Alghalith, Moawia (2019): The distribution of the average of lognormal variables and exact Pricing of the Arithmetic Asian Options: A Simple, closedform Formula.
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Abstract
We overcome a longstanding obstacle in statistics. In doing so, we show that the distribution of the sum of lognormal variables is lognormal. Furthermore, we offer a breakthrough result in finance. In doing so, we introduce a simple, exact and explicit formula for pricing the arithmetic Asian options. The pricing formula is as simple as the classical BlackScholes formula.
Item Type:  MPRA Paper 

Original Title:  The distribution of the average of lognormal variables and exact Pricing of the Arithmetic Asian Options: A Simple, closedform Formula 
Language:  English 
Keywords:  Arithmetic Asian option pricing, the arithmetic average of the price, average of lognormal, the BlackScholes 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:  101778 
Depositing User:  Moawia Alghalith 
Date Deposited:  13 Jul 2020 06:00 
Last Modified:  13 Jul 2020 06:00 
References:  Aprahamian, H. and B. Maddah (2015). Pricing Asian options via compound gamma and orthogonal polynomials. Applied Mathematics and Computation, 264, 2143. 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, 381389. Corsaro, S., I. Kyriakou, D. Marazzina, and Z. Marino (2019). A general framework for pricing Asian options under stochastic volatility on parallel architectures. European Journal of Operational Research, 272, 10821095. Cui, Z., L. Chihoon , and Y. Liu (2018). Singletransform formulas for pricing Asian options in a general approximation framework under Markov processes. European Journal of Operational Research, 266, 11341139. Curran, M. (1994). Valuing Asian and portfolio options by conditioning on the geometric mean price. Management Science, 40, 17051711. 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, 4974. Fusai, G., D. Marazzina, and M. Marena (2011). Pricing discretely monitored Asian options by maturity randomization. SIAM Journal on Financial Mathematics, 2, 383403. Gambaro, A.M., I. Kyriakou, and G. Fusai (2020). General lattice methods for arithmetic Asian options. European Journal of Operational Research, 282, 11851199. Lapeyre, B., E. and Temam (2001). Competitive Monte Carlo methods for the pricing of Asian options. Journal of Computational Financ, 5, 3958. 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, 125. Linetsky, V. (2004). Spectral expansions for Asian (average price) options. Operations Research, 52, 856867. Willems, S. (2019). Asian option pricing with orthogonal polynomials. Quantitative Finance, 19, 605618. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/101778 
Available Versions of this Item

The distribution of the average of lognormal variables and Exact Pricing of the Arithmetic Asian Options: A Simple, closedform Formula. (deposited 10 Dec 2019 14:22)

The distribution of the average of lognormal variables and exact Pricing of the Arithmetic Asian Options: A Simple, closedform Formula. (deposited 18 Mar 2020 07:47)

The distribution of the average of lognormal variables and exact Pricing of the Arithmetic Asian Options: A Simple, closedform Formula. (deposited 07 Jul 2020 07:15)
 The distribution of the average of lognormal variables and exact Pricing of the Arithmetic Asian Options: A Simple, closedform Formula. (deposited 13 Jul 2020 06:00) [Currently Displayed]

The distribution of the average of lognormal variables and exact Pricing of the Arithmetic Asian Options: A Simple, closedform Formula. (deposited 07 Jul 2020 07:15)

The distribution of the average of lognormal variables and exact Pricing of the Arithmetic Asian Options: A Simple, closedform Formula. (deposited 18 Mar 2020 07:47)