American Call Options Under Jump‐Diffusion Processes – A Fourier Transform Approach

References

• Abramowitz , M. and Stegun , I. A. 1970 . Handbook of Mathematical Functions , New York : Dover .
   Google Scholar
• Ahn , C. M. and Thompson , H. E. 1992 . The impact of jump risks on nominal interest rates and foreign exchange rates. . Review of Quantitative Finance and Accounting , 2 (1) : 17 – 31 .
   Google Scholar
• Alobaidi , G. and Mallier , R. 2002 . Laplace transform and the American straddle. . Journal of Applied Mathematics , 2 (3) : 121 – 129 .
   Google Scholar
• Amin , K. I. 1993 . Jump diffusion option valuation in discrete time. . Journal of Finance , 48 (5) : 1833 – 1863 .
   Web of Science ®Google Scholar
• Andersen , L. and Andreasen , J. 2000 . Jump‐diffusion processes: volatility smile fitting and numerical methods for option pricing. . Review of Derivatives Research , 4 (3) : 231 – 262 .
   Google Scholar
• Ball , C. and Torous , W. 1985 . On jumps in common stock prices and their impact on call option pricing. . Journal of Finance , 40 (1) : 155 – 173 .
   Web of Science ®Google Scholar
• Barone‐Adesi , G. 2005 . The saga of the American put. . Journal of Banking and Finance , 29 (11) : 2909 – 2918 .
   Web of Science ®Google Scholar
• Bates , D. S. 1996 . Jumps and stochastic volatility: Exchange rate processes implicit in deutshe mark options. . Review of Financial Studies , 9 (1) : 69 – 107 .
   Web of Science ®Google Scholar
• Briani , M. , Chioma , C. L. and Natalini , R. 2004 . Convergence of numerical schemes for viscosity solutions to integro‐differential degenerate parabolic problems arising in financial theory. . Numerische Mathematik , 98 (4) : 607 – 646 .
   Web of Science ®Google Scholar
• Broadie , M. and Yamamoto , Y. 2003 . Application of the fast Gauss transform to option pricing. . Management Science , 49 (8) : 1071 – 1088 .
   Web of Science ®Google Scholar
• Carr , P. and Hirsa , A. 2003 . Why be backward? Forward equations for American options. . Risk , 16 (1) : 103 – 107 .
   Google Scholar
• Carr , P. and Madan , D. B. 1999 . Option valuation using the fast Fourier transform. . Journal of Computational Finance , 2 (4) : 61 – 73 .
   Google Scholar
• Cheang , G. , Chiarella , C. and Ziogas , A. 2006 . “ American‐style options on two assets under jump‐diffusion processes ” . Working Paper, University of Technology, Sydney
   Google Scholar
• Chen , X. and Chadam , J. 2007 . A mathematical analysis of the optimal exercise boundary for American put options. . SIAM Journal on Mathematical Analysis , 38 (5) : 1613 – 1641 .
   Web of Science ®Google Scholar
• Chiarella , C. , Kucera , A. and Ziogas , A. 2004 . “ A survey of the integral representation of American option prices ” . Research Paper, No. 118, Quantitative Finance Research Centre, University of Technology, Sydney
   Google Scholar
• Chiarella , C. and Ziogas , A. 2005 . Evaluation of American strangles. . Journal of Economic Dynamics and Control , 29 (1–2) : 31 – 62 .
   Web of Science ®Google Scholar
• Chiarella , C. and Ziogas , A. 2006 . “ A Fourier transform analysis of the American call option on assets driven by jump‐diffusion processes ” . Research Paper, No. 174, Quantitative Finance Research Centre, University of Technology, Sydney
   Google Scholar
• Debnath , L. 1995 . Integral Transforms and their Applications , Baton Rouge : CRC Press .
   Google Scholar
• d'Halluin , Y. , Forsyth , P. and Labahn , G. 2004 . A penalty method for American options with jump diffusion processes. . Numerische Mathematik , 97 (2) : 321 – 352 .
   Web of Science ®Google Scholar
• Geske , R. and Johnson , H. E. 1984 . The American put option valued analytically. . Journal of Finance , 39 (5) : 1511 – 1524 .
   Web of Science ®Google Scholar
• Gukhal , C. R. 2001 . Analytical valuation of American options on jump‐diffusion processes. . Mathematical Finance , 11 (1) : 97 – 115 .
   Web of Science ®Google Scholar
• Jacka , S. D. 1991 . Optimal stopping and the American put. . Mathematical Finance , 1 (2) : 1 – 14 .
   Google Scholar
• Jamshidian , F. 1992 . An analysis of American options. . Review of Futures Markets , 11 (1) : 72 – 80 .
   Google Scholar
• Jamshidian , F. 2007 . The duality of optimal exercise and domineering claims: a Doob–Meyer decomposition approach to the Snell envelope. . Statistics: An International Journal of Probability and Stochastic Processes , 79 (1–2) : 27 – 60 .
   Google Scholar
• Jarrow , R. A. and Rosenfeld , E. 1984 . Jump risks and the intertemporal capital asset pricing model. . Journal of Business , 57 (3) : 337 – 351 .
   Google Scholar
• Jorion , P. 1988 . On jump processes in the foreign exchange and stock markets. . Review of Financial Studies , 1 (4) : 427 – 455 .
   Web of Science ®Google Scholar
• Kallast , S. and Kivinukk , A. 2003 . Pricing and hedging American options using approximations by Kim integral equations. . European Finance Review , 7 (3) : 361 – 383 .
   Google Scholar
• Karatzas , I. 1988 . On the pricing of American options. . Applied Mathematics and Optimization , 17 (1) : 37 – 60 .
   Web of Science ®Google Scholar
• Kim , I. J. 1990 . The analytic valuation of American options. . Review of Financial Studies , 3 (4) : 547 – 572 .
   Web of Science ®Google Scholar
• Kou , S. G. 2002 . A jump‐diffusion model for option pricing. . Management Science , 48 (8) : 1086 – 1101 .
   Web of Science ®Google Scholar
• Kuske , R. A. and Keller , J. B. 1998 . Optimal exercise boundary for an American put option. . Applied Mathematical Finance , 5 (2) : 107 – 116 .
   Google Scholar
• Lee , R. W. 2004 . Option pricing by transform methods: Extensions, unification and error control. . Journal of Computational Finance , 7 (3) : 51 – 86 .
   Google Scholar
• Lewis , A. L. 2000 . Option Valuation under Stochastic Volatility , California : Finance Press .
   Google Scholar
• McKean , H. P. 1965 . Appendix: A free boundary value problem for the heat equation arising from a problem in mathematical economics. . Industrial Management Review , 6 (2) : 32 – 39 .
   Google Scholar
• Merton , R. C. 1976 . Option pricing when underlying stock returns are discontinuous. . Journal of Financial Economics , 3 (1–2) : 125 – 144 .
   Web of Science ®Google Scholar
• Meyer , G. H. 1998 . The numerical valuation of options with underlying jumps. . Acta Mathematica , 67 (1) : 69 – 82 .
   Google Scholar
• Myneni , R. 1992 . The pricing of the American option. . The Annals of Applied Probability , 2 : 1 – 23 .
   Google Scholar
• Pelsser , A. 2000 . Pricing double barrier options using Laplace transforms. . Finance and Stochastics , 4 (1) : 95 – 104 .
   Google Scholar
• Peskir , G. 2005 . On the American option problem. . Mathematical Finance , 15 (1) : 169 – 181 .
   Web of Science ®Google Scholar
• Pham , H. 1997 . Optimal stopping, free boundary, and American option in a jump‐diffusion model. . Applied Mathematics and Optimization , 35 (2) : 145 – 164 .
   Web of Science ®Google Scholar
• Scott , L. O. 1997 . Pricing stock options in a jump‐diffusion model with stochastic volatility and interest rates: applications of Fourier inversion methods. . Mathematical Finance , 7 (4) : 413 – 426 .
   Web of Science ®Google Scholar
• Wilmott , P. , Dewynne , J. and Howison , S. 1993 . Option Pricing: Mathematical Models and Computation , London : Oxford Financial Press .
   Google Scholar