Probability of multiple crossings and pricing of double barrier options |
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| Affiliation: | 1. Assistant Professor Department of Computer Science and Engineering Anna University Regional Office, Madurai, Tamilnadu, India;2. Professor Department of Information Technology K.L.N.College of Engineering, Pottapalayam, Sivaganga, Tamil Nadu, India;1. Indian Institute of Technology, Kanpur, India;2. Department of Economics, Jadavpur University, India;3. Centre for Studies in Social Sciences, Calcutta, India;4. IZA, Bonn, Germany;1. School of Statistics, Beijing Normal University, Beijing, China;2. Department of Quantitative Finance, National Tsing Hua University, Taiwan, China;3. Discipline of Business Analytics, University of Sydney Business School, Econometric Institute, Erasmus School of Economics, Erasmus University Rotterdam, The Netherlands;4. Department of Quantitative Economics, Complutense University of Madrid, Spain, China;5. Department of Finance and Big Data Research Center, Asia University, Taiwan, China;6. Department of Economics and Finance, Hang Seng Management College, Hong Kong;7. Department of Economics, Lingnan University, Hong Kong;8. Department of Mathematics, Hong Kong Baptist University, Hong Kong |
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| Abstract: | This paper derives pricing formulas of standard double barrier option, generalized window double barrier option and chained option. Our method is based on probabilitic approach. We derive the probability of multiple crossings of curved barriers for Brownian motion with drift, by repeatedly applying the Girsanov theorem and the reflection principle. The price of a standard double barrier option is presented as an infinite sum that converges very rapidly. Although the price formula of standard double barrier option is the same with Kunitomo and Ikeda (1992), our method gives an intuitive interpretation for each term in the infinite series. From the intuitive interpretation we present the way how to approximate the infinite sum in the pricing formula and an error bound for the given approximation. Guillaume (2003) and Jun and Ku (2013) assumed that barriers are constant to price barrier options. We extend constant barriers of window double barrier option and chained option to curved barriers. By employing multiple crossing probabilities and previous skills we derive closed formula for prices of 16 types of the generalized chained option. Based on our analytic formulas we compute Greeks of chained options directly. |
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| Keywords: | Multiple crossing Double barrier Exotic option Window option Chained option |
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