Pricing Asian Options Under a Hyper-Exponential Jump Diffusion Model

References

• Abate J., Whitt W. The Fourier-series method for inverting transforms of probability distributions. Queueing Systems (1992) 10(1–2):5–88Crossref, Google Scholar
• Albrecher H., Vanmaele M., De Schepper A., Dhaene J., Reynaerts H., Schoutens W., Van Goethem P. The valuation of Asian options for market models of exponential Lévy type. Proc. 2nd Actuarial Financial Math. Day (2004) (Royal Flemish Academy of Belgium for Sciences and the Arts, Brussels) 11–20Google Scholar
• Albrecher H., Predota M. On Asian option pricing for NIG Lévy processes. J. Comput. Appl. Math. (2004) 172(1):153–168Crossref, Google Scholar
• Albrecher H., Mayer P. A., Schoutens W. General lower bounds for arithmetic Asian option prices. Appl. Math. Finance (2008) 15(2):123–149Crossref, Google Scholar
• Applebaum D.Lévy Processes and Stochastic Calculus (2004) (Cambridge University Press, Cambridge, UK) Crossref, Google Scholar
• Bayraktar E., Xing H. Pricing Asian options for jump diffusions. Math. Finance (2011) 21(1):117–143Crossref, Google Scholar
• Broadie M., Glasserman P., Alexander C. Simulation in option pricing and risk management. Handbook of Risk Management and Analysis (1999) (Wiley, Chichester, UK) 173–207Google Scholar
• Cai N. On first passage times of a hyper-exponential jump diffusion process. Oper. Res. Lett. (2009) 37(2):127–134Crossref, Google Scholar
• Cai N., Kou S. G. Option pricing under a mixed-exponential jump diffusion model. Management Sci. (2011) 57(11):2067–2081Link, Google Scholar
• Cai N., Kou S. G., Liu Z. A two-sided Laplace inversion algorithm with computable error bounds and its application in financial engineering. (2008) . Working paper, Hong Kong University of Science and Technology, Hong Kong, and Columbia University, New YorkGoogle Scholar
• Carmona P., Petit F., Yor M. On the exponential functionals of certain Lévy processes. Stochastics and Stochastic Rep. (1994) 47(1–2):71–101Crossref, Google Scholar
• Carr P., Madan D. B. Option valuation using the fast Fourier transform. J. Comput. Finance (1999) 2(4):61–73Crossref, Google Scholar
• Carr P., Schröder M. Bessel processes, the integral of geometric Brownian motion, and Asian options. Theory Probab. Appl. (2004) 48(3):400–425Crossref, Google Scholar
• Choudhury G. L., Lucantoni D. M., Whitt W. Multidimensional transform inversion with applications to the transient M/G/1 queue. Ann. Appl. Probability (1994) 4(3):719–740Crossref, Google Scholar
• Craddock M., Heath D., Platen E. Numerical inversion of Laplace transforms: A survey of techniques with applications to derivative pricing. J. Computat. Finance (2000) 4(1):57–81Crossref, Google Scholar
• Curran M. Valuing Asian and portfolio options by conditioning on the geometric mean. Management Sci. (1994) 40(12):1705–1711Link, Google Scholar
• Dewynne J. N., Shaw W. T. Differential equations and asymptotic solutions for arithmetic Asian options: “Black-Scholes formulae” for Asian rate calls. Eur. J. Appl. Math. (2008) 19(4):353–391Crossref, Google Scholar
• Dubois F., Lelièvre T. Efficient pricing of Asian options by the PDE approach. J. Comput. Finance (2004) 8(2):55–64Crossref, Google Scholar
• Dufresne D. Laguerre series for Asian and other options. Math. Finance (2000) 10(4):407–428Crossref, Google Scholar
• Dufresne D. The integral of geometric Brownian motion. Adv. Appl. Probab. (2001) 33(1):223–241Crossref, Google Scholar
• Fu M. C., Madan D. B., Wang T. Pricing continuous Asian options: A comparison of Monte Carlo and Laplace transform inversion methods. J. Comput. Finance (1999) 2(2):49–74Crossref, Google Scholar
• Fusai G. Pricing Asian option via Fourier and Laplace transforms. J. Comput. Finance (2004) 7(3):87–106Crossref, Google Scholar
• Geman H., Yor M. Bessel processes, Asian options, and perpetuities. Math. Finance (1993) 3(4):349–375Crossref, Google Scholar
• Glasserman P.Monte Carlo Methods in Financial Engineering (2003) (Springer, New York) Crossref, Google Scholar
• Henderson V., Hobson D., Shaw W. T., Wojakowski R. Bounds for in-progress oating-strike Asian options using symmetry. Ann. Oper. Res. (2007) 151(1):81–98Crossref, Google Scholar
• Ingersoll J. E.Theory of Financial Decision Making (1987) (Rowman and Littlefield, Lanham, MD) Google Scholar
• Ju N. Pricing Asian and basket options via Taylor expansion. J. Comput. Finance (2002) 5(3):79–103Crossref, Google Scholar
• Kou S. G. A jump-diffusion model for option pricing. Management Sci. (2002) 48(8):1086–1101Link, Google Scholar
• Lapeyre B., Temam E. Competitive Monte Carlo methods for the pricing of Asian options. J. Comput. Finance (2001) 5(1):39–57Crossref, Google Scholar
• Levendorskiĭ S. Pricing of the American put under Lévy processes. Internat. J. Theoret. Appl. Finance (2004) 7(3):303–336Crossref, Google Scholar
• Lewis A. Asian connections. Wilmott Magazine (2002) September):57–63Google Scholar
• Linetsky V. Spectral expansions for Asian (average price) options. Oper. Res. (2004) 52(6):856–867Link, Google Scholar
• Matsumoto H., Yor M. Exponential functionals of Brownian motion, I: Probability laws at fixed times. Probab. Surveys (2005a) 2:312–347Crossref, Google Scholar
• Matsumoto H., Yor M. Exponential functionals of Brownian motion, II: Some related diffusion processes. Probab. Surveys (2005b) 2:348–384Crossref, Google Scholar
• Milevsky M. A., Posner S. E. Asian options, the sum of lognormals and the reciprocal gamma distribution. J. Financial Quant. Anal. (1998) 33(3):409–422Crossref, Google Scholar
• Øksendal B., Sulem A.Applied Stochastic Control of Jump Diffusions (2004) (Springer, New York) Google Scholar
• Petrella G. An extension of the Euler Laplace transform inversion algorithm with applications in option pricing. Oper. Res. Lett. (2004) 32(4):380–389Crossref, Google Scholar
• Rogers L., Shi Z. The value of an Asian option. J. Appl. Probab. (1995) 32(4):1077–1088Crossref, Google Scholar
• Schiff J.The Laplace Transform: Theory and Applications (1999) (Springer, New York) Crossref, Google Scholar
• Schröder M. Analytical ramifications of derivatives valuation: Asian options and special functions. (2002) . Working paper, University of Mannheim, Mannheim, GermanyGoogle Scholar
• Shaw W. T.Modelling Financial Derivatives with Mathematica (1998) (Cambridge University Press, Cambridge, UK) Google Scholar
• Shaw W. T. A reply to pricing continuous Asian options by Fu, Madan and Wang. (2000) . Working paper, University College, LondonGoogle Scholar
• Shaw W. T. Pricing Asian options by contour integration, including asymptotic methods for low volatility. (2002) . Working paper, University College, LondonGoogle Scholar
• Shreve S. E.Stochastic Calculus for Finance II (2004) (Springer, New York) Crossref, Google Scholar
• Thompson G. W. P. Fast narrow bounds on the value of Asian options. (1998) . Working paper, Cambridge University, Cambridge, UKGoogle Scholar
• Turnbull S. M., Wakeman L. M. A quick algorithm for pricing European average options. J. Financial Quant. Anal. (1991) 26(3):377–389Crossref, Google Scholar
• Vecer J. A new PDE approach for pricing arithmetic average Asian options. J. Comput. Finance (2001) 4(4):105–113Crossref, Google Scholar
• Vecer J. Unified Asian pricing. Risk (2002) 15(6):113–116Google Scholar
• Vecer J., Xu M. Pricing Asian options in a semi-martingale model. Quant. Finance (2004) 4(2):170–175Crossref, Google Scholar
• Yor M.Exponential Functionals of Brownian Motion and Related Processes (2001) (Springer, New York) Crossref, Google Scholar
• Zhang J. E. A semi-analytical method for pricing and hedging continuously sampled arithmetic average rate options. J. Comput. Finance (2001) 5(1):1–20Crossref, Google Scholar
• Zhang J. E. Pricing continuously sampled Asian options with perturbation method. J. Futures Markets (2003) 23(6):535–560Crossref, Google Scholar