Exercise boundary of the American put near maturity in an exponential Lévy model
We study the behavior of the critical price of an American put option near maturity in an exponential Lévy model. In particular, we prove that in situations where the limit of the critical price is equal to the strike price, the rate of convergence to the limit is linear if and only if the underlyin...
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| Veröffentlicht in: | Finance and stochastics 2013-04, Vol.17 (2), p.355-394 |
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| container_title | Finance and stochastics |
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| creator | Lamberton, Damien Mikou, Mohammed Adam |
| description | We study the behavior of the critical price of an American put option near maturity in an exponential Lévy model. In particular, we prove that in situations where the limit of the critical price is equal to the strike price, the rate of convergence to the limit is linear if and only if the underlying Lévy process has finite variation. In the case of infinite variation, a variety of rates of convergence can be observed: we prove that when the negative part of the Lévy measure exhibits an
α
-stable density near the origin, with 1<
α |
| doi_str_mv | 10.1007/s00780-012-0194-z |
| format | Article |
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α
-stable density near the origin, with 1<
α
<2, the convergence rate is ruled by
, where
θ
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α
-stable density near the origin, with 1<
α
<2, the convergence rate is ruled by
, where
θ
is the time until maturity.</description><subject>Algebra</subject><subject>Convergence</subject><subject>Economic models</subject><subject>Economic theory</subject><subject>Economic Theory/Quantitative Economics/Mathematical Methods</subject><subject>Economics</subject><subject>Finance</subject><subject>Financial services</subject><subject>Insurance</subject><subject>Interest rates</subject><subject>Linear models</subject><subject>Management</subject><subject>Markov analysis</subject><subject>Mathematics</subject><subject>Mathematics and Statistics</subject><subject>Maturity</subject><subject>Price theory</subject><subject>Pricing policies</subject><subject>Probability</subject><subject>Probability Theory and Stochastic Processes</subject><subject>Quantitative Finance</subject><subject>Securities prices</subject><subject>Statistics for Business</subject><subject>Stochastic models</subject><subject>Stochastic 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In particular, we prove that in situations where the limit of the critical price is equal to the strike price, the rate of convergence to the limit is linear if and only if the underlying Lévy process has finite variation. In the case of infinite variation, a variety of rates of convergence can be observed: we prove that when the negative part of the Lévy measure exhibits an
α
-stable density near the origin, with 1<
α
<2, the convergence rate is ruled by
, where
θ
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| ispartof | Finance and stochastics, 2013-04, Vol.17 (2), p.355-394 |
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| source | SpringerNature Journals; EBSCOhost Business Source Complete |
| subjects | Algebra Convergence Economic models Economic theory Economic Theory/Quantitative Economics/Mathematical Methods Economics Finance Financial services Insurance Interest rates Linear models Management Markov analysis Mathematics Mathematics and Statistics Maturity Price theory Pricing policies Probability Probability Theory and Stochastic Processes Quantitative Finance Securities prices Statistics for Business Stochastic models Stochastic processes Studies U.S.A |
| title | Exercise boundary of the American put near maturity in an exponential Lévy model |
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