288
Views
4
CrossRef citations to date
0
Altmetric
Original Articles

PIDE and Solution Related to Pricing of Lévy Driven Arithmetic Type Floating Asian Options

, &
Pages 630-652 | Received 14 Dec 2014, Accepted 26 Feb 2015, Published online: 24 Jun 2015

References

  • Almendral, A., and Oosterlee, C.W. 2005. Numerical valuation of options with jumps in the underlying. Applied Numerical Mathematics 53:1–18.
  • Amaral, L., Plerou, V., Gopikeishnan, P., Meyer, M., and Stanly, H. 2000. The distribution of returns of stock prices. International Journal of Theoretical and Applied Finance 3:365–369.
  • Applebaum, D. 2004. Lévy Processes and Stochastic Calculus. Cambridge, UK: Cambridge University Press.
  • Amin, K. 1993. Jump diffusion option valuation in discrete time. Journal of Finance 48(5):1833–1863.
  • Albrecher, H. 2004. The valuation of Asian options for market models of exponential Lévy type. In Proceedings of the 2nd Actuarial and Financial Mathematics Day, ed. Brussels, M., et al. Royal Flemish Academy of Belgium for Arts and Sciences, 11–20.
  • Broadie, M., and Glasserman, P. 1996. Estimating security price derivatives using simulation, Management Science 42:269–285.
  • Broadie, M., Glasserman, P., and Kou, S.G. 1999. Connecting discrete and continuous path-dependent options. Finance and Stochastics 3:55–82.
  • Benhamou, E. 2002. Fast Fourier transform for discrete Asian options. Journal of Computational Finance 49–68. [Online only September 24]
  • Chan, T. 1999. Pricing contingent claims on stocks derived by Lévy processes. Annals of Applied Probability 9(2):504–528.
  • Carr, P., and Mayo, A. 2007. On the numerical evaluation of option prices in jump diffusion processes. European Journal of Finance 13(4):353–372.
  • Carr, P., and Madan, D. 1999. Option valuation using the fast Fourier transform. Journal of Computational Finance 2(4):61–73.
  • Clift, S., and Forsyth, P. 2008. Numerican solution of two asset jump di_usion models for option valuation. Applied Numerical Mathematics 58(6):743–782.
  • Cont, R., and Tankov, P. 2004. Financial Modelling with Jump Processes. Financial Mathematics Series. Boca Raton, FL: Chapman & Hall/CRC Press.
  • Cont, R., and Tankov, P. 2002. Calibration of Jump-Diffusion Option Pricing Models: A Robust Non-Parametric Approach. Rapport Interne CMAP No. 490.
  • Debnath, L., and Bhatta, D. 2006. Integral Transforms and Their Applications. Boca Raton, FL: Chapman Hall/CRC Press.
  • D’Halluin, Y., Forsyth, P., and Vetzal, K. 2005. Robust numerical methods for contingent claims under jump diffusion processes. IMA Journal of Numerical Analysis 25(1):87–112.
  • Elshegmani, Z.A., Ahmad, R.R., and Jamaan, S.H. 2011. On the modified arithmetic Asian Option equation and its analytical solution. Applied Mathematical Sciences 5:1217–1227.
  • Föllmer, H., and Schweizer, M. 1991. Hedging of contingent claims under incomplete information. In Applied Stochastic Analysis, eds. Davis, M.H. A. and Elliott, R.J. Stochastics Monographs, 5. New York: Gordon and Breach, 389–414.
  • Frontczak, R., and Schöbel, R. 2010. On modified Mellin transforms, Gauss-Laguerre quadrature, and the valuation of American call options. Journal of Computation and Applied Mathematics 234(5):1559–1571
  • Geman, H., and Yor, M. 1993. Bessel processes, Asian Option, and perpetuities. Journal of Mathematical Finance 3(4):349–375
  • Dahlquist, G., and Björck, A. 2008. Numerical Methods in Scientific Computing, 33. Philadelphia: SIAM.
  • Hilliard, J., and Schwartz, A. 2005. Pricing European and American derivatives under a jump-diffusion process: A bivariate tree approach. Journal of Financial and Quantitative Analysis 40(3):671–691.
  • Lévy, E. 1992. Pricing European average rate currency options. Journal of International Money and Finance 11:474–491.
  • Lee, R. 2004. Option pricing by transform methods: Extensions, unification, and error control. Journal of Computational Finance 7(3):51–86.
  • Mayo, A. 2008. Methods for the rapid solution of the pricing PIDEs in exponential and Merton models. Journal of Computational and Applied Mathematics 222(1):128–143.
  • Papapantoleon, A. 2008. An Introduction to Lévy Processes With Applications in Finance. Lecture Notes, TU Vienna. arXiv/0804.0482.
  • Panini, R., and Srivastav, R.P. 2004. Option pricing with Mellin transform. Mathematical and Computer Modelling 40:43–56.
  • Rogers, L., and Shi, Z. 1995. The value of an Asian option. Journal of Applied Probability 32:1277–1088.
  • Schoutens, W. 2003. Lévy Processes in Finance: Pricing Financial Derivatives, 1st ed Dordrecht: Wiley.
  • Schoutens, W., and Symens, S. 2003. The pricing of exotic options by Monte Carlo simulations in a Lévy market with stochastic volatility. International Journal of Theoretical and Applied Finance 6(8):839–864.
  • SenGupta, I. 2014. Pricing Asian options in financial markets using Mellin transforms. Electronic Journal of Differential Equations 234:1–9.
  • Turnbull, S., and Wakeman, L. 1991. A quick algorithm for pricing European average options. Journal of Financial and Quantitative Analysis 26:377–389.
  • Vecer, J., and Xu, M. 2004. Pricing Asian options in a semimartingale model. Quantitative Finance 4:170–175.
  • Vorst, T.C. F. 1992. Prices and hedge ratios of average exchange rate options. International Review of Financial Analysis 1:179–193.
  • Jörg, W. 2004. Fast construction of the Fejér and Clenshaw-Curtis quadrature rules. BIT Numerical Mathematics 43(1):1–18.
  • Yang, Z., Ewald, C.O., and Menkens, O. 2011. Pricing and hedging of Asian options: quasi-explicit solutions via Malliavia calculus. Mathematical Methods of Operations Research 74:93–120.
  • Zhang, B., and Oosterlee, C.W. 2013. Efficient pricing of European-style Asian options under exponential Lévy processes based on Fourier cosine expansions. SIAM Journal on Financial Mathematics 74:399–426.
  • Zhang, B., and Oosterlee, C.W. 2014. Pricing of early-exercise Asian options under Lévy processes based on Fourier cosine expansions. Applied Numerical Mathematics 74:14–30.
  • Zhang J.E. 2003. Pricing continuously sampled Asian options with perturbation method. Journal of Futures Markets 23(6):535–560.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.