{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,12]],"date-time":"2025-10-12T11:11:58Z","timestamp":1760267518622,"version":"build-2065373602"},"reference-count":29,"publisher":"MDPI AG","issue":"1","license":[{"start":{"date-parts":[[2018,1,18]],"date-time":"2018-01-18T00:00:00Z","timestamp":1516233600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this paper we consider pricing problems of the geometric average Asian options under a non-Gaussian model, in which the underlying stock price is driven by a process based on non-extensive statistical mechanics. The model can describe the peak and fat tail characteristics of returns. Thus, the description of underlying asset price and the pricing of options are more accurate. Moreover, using the martingale method, we obtain closed form solutions for geometric average Asian options. Furthermore, the numerical analysis shows that the model can avoid underestimating risks relative to the Black-Scholes model.<\/jats:p>","DOI":"10.3390\/e20010071","type":"journal-article","created":{"date-parts":[[2018,1,18]],"date-time":"2018-01-18T12:19:48Z","timestamp":1516277988000},"page":"71","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["Non-Gaussian Closed Form Solutions for Geometric Average Asian Options in the Framework of Non-Extensive Statistical Mechanics"],"prefix":"10.3390","volume":"20","author":[{"given":"Pan","family":"Zhao","sequence":"first","affiliation":[{"name":"College of Finance and Mathematics, West Anhui University, Lu\u2019an 237012, China"},{"name":"Financial Risk Intelligent Control and Prevention Institute of West Anhui University, Lu\u2019an 237012, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Benda","family":"Zhou","sequence":"additional","affiliation":[{"name":"College of Finance and Mathematics, West Anhui University, Lu\u2019an 237012, China"},{"name":"Financial Risk Intelligent Control and Prevention Institute of West Anhui University, Lu\u2019an 237012, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Jixia","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Mathematics and Information Sciences, Henan Normal University, Xinxiang 453002, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,1,18]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1086\/260062","article-title":"The pricing of options and corporate liabilities","volume":"81","author":"Black","year":"1973","journal-title":"J. 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