Spectral Expansions for Asian (Average Price) Options

References

• Abramowitz M., Stegun I. A.Handbook of Mathematical Functions (1972) (Dover, New York) Google Scholar
• Borodin A. N., Salminen P.Handbook of Brownian Motion (1996) (Birkhauser, Boston, MA) Crossref, Google Scholar
• Boyle P. P. New life forms on the option landscape. J. Financial Engrg. (1996) 2(3):217–252Google Scholar
• Boyle P. P., Emanuel D. Options on the general mean. (1980) . Working paper, University of British Columbia, Vancouver. British Columbia, CanadaGoogle Scholar
• Boyle P. P., Broadie M., Glasserman P. Monte Carlo methods for security pricing. J. Econom. Dynam. Control (1997) 21:1267–1321Crossref, Google Scholar
• Buchholz H.The Confluent Hypergeometric Function (1969) (Springer, Berlin Germany) Crossref, Google Scholar
• Carmona P., Petit F., Yor M., Yor M. On the distribution and asymptotic results for exponential functionals of Levý processes. Exponential Functionals and Principal Values Related to Brownian Motion. Biblioteca de la Revista Matematica Iberoamericana(Madrid, Spain) 73–121Google Scholar
• Comtet A., Monthus C. Diffusion in a one-dimensional random medium and hyperbolic Brownian motion. J. Physics A (1996) 29:1331–1345Crossref, Google Scholar
• Comtet A., Monthus C., Yor M. Exponential functionals of Brownian motion and disordered systems. J. Appl. Probab. (1998) 35:255–271Crossref, Google Scholar
• Craddock M., Heath D., Platen E. Numerical inversion of Laplace transforms: A survey of techniques with applications to derivatives pricing. J. Computational Finance (2000) 4(1):57–81Crossref, Google Scholar
• Davydov D., Linetsky V. Pricing options on scalar diffusions: An eigenfunction expansion approach. Oper. Res. (2003) 51:185–209Link, Google Scholar
• Donati-Martin C., Ghomrasni R., Yor M. On certain Markov processes attached to exponential functionals of Brownian motion: Applications to Asian options. Revista Matematica Iberoamericana (2001) 17(1):179–193MadridCrossref, Google Scholar
• Dufresne D. Weak convergence of random growth processes with applications to insurance. Insurance: Math. Econom. (1989) 8:187–201Crossref, Google Scholar
• Dufresne D. The distribution of a perpetuity,with applications to risk theory and pension funding. Scandinavian Actuarial J. (1990) 39–79Crossref, Google Scholar
• Dufresne D. Laguerre series for Asian and other options. Math. Finance (2000) 10:407–428Crossref, Google Scholar
• Dufresne D. The integral of geometric Brownian motion. Adv. Appl. Probab. (2001) 33:223–241Crossref, Google Scholar
• Dunford N., Schwartz J.Linear Operators. Part II: Spectral Theory(Self-Adjoint Operators in Hilbert Spaces) (1963) (Wiley, NJ) Google Scholar
• Erdelyi A.Higher Transcendental Functions (1953) 2(McGraw-Hill, New York) Google Scholar
• Eydeland A., Geman H. Domino effect. RISK (1995) 8(4):65–67Google Scholar
• Falloon W. Windows on risk. RISK(June):42–45Google Scholar
• Fu M., Madan D., Wang T. Pricing Asian options: A comparison of analytical and Monte Carlo methods. J. Computational Finance (1998) 2(2):49–74Crossref, Google Scholar
• Geman H., Yor M. Bessel processes, Asian options and perpetuities. Math. Finance (1993) 3:349–375Crossref, Google Scholar
• Gorovoi V., Linetsky V. Black's model of interest rates as options, eigenfunction expansions and Japanese interest rates. Math. Finance (2004) 14:49–78Crossref, Google Scholar
• Gradshteyn I. S., Ryzhik I. M.Tables of Integrals, Series and Products (1994) (Academic Press, New York) Google Scholar
• Grosche C. The path integral on the Poincaré upper half plane with a magnetic field and for the Morse potential. Ann. Phys. (1988) 187:110–134Crossref, Google Scholar
• Ikeda N., Matsumoto H. Brownian motion on the hyperbolic plane and Selberg trace formula. J. Funct. Anal. (1999) 163:63–110Crossref, Google Scholar
• Ito K., McKean H.Diffusion Processes and Their Sample Paths (1974) (Springer, Berlin, Germany) Google Scholar
• Kemna A., Vorst A. A pricing method for options based on average values. J. Banking Finance (1990) 14:113–129Crossref, Google Scholar
• Kent J. Eigenvalue expansions for diffusion hitting times. Z. Wahrsch. verw. Geb. (1980) 52:309–319Crossref, Google Scholar
• Lewis A. Applications of eigenfunction expansions in continuous-time finance. Math. Finance (1998) 8:349–383Crossref, Google Scholar
• Lewis A. Asian connections. Wilmott Magazine (2002) September):57–63Google Scholar
• Linetsky V. The spectral decomposition of the option value. Internat. J. Theoretical Appl. Finance (2004a) 7:337–384Crossref, Google Scholar
• Linetsky V. Lookback options and diffusion times: A spectral expansion approach. Finance and Stochastics (2004b) 8:373–398Crossref, Google Scholar
• Lipton A. Similarities via self-similarities. RISK (1999) September):101–105Google Scholar
• Marcozzi M. D. On the valuation of Asian options by variational methods. SIAM J. Sci. Comput. (2003) 24:1124–1140Crossref, Google Scholar
• McKean H. Elementary solutions for certain parabolic partial differential equations. Trans. Amer. Math. Soc. (1956) 82:519–548Crossref, Google Scholar
• Milevsky M. A., Posner S. E. Asian options, the sum of lognormals, and the reciprocal gamma distribution. J. Financial Quant. Anal. (1998) 33:409–422Crossref, Google Scholar
• Monthus C., Comtet A. On the flux distribution in a one-dimensional disordered system. J. Phys. I (France) (1994) 4:635–653Crossref, Google Scholar
• Morse P. M. Diatomic molecules according to the wave mechanics: II. Vibrational levels. Physical Rev. (1929) 34:57–64Crossref, Google Scholar
• Prudnikov A. P., Brychkov Yu A., Marichev O. I.Integrals and Series (1986) 2(Gordon and Breach, New York) Google Scholar
• Rogers L. C. G., Shi Z. The value of an Asian option. J. Appl. Probab. (1995) 32:1077–1088Crossref, Google Scholar
• Schenzle A., Brand H. Multiplicative stochastic processes in statistical physics. Physical Rev. A (1979) 20:1628–1647Crossref, Google Scholar
• Shaw W.Modeling Financial Derivatives with Mathematica (1997) (Cambridge University Press, Cambridge, U.K.) Google Scholar
• Shaw W. Pricing Asian options by contour integration including asymptotic methods for low volatility. (2002) . Working paper, Nomura. London, U.K.Google Scholar
• Shrivastava H. M., Vasil'ev Yu. V., Yakubovich S. B. A class of index transforms with Whittaker's function in the index. Quart. J. Math. Oxford (1998) 49(2):375–394Crossref, Google Scholar
• Slater L. J.Confluent Hypergeometric Functions (1960) (Cambridge University Press, Cambridge, U.K.) Google Scholar
• Thompson G. W. P. Fast narrow bounds on the value of Asian options. (1999) . Working paper, Judge Institute of Management, University of Cambridge, Cambridge, U.K.Google Scholar
• Turnbull S., Wakeman L. A quick algorithm for pricing European average options. J. Financial Quant. Anal. (1992) 26:377–389Crossref, Google Scholar
• Vecer J. A new PDE approach for pricing arithmetic average Asian options. J. Computational Finance (2001) 4(4):105–113Crossref, Google Scholar
• Vecer J. Unified Asian pricing. RISK (2002) June):113–116Google Scholar
• Wong E., Bellman R. The construction of a class of stationary Markoff processes. Sixteenth Symposium in Applied Mathematics—Stochastic Processes in Mathematical Physics and Engineering (1964) (American Mathematical Society, Providence, RI) 264–276Crossref, Google Scholar
• Yakubovich S. B.Index Transforms (1996) (World Scientific, Singapore) Crossref, Google Scholar
• Yor M. On some exponential functionals of Brownian motion. Adv. Appl. Probab. (1992) 24:509–531Crossref, Google Scholar
• Yor M.Exponential Functionals of Brownian Motion and Related Processes (2001) (Springer, Berlin, Germany) Crossref, Google Scholar
• Zvan R., Forsyth P., Vetzal K. Robust numerical methods for PDE models of Asian options. J. Computational Finance (1997) 1(2):39–78Crossref, Google Scholar