://ssrn/com/abstract=520542
   Google Scholar
• Levendorskiǐ S Z 2004e American and European options near expiry, under Markov processes with jumps Working Paper (October 27), http://ssrn/com/abstract=520544
   Google Scholar
• Levendorskiǐ S Z 2004f Consistency conditions for affine term structure models II. Option pricing under diffusions with embedded jumps Working Paper http://ssrn/com/abstract=627622
   Google Scholar
• Levendorskiǐ S Z Zherder V M 2002 Fast option pricing under regular Lévy processes of exponential type Working Paper
   Google Scholar
• Lipton A 2002 Assets with jumps Risk 147 53
   Google Scholar
• Madan , D B and Chang , E C . 1998 . The variance Gamma process and option pricing . European Finance Review , 2 : 79 – 105 .
   Google Scholar
• Matache A- M von Petensdorff T Schwab C 2003 Wavelet Galerkin pricing of American options on Lévy driven assets Working Paper http://www.stat.math.ethz.ch/sam/projects
   Google Scholar
• Matacz , A . 2000 . Financial modeling and option theory with the Truncated Levy Process . Int. J. Theoretical and Applied Finance , 3 : 143 – 60 .
   Google Scholar
• McKean , H P Jr . 1965 . Appendix: a free boundary problem for the heat equation arising from a problem in Mathematical Economics . Indust. Mang. Rev , 6 : 32 – 9 .
   Web of Science ®Google Scholar
• Merton , R C . 1973 . The theory of rational option pricing . Bell J. Economics , 4 : 141 – 83 .
   Web of Science ®Google Scholar
• Mordecki , E . 2002a . Optimal stopping and perpetual options for Lévy processes . Finance and Stochastics , 6 : 473 – 93 .
   Web of Science ®Google Scholar
• Mordecki , E . 2002b . Perpetual Options for Lévy Processes in the Bachelier Model . Proceedings of the Steklov Mathematical Institute , 237 : 256 – 64 .
   Google Scholar
• Mordecki E 2004 A note on Optimal stopping and perpetual options under Lévy processes Working Paper May, http//:www.cmat.edu.uy/ mordecki/articles/note
   Google Scholar
• Musiela M Rutkowski M 1997 Martingale Methods in Financial Modelling Berlin–Heidelberg–New York Springer-Verlag
   Google Scholar
• Sato K 1999 Lévy Processes and Infinitely Divisible Distributions Cambridge Cambridge University Press
   Google Scholar