Pricing bounds for discrete arithmetic Asian options under Lévy models
AbstractAnalytical bounds for Asian options are almost exclusively available in the Black–Scholes framework. In this paper we derive bounds for the price of a discretely monitored arithmetic Asian option when the underlying asset follows an arbitrary Lévy process. Explicit formulas are given for Kou’s model, Merton’s model, the normal inverse Gaussian model, the CGMY model and the variance gamma model. The results are compared with the comonotonic upper bound, existing numerical results, Monte carlo simulations and in the case of the variance gamma model with an existing lower bound. The method outlined here provides lower and upper bounds that are quick to evaluate, and more accurate than existing bounds.
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Bibliographic InfoArticle provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.
Volume (Year): 389 (2010)
Issue (Month): 22 ()
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Asian options; Analytical bounds; Lévy models;
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- Raberto, Marco & Scalas, Enrico & Cuniberti, Gianaurelio & Riani, Massimo, 1999.
"Volatility in the Italian stock market: an empirical study,"
Physica A: Statistical Mechanics and its Applications,
Elsevier, vol. 269(1), pages 148-155.
- Marco Raberto & Enrico Scalas & Gianaurelio Cuniberti & Massimo Riani, 2004. "Volatility in the Italian Stock Market: An Empirical Study," Finance 0411006, EconWPA.
- Marco Raberto & Enrico Scalas & Gianaurelio Cuniberti & Massimo Riani, 1999. "Volatility in the Italian Stock Market: an Empirical Study," Papers cond-mat/9903221, arXiv.org.
- Fusai, Gianluca & Meucci, Attilio, 2008. "Pricing discretely monitored Asian options under Levy processes," Journal of Banking & Finance, Elsevier, vol. 32(10), pages 2076-2088, October.
- Turnbull, Stuart M. & Wakeman, Lee Macdonald, 1991. "A Quick Algorithm for Pricing European Average Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 26(03), pages 377-389, September.
- Enrico Scalas & Rudolf Gorenflo & Francesco Mainardi, 2004.
"Fractional calculus and continuous-time finance,"
- Scalas, Enrico & Gorenflo, Rudolf & Mainardi, Francesco, 2000. "Fractional calculus and continuous-time finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 284(1), pages 376-384.
- Kemna, A. G. Z. & Vorst, A. C. F., 1990. "A pricing method for options based on average asset values," Journal of Banking & Finance, Elsevier, vol. 14(1), pages 113-129, March.
- S. G. Kou, 2002. "A Jump-Diffusion Model for Option Pricing," Management Science, INFORMS, vol. 48(8), pages 1086-1101, August.
- D. Lemmens & M. Wouters & J. Tempere & S. Foulon, 2008. "A path integral approach to closed-form option pricing formulas with applications to stochastic volatility and interest rate models," Papers 0806.0932, arXiv.org.
- Friedrich Hubalek & Carlo Sgarra, 2006. "Esscher transforms and the minimal entropy martingale measure for exponential Levy models," Quantitative Finance, Taylor & Francis Journals, vol. 6(2), pages 125-145.
- Mariani, M.C. & Liu, Y., 2007. "Normalized truncated Levy walks applied to the study of financial indices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 377(2), pages 590-598.
- Hélyette Geman & Marc Yor, 1993. "Bessel Processes, Asian Options, And Perpetuities," Mathematical Finance, Wiley Blackwell, vol. 3(4), pages 349-375.
- Merton, Robert C., 1975.
"Option pricing when underlying stock returns are discontinuous,"
787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
- Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
- Linetsky, Vadim, 1998. "The Path Integral Approach to Financial Modeling and Options Pricing," Computational Economics, Society for Computational Economics, vol. 11(1-2), pages 129-63, April.
- Salvatore Micciche` & Giovanni Bonanno & Fabrizio Lillo & Rosario N. Mantegna, 2002.
"Volatility in Financial Markets: Stochastic Models and Empirical Results,"
- Miccichè, Salvatore & Bonanno, Giovanni & Lillo, Fabrizio & Mantegna, Rosario N, 2002. "Volatility in financial markets: stochastic models and empirical results," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 314(1), pages 756-761.
- Yanhui Liu & Parameswaran Gopikrishnan & Pierre Cizeau & Martin Meyer & Chung-Kang Peng & H. Eugene Stanley, 1999. "The statistical properties of the volatility of price fluctuations," Papers cond-mat/9903369, arXiv.org, revised Mar 1999.
- Matsushita, Raul & Rathie, Pushpa & Da Silva, Sergio, 2003.
"Exponentially damped Lévy flights,"
Physica A: Statistical Mechanics and its Applications,
Elsevier, vol. 326(3), pages 544-555.
- Mantegna, Rosario N & Palágyi, Zoltán & Stanley, H.Eugene, 1999. "Applications of statistical mechanics to finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 274(1), pages 216-221.
- H. Albrecher & P. A. Mayer & W. Schoutens, 2008. "General Lower Bounds for Arithmetic Asian Option Prices," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(2), pages 123-149.
- Nielsen, J. Aase & Sandmann, Klaus, 2003. "Pricing Bounds on Asian Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 38(02), pages 449-473, June.
- Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: applications," Insurance: Mathematics and Economics, Elsevier, vol. 31(2), pages 133-161, October.
- Parameswaran Gopikrishnan & Vasiliki Plerou & Luis A. Nunes Amaral & Martin Meyer & H. Eugene Stanley, 1999. "Scaling of the distribution of fluctuations of financial market indices," Papers cond-mat/9905305, arXiv.org.
- Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: theory," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 3-33, August.
- Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
- Michael Curran, 1994. "Valuing Asian and Portfolio Options by Conditioning on the Geometric Mean Price," Management Science, INFORMS, vol. 40(12), pages 1705-1711, December.
- Erik Van der Straeten & Christian Beck, 2009. "Superstatistical fluctuations in time series: Applications to share-price dynamics and turbulence," Papers 0901.2271, arXiv.org, revised Sep 2009.
- Alexander Novikov & Nino Kordzakhia, 2013. "On lower and upper bounds for Asian-type options: a unified approach," Papers 1309.2383, arXiv.org.
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