×

zbMATH — the first resource for mathematics

An efficient transform method for Asian option pricing. (English) Zbl 1357.91053

MSC:
91G60 Numerical methods (including Monte Carlo methods)
65C20 Probabilistic models, generic numerical methods in probability and statistics
65T50 Numerical methods for discrete and fast Fourier transforms
65D07 Numerical computation using splines
62P05 Applications of statistics to actuarial sciences and financial mathematics
60E10 Characteristic functions; other transforms
91G20 Derivative securities (option pricing, hedging, etc.)
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] H. Albrecher, P. Mayer, and W. Schoutens, General lower bounds for arithmetic Asian option prices, Appl. Math. Finance, 15 (2008), pp. 123–149. · Zbl 1134.91394
[2] H. Albrecher and M. Predota, Bounds and approximations for discrete Asian options in a variance-gamma model, Grazer Math. Ber., 345 (2002), pp. 35–57. · Zbl 1053.91056
[3] B. Alziary, J. P. Dechamps, and P. F. Koehl, PDE approach to Asian options: Analytical numerical evidence, J. Banking Finance, 21 (1997), pp. 613–640.
[4] J. Andreasen, The pricing of discretely sampled Asian and lookback options: A change of numeraire approach, J. Comput. Finance, 1 (1998), pp. 15–36.
[5] O. Barndorff-Nielsen, Processes of normal inverse Gaussian type, Finance Stoch., 2 (1997), pp. 41–68. · Zbl 0894.90011
[6] E. Benhamou, Fast Fourier transform for discrete Asian options, J. Comput. Finance, 6 (2002), pp. 49–61.
[7] S. Boyarchenko and S. Levendorskii, Non-Gaussian Merton-Black-Scholes Theory, Adv. Ser. Stat. Sci. Appl. Probab. 9, World Scientific, River Edge, NJ, 2002.
[8] S. Boyarchenko and S. Levendorskii, Efficient versions of the Fourier transform in applications to option pricing, J. Comp. Finance, 18 (2014).
[9] S. Boyarchenko and S. Levendorskii, Option pricing for truncated Levy processes, Int. J. Theor. App. Finance, 3 (2000), pp. 549–552. · Zbl 0973.91037
[10] P. Carr, H. Geman, D. B. Madan, and M. Yor, The fine structure of asset returns: An empirical investigation, J. Business, 75 (2002), pp. 305–332.
[11] A. Carverhill and L. Clewlow, Flexible convolution: Valuing average rate (Asian) options, Risk, 3 (1990), pp. 25–29.
[12] A. Cerny and I. Kyriakou, An improved convolution algorithm for discretely sampled Asian options, Quant. Finance, 11 (2011), pp. 381–389. · Zbl 1232.91653
[13] O. Christensen, An Introduction to Frames and Riesz Bases, Birkhäuser, Boston, 2003. · Zbl 1017.42022
[14] T. Dai and Y. Lyuu, Accurate and efficient lattice algorithms for American-style Asian options with range bounds, Appl. Math. Comput., 209 (2009), pp. 238–253. · Zbl 1156.91365
[15] M. De Innocentis and S. Levendorskii, Pricing discrete barrier options and credit default swaps under Levy processes, Quant. Finance, 14 (2014), pp. 1337–1365. · Zbl 1402.91825
[16] P. Den Iseger and E. Oldenkamp, Pricing guaranteed return rate products and discretely sampled Asian options, J. Comput. Finance, 9 (2006), pp. 1–39.
[17] J. Dewynne and P. Wilmott, Asian options as linear complementary problems, Adv. Futures Options Res., 8 (1995), pp. 145–173.
[18] E. Eberlein and A. Papapantoleon, Equivalence of floating and fixed strike Asian and lookback options, Stochastic Process. Appl., 115 (2005), pp. 31–40. · Zbl 1114.91049
[19] F. Fang and C. W. Oosterlee, A novel pricing method for European options based on Fourier-cosine series expansions, SIAM J. Sci. Comput., 31 (2009), pp. 826–848. · Zbl 1186.91214
[20] L. Feng and X. Lin, Inverting analytic characteristic functions and financial applications, SIAM J. Finan. Math., 4 (2013), pp. 372–398. · Zbl 1282.60021
[21] L. Feng and V. Linetsky, Pricing discretely monitored barrier options and defaultable bonds in Levy process models: A fast Hilbert transform approach, Math. Finance, 18 (2008), pp. 337–384. · Zbl 1141.91438
[22] G. Fusai, D. Marazzina, and M. Marena, Pricing discretely monitored Asian options by maturity randomization, SIAM J. Finance Math., 2 (2011), pp. 383–403. · Zbl 1215.91079
[23] G. Fusai and A. Meucci, Pricing discretely monitored Asian options under Levy processes, J. Banking Finance, 32 (2008), pp. 2076–2088.
[24] H. Geman and D. B. Madan, Risks in returns: A pure jump perspective, in Exotic Option Pricing and Advanced Levy Models, A. Kyprianou, W. Schountens and P. Wilmott, eds., Wiley, Chichester, 2005, pp. 51–66.
[25] C. Heil, A Basis Theory Primer. Birkhauser, New York, 2011. · Zbl 1227.46001
[26] N. Ju, Pricing Asian and basket options via Taylor expansion, J. Comput. Finance, 5 (2002), pp. 79–103.
[27] A. Kemna and A. Vorst, A pricing method for options based on average asset values, J. Banking and Finance, 14 (1990), pp. 113–129.
[28] J. L. Kirkby, Efficient option pricing by frame duality with the fast Fourier transform, SIAM J. Finan. Math., 6 (2015), pp. 713–747. · Zbl 1320.91155
[29] J. L. Kirkby, Robust option pricing with characteristic functions and the B-spline order of density projection, J. Comput. Finance, to appear.
[30] J. L. Kirkby and S. Deng, Static hedging and pricing of exotic options with payoff frames, Math. Finance., under review. · Zbl 1411.91567
[31] D. Lemmens, L. Z. J. Liang, J. Tempere, and A. De Schepper, Pricing bounds for discrete arithmetic Asian options under Levy models, Phys. A, 389 (2010), pp. 5193–5207.
[32] S.Z. Levendorskii and J. Xie, Pricing Discretely sampled Asian Options Under Levy Processes, , 2012.
[33] D. Madan and E. Seneta, The variance gamma (v.g.) model for share market returns, J. Business, 63 (1990), pp. 511–524.
[34] J. Nielsen and K. Sandmann, Pricing bounds on Asian options, J. Finance Quant. Anal., 38 (2003), pp. 449–473.
[35] P. Sabino, Monte Carlo methods and path-generation techniques for pricing multi-asset path- dependent options, preprint, , 2007.
[36] K-I. Sato, Levy Processes and Infinitely Divisible Distributions, Cambridge University Press, Cambridge, 1999. · Zbl 0973.60001
[37] F. Stenger, Numerical Methods based on Sinc and Analytic Functions, Springer-Verlag, New York, 1993. · Zbl 0803.65141
[38] M. Unser and I. Daubechies, On the approximation power of convolution-based least squares versus interpolation, IEEE Trans. Signal Process., 45 (1997), pp. 1697–1711. · Zbl 0879.94005
[39] M. Unser, Vanishing moments and the approximation power of wavelet expansions, In Proceedings of the 1996 IEEE International Conference on Image Processing, IEEE, Piscataway, NJ, 1996, pp. 629–632.
[40] J. Vecer, A new PDE approach for pricing arithmetic average Asian options, J. Comput. Finance, 4 (2001), pp. 105–115.
[41] B. Zhang and C. W. Oosterlee, Efficient pricing of European-style Asian options under exponential Lévy processes based on Fourier cosine expansions, SIAM J. Finan. Math., 4 (2013), pp. 399–426. · Zbl 1282.65023
[42] J. E. Zhang, Pricing continuously sampled Asian options with perturbation method, J. Futures Markets, 23 (2003), pp. 535–560.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.