An excellent approximation for the m out of n day provision |
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| Institution: | 1. School of Finance, Southwestern University of Finance and Economics, Chengdu, Sichuan, PR China;2. School of Economics and Management, Southwest Jiaotong University, Chengdu, Sichuan, PR China;1. Department of Financial Engineering and Actuarial Mathematics, Soochow University, Taipei 10048, Taiwan;2. College of Management, Yuan Ze University, Taoyuan 32003, Taiwan;3. Department of Quantitative Finance, National Tsing Hua University, Hsinchu 30010, Taiwan;1. Chulalongkorn University, Sasin Graduate Institute of Business Administration, Bangkok, Thailand;2. Chulalongkorn University, College of Population Studies, Bangkok, Thailand;3. Pennsylvania State University, School of Graduate Professional Studies, Malvern, PA, USA;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. 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;1. Business School, Jilin University, Changchun, 130012, China;2. Faculty of Education, The University of Hong Kong, Hong Kong |
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| Abstract: | The m out of n day provision (MooN) of convertible bonds is difficult to handle. To approximating the MooN better, this paper proposes an approach named the conditional range probability (CRP). CRP is the simulated probability of the MooN being reached within a price range at a future time, conditional on today’s price of the underlying, and can be incorporated into any conventional derivatives pricing method. For a purposely designed exotic call option with a 20 out of 30 day provision, CRP under finite difference is found to outperform significantly several existing approaches and produce a mean pricing error of 1% over a wide range of initial underlying prices for the exotic call. The result implies that finite difference utilizing CRP will yield excellent approximating prices for convertible bonds. |
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| Keywords: | Soft call provision Simulated conditional range probabilities 20 out of 30 day provision |
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