Leveraged Lévy processes as models for stock prices

References

• Andersen , L and Andreasen , J . 2000 . Jump-diffusion processes: volatility smile fitting and numerical methods for option pricing . Rev. Deriv. Res. , 4 : 231 – 262 .
   Google Scholar
• Applebaum , D . 2004 . Lévy Processes and Stochastic Calculus , Cambridge : Cambridge University Press .
   Google Scholar
• Black , F . 1976 . “ Studies of stock price volatility changes ” . In Proceedings of the Business and Economic Statistic Section 177 – 181 .
   Google Scholar
• Bouchaud , J , Matacz , A and Potters , M . 2001 . Leverage effect in financial markets: the retarded volatility model . Phys. Rev. Lett. , 87 : 228701 – 228704 .
   PubMed Web of Science ®Google Scholar
• Campbell , JY and Kyle , AS . 1993 . Smart money, noise trading and stock price behaviour . Rev. Econ. Stud. , 60 : 1 – 34 .
   Web of Science ®Google Scholar
• Carr , P , Geman , H , Madan , DB and Yor , M . 2002 . The fine structure of asset returns: an empirical investigation . J. Business , 75 : 305 – 332 .
   Web of Science ®Google Scholar
• Carr , P , Geman , H , Madan , DB and Yor , M . 2003 . Stochastic volatility for Lévy processes . Math. Finance , 13 : 345 – 382 .
   Web of Science ®Google Scholar
• Carr , P , Geman , H , Madan , DB and Yor , M . 2004 . From local volatility to local Lévy models . Quant. Finance , 4 : 581 – 588 .
   Web of Science ®Google Scholar
• Carr , P and Wu , L . 2004 . Time-changed Lévy processes and option pricing . J. Financial Econ. , 71 : 113 – 141 .
   Web of Science ®Google Scholar
• Chan , T . 1999 . Pricing contigent claims on stocks driven by Lévy processes . Ann. Appl. Probab. , 9 : 504 – 528 .
   Web of Science ®Google Scholar
• Cox , J . 1996 . Notes on option pricing I: Constant elasticity of variance diffusion . J. Portfol. Mgmt , 23 : 5 – 17 .
   Google Scholar
• Cox , J and Ross , SA . 1976 . The valuation of options for alternative stochastic processes . J. Financial Econ. , 3 : 145 – 166 .
   Web of Science ®Google Scholar
• Derman , E and Kani , I . 1994 . Riding on a simile . Risk , 7 : 32 – 39 .
   Google Scholar
• D'Halluin , Y , Forsyth , P and Labahn , G . 2003 . “ A penalty method for American options with jump-diffusion processes ” . Working Paper University of Waterloo .
   Google Scholar
• Dupire , B . 1994 . Pricing with a smile . Risk , 7 : 18 – 20 .
   Google Scholar
• Etheridge , A . 2002 . A Course in Financial Calculus , Cambridge : Cambridge University Press .
   Google Scholar
• Geman , H , Madan , D and Yor , M . 2001 . Time changes for Lévy processes . Math. Finance , 11 : 79 – 96 .
   Web of Science ®Google Scholar
• Glosten , LR , Jagannathan , R and Runkle , D . 1993 . Relationship between the expected value and the volatility of the nominal excess return on stocks . J. Finance , 48 : 1779 – 1802 .
   Web of Science ®Google Scholar
• Lamperti , J . 1962 . Semi-stable stochastic processes . Trans. Am. Math. Soc. , 104 : 62 – 78 .
   Google Scholar
• Lamperti , J . 1972 . Semi-stable Markov processes . I.Z. Wahrscheinlichkeitstheorie Verw. Gebiete ,
   Google Scholar
• Madan , DB and Eberlein , E . 2006 . “ Sato processes and the valuation of structured products ” . Working Paper Available online at: http://ssrn.com/abstract=957167
   Google Scholar
• Madan , DB and Yor , M . 2005 . “ CGMY and Meixner subordinators are absolutely continuous with respect to one sided stable subordinators ” . Working Paper
   Google Scholar
• Masoliver , J and Perello , J . 2002 . A correlated stochastic volatility model measuring leverage and other stylized facts . Int. J. Theor. Appl. Finance , 5 : 541 – 562 .
   Google Scholar
• Matache , AM , Petersdorff , TV and Schwab , C . 2004 . Fast deterministic pricing of options on Lévy driven assets . M2AN Math. Model. Numer. Anal. , 38 : 37 – 71 .
   Web of Science ®Google Scholar
• Nelson , DB . 1991 . Conditional heteroskedasticity in asset pricing: a new approach . Econometrica , 59 : 347 – 370 .
   Web of Science ®Google Scholar
• Schroder , M . 1989 . Computing the constant elasticity of variance option pricing formula . J. Finance , 44 : 211 – 219 .
   Web of Science ®Google Scholar
• Williams , D . 1974 . Path decomposition and continuity of local time for one-dimensional diffusions . Proc. London Math. Soc. , 28 : 738 – 768 .
   Web of Science ®Google Scholar
• Xiao , Y . 2005 . “ Leveraged Lévy processes as models for stock prices ” . PhD thesis University of Maryland . Available online at: https://drum.umd.edu/dspace/bitstream/1903/3064/1/umi-umd-2871.pdf
   Google Scholar
• Yor , M , Carmona , P and Petit , F . 1994 . On exponential functionals of certain Lévy processes . Stochast. Stochast. Rep. , 47 : 71 – 101 .
   Google Scholar
• Yu , J . 2005 . On leverage in a stochastic volatility model . J. Econometr. , 127 ( 2 ) : 165 – 178 .
   Web of Science ®Google Scholar