Alghalith, Moawia (2019): The distribution of the average of log-normal variables and Exact Pricing of the Arithmetic Asian Options: A Simple, closed-form Formula.
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Abstract
We introduce a simple, exact and closed-form formula for pricing the arithmetic Asian options. The pricing formula is as simple as the classical Black-Scholes formula. In doing so, we show that the distribution of the continuous average of log-normal variables is log-normal.
Item Type: | MPRA Paper |
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Original Title: | The distribution of the average of log-normal variables and Exact Pricing of the Arithmetic Asian Options: A Simple, closed-form Formula |
Language: | English |
Keywords: | Arithmetic Asian option pricing, the arithmetic average of the price, average of log-normal, the Black-Scholes formula. |
Subjects: | C - Mathematical and Quantitative Methods > C0 - General > C00 - General C - Mathematical and Quantitative Methods > C0 - General > C01 - Econometrics C - Mathematical and Quantitative Methods > C0 - General > C02 - Mathematical Methods C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General G - Financial Economics > G0 - General |
Item ID: | 97324 |
Depositing User: | Moawia Alghalith |
Date Deposited: | 10 Dec 2019 14:22 |
Last Modified: | 10 Dec 2019 14:22 |
References: | Aprahamian, H. and B. Maddah (2015). Pricing Asian options via compound gamma and orthogonal polynomials. Applied Mathematics and Computation 264, 21--43. Asmussen, S., P.-O. Goffard, and P. J. Laub (2016). Orthonormal polynomial expansions and lognormal sum densities. arXiv preprint arXiv:1601.01763. Cerny, A. and I. Kyriakou (2011). An improved convolution algorithm for discretely sampled Asian options. Quantitative Finance 11, 381--389. Curran, M. (1994). Valuing Asian and portfolio options by conditioning on the geometric mean price. Management Science, 40, 1705--1711. Fu, M. C., D. B. Madan, and T. Wang (1999). Pricing continuous Asian options: a comparison of Monte Carlo and Laplace transform inversion methods. Journal of Computational Finance 2, 49--74. Fusai, G., D. Marazzina, and M. Marena (2011). Pricing discretely monitored Asian options by maturity randomization. SIAM Journal on Financial Mathematics 2, 383--403. Lapeyre, B., E. Temam, et al. (2001). Competitive Monte Carlo methods for the pricing of Asian options. Journal of Computational Finance 5, 39--58. Li, W. and S. Chen (2016). Pricing and hedging of arithmetic Asian options via the Edgeworth series expansion approach. The Journal of Finance and Data Science 2, 1--25. Linetsky, V. (2004). Spectral expansions for Asian (average price) options. Operations Research 52, 856--867. Willems, S. (2019). Asian option pricing with orthogonal polynomials, Quantitative Finance, 19, 605-618. |
URI: | https://mpra.ub.uni-muenchen.de/id/eprint/97324 |
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The distribution of the average of log-normal variables and Exact Pricing of the Arithmetic Asian Options: A Simple, closed-form Formula. (deposited 10 Dec 2019 14:22)
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- The distribution of the average of log-normal variables and exact Pricing of the Arithmetic Asian Options: A Simple, closed-form Formula. (deposited 18 Mar 2020 07:47)