Approximate analytic solution for Asian options with stochastic volatility |
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| Institution: | 1. Department of Financial Engineering and Actuarial Mathematics, Soochow University, 56, Kuei-Yang Street, Section 1, Taipei 100, Taiwan;2. Deputy Manager, Market Risk Management Department, Fubon Financial Holding Company, Taiwan;1. Department of Accounting, National Yunlin University of Science & Technology, 123 University Road, Section 3, Douliou, Yunlin 64002, ROC Taiwan;2. Department of Accounting and Information Systems, Asia University, 500, Lioufeng Rd., Wufeng, Taichung 41354, ROC Taiwan;3. Executive Officer of Budget Section, Department of Accounting K-12 Education Administration, Ministry of Education, Taiwan, ROC;1. Department of Mathematical Sciences, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 34141, Republic of Korea;2. School of Business Administration, Ulsan National Institute of Science and Technology (UNIST), Ulsan 44919, Republic of Korea;1. ISCAL – Lisbon Accounting and Business School, Instituto Politécnico de Lisboa, Av. Miguel Bombarda, 20, 1069-035 Lisbon, Portugal;2. SOCIUS – Research Centre in Economic and Organizational Sociology, CSG – Research in Social Sciences and Management, Rua Miguel Lupi, 20, 1249-078 Lisbon, Portugal;3. ISEG – Lisbon School of Economics and Management, Universidade de Lisboa, Portugal;4. UECE – Research Unit on Complexity and Economics, Rua Miguel Lupi, 20, 1249-078 Lisbon, Portugal;1. Institute of Business Research, University of Economics Ho Chi Minh City, Viet Nam;2. South Ural State University, 76, Lenin prospekt, Chelyabinsk, Russian Federation;3. Institute of Business Research and CFVG Ho Chi Minh City, University of Economics Ho Chi Minh City, Viet Nam;1. Western Kentucky University, Bowling Green KY42101, USA;2. Utah Valley University, Orem, UT 84058, USA;3. Indiana Business Research Center, Indiana University, Bloomington, IN 47405, USA |
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| Abstract: | The valuation of Asian options is complicated because the arithmetic average of lognormal random variables is no longer lognormal. Furthermore, the stochastic volatility inherent in financial asset prices is easily observed. However, few academic studies consider the pricing and hedging of Asian options with stochastic volatility, despite the popularity of such options. This study extends the work of Hull and White (1987) and integrates the Taylor series expansion technique to derive an approximate analytic solution for Asian options with stochastic volatility. Numerical experiments show that the proposed approximate analytic solution performs favorably and is computationally efficient compared with large-sample simulations. The approximate analytic solution provides a practical approach for pricing and hedging Asian options with stochastic volatility and is both easy to implement and desirable in terms of computing speed. |
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| Keywords: | Asian option Approximate analytic solution Lognormal Stochastic volatility Taylor series expansion |
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