Option pricing and hedging under a stochastic volatility Lévy process model

Bates D. S. (1996) Jumps and stochastic volatility: The exchange rate processes implicit in deutschemark options. Review of Financial Studies 9(1): 69–107 Black F., Scholes M. (1973) The pricing of options and corporate liabilities. Journal of Political Economy 81(3): 637–654 Boyarchenko S.I., Levendorskiĭ S.Z. (2002) Non-Gaussian Merton-Black-Scholes theory. World Scientific, New Jersey Buffington J., Elliott R. J. (2002) American options with regime switching. International Journal of Theoretical and Applied Finance 5(5): 497–514 Carr P., Geman H., Madan D., Yor M. (2003) Stochastic volatility for Lévy processes. Mathematical Finance 3: 345–382 Carr P., Madan D. (1999) Option valuation using the fast Fourier transform. Journal of Computational Finance 2(4): 61–73 Cont R., Tankov P. (2004) Financial modelling with jump processes. Chapman & Hall/CRC, London Duan J.-C. (1995) The GARCH option pricing model. Mathematical Finance 5(1): 13–32 Elliott R. J., Chan L., Siu T. K. (2005) Option pricing and Esscher transform under regime switching. Annals of Finance 1(4): 423–432 Elliott R. J., Kopp P. E. (2010) Mathematics of financial markets. (2nd ed). Springer, New York Föllmer H., Schweizer M. (1991) Hedging of contingent claims under incomplete information. In: Davis M.H.A, Elliott R.J. (eds) Applied stochastic analysis (Vol. 5). Gordon and Breach, New York, pp 389–414 Föllmer H., Sondermann D. (1986) Hedging of non-redundant contingent claims. In: Hildenbrand W., Mas-Colell A. (eds) Contributions to Mathematical Economics. North-Holland Press, Amsterdam, pp 205–223 Fujiwara T., Miyahara Y. (2003) The minimal entropy martingale measures for geometric Lévy processes. Finance & Stochastics 7: 509–531 Gerber H., Shiu E. (1994) Option pricing by Esscher transforms. Transactions of the Society of Actuaries XLVI: 99–140 Heston S. L. (1993) A closed form solution for options with stochastic volatility with applications to bond and currency options. Review of Financial Studies 6: 327–343 Jackson K. R., Jaimungal V., Surkov S. (2007) Option pricing with regime switching Lévy processes using fourier space time stepping. Journal of Computational Finance 12(2): 1–29 Kim Y., Lee J. H. (2007) The relative entropy in CGMY processes and its applications to finance. Mathematical Methods of Operations Research 66(2): 327–338 Kim Y. S., Rachev S. T., Bianchi M. L., Fabozzi F. J. (2010) Tempered stable and tempered infinitely divisible GARCH models. Journal of Banking & Finance 34: 2096–2109 Kim Y. S., Rachev S. T., Chung D. M., Bianchi M. L. (2009) The modified tempered stable distribution, GARCH-models and option pricing. Probability and Mathematical Statistics 29(1): 91–117 Lewis, A. L. (2001). A simple option formula for general jump-diffusion and other exponential Lévy processes. Available from http://www.optioncity.net. Liu, R. H., Zhang, Q., & Yin, G. (2006). Option pricing in a regime switching model using the fast Fourier transform. Journal of Applied Mathematics and Stochastic Analysis 1–22. Article ID: 18109, doi:10.1155/JAMSA/2006/18109. Menn C., Rachev S.T. (2009) Smoothly truncated stable distributions, GARCH-models, and option pricing. Mathematical Methods in Operation Research 69(3): 411–438 Rachev S. T., Kim Y. S., Bianchi M. L., Fabozzi F. J. (2011) Financial models with y processes and volatility clustering. Wiley, New Jersey Rachev S. T., Mittnik S. (2000) Stable paretian models in finance. Wiley, New York Sato K. (1999) Lévy processes and infinitely divisible distributions. Cambridge University Press, Cambridge