A Markov Chain Approximation for American Option Pricing in Tempered Stable-GARCH Models
This paper considers the American option pricing problem under the stochastic volatility models. In particular, we introduce the GARCH model with two heavy-tailed distributions: classical tempered stable (CTS) and normal tempered stable (NTS) distribution. Then we apply the Markov chain approach to...
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2016-01-01
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| Series: | Frontiers in Applied Mathematics and Statistics |
| Subjects: | |
| Online Access: | http://journal.frontiersin.org/Journal/10.3389/fams.2015.00013/full |
| _version_ | 1819203873147977728 |
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| author | Xiang eShi Lihua eZhang Young Shin Aaron Kim |
| author_facet | Xiang eShi Lihua eZhang Young Shin Aaron Kim |
| author_sort | Xiang eShi |
| collection | DOAJ |
| description | This paper considers the American option pricing problem under the stochastic volatility models. In particular, we introduce the GARCH model with two heavy-tailed distributions: classical tempered stable (CTS) and normal tempered stable (NTS) distribution. Then we apply the Markov chain approach to compute the prices of American style options under these two models. Minimal entropy provides a convenient way to construct equivalent martingale measure (EMM) and allows us to overcome the difficulties in incorporating the Markov chain approximation. The convergence of the approximation is also proved. Both numerical and empirical results are analyzed to show the advantages and drawbacks of our approach. |
| first_indexed | 2024-12-23T04:26:50Z |
| format | Article |
| id | doaj.art-b1b31e14d6aa457b8bc69b1ced49703c |
| institution | Directory Open Access Journal |
| issn | 2297-4687 |
| language | English |
| last_indexed | 2024-12-23T04:26:50Z |
| publishDate | 2016-01-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Applied Mathematics and Statistics |
| spelling | doaj.art-b1b31e14d6aa457b8bc69b1ced49703c2022-12-21T18:00:07ZengFrontiers Media S.A.Frontiers in Applied Mathematics and Statistics2297-46872016-01-01110.3389/fams.2015.00013162421A Markov Chain Approximation for American Option Pricing in Tempered Stable-GARCH ModelsXiang eShi0Lihua eZhang1Young Shin Aaron Kim2Stony Brook UniversityZhejiang University of TechnologyStony Brook UniversityThis paper considers the American option pricing problem under the stochastic volatility models. In particular, we introduce the GARCH model with two heavy-tailed distributions: classical tempered stable (CTS) and normal tempered stable (NTS) distribution. Then we apply the Markov chain approach to compute the prices of American style options under these two models. Minimal entropy provides a convenient way to construct equivalent martingale measure (EMM) and allows us to overcome the difficulties in incorporating the Markov chain approximation. The convergence of the approximation is also proved. Both numerical and empirical results are analyzed to show the advantages and drawbacks of our approach.http://journal.frontiersin.org/Journal/10.3389/fams.2015.00013/fullMarkov chainGARCHAmerican optionsTempered stable distributionMinimal entropy |
| spellingShingle | Xiang eShi Lihua eZhang Young Shin Aaron Kim A Markov Chain Approximation for American Option Pricing in Tempered Stable-GARCH Models Frontiers in Applied Mathematics and Statistics Markov chain GARCH American options Tempered stable distribution Minimal entropy |
| title | A Markov Chain Approximation for American Option Pricing in Tempered Stable-GARCH Models |
| title_full | A Markov Chain Approximation for American Option Pricing in Tempered Stable-GARCH Models |
| title_fullStr | A Markov Chain Approximation for American Option Pricing in Tempered Stable-GARCH Models |
| title_full_unstemmed | A Markov Chain Approximation for American Option Pricing in Tempered Stable-GARCH Models |
| title_short | A Markov Chain Approximation for American Option Pricing in Tempered Stable-GARCH Models |
| title_sort | markov chain approximation for american option pricing in tempered stable garch models |
| topic | Markov chain GARCH American options Tempered stable distribution Minimal entropy |
| url | http://journal.frontiersin.org/Journal/10.3389/fams.2015.00013/full |
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