### Abstract

Original language | English |
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Place of Publication | Eindhoven |

Publisher | Eurandom |

Number of pages | 34 |

Publication status | Published - 2008 |

### Publication series

Name | Report Eurandom |
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Volume | 2008041 |

ISSN (Print) | 1389-2355 |

### Fingerprint

### Cite this

*Convergence of option rewards for Markov type price processes modulated by stochastic indices*. (Report Eurandom; Vol. 2008041). Eindhoven: Eurandom.

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*Convergence of option rewards for Markov type price processes modulated by stochastic indices*. Report Eurandom, vol. 2008041, Eurandom, Eindhoven.

**Convergence of option rewards for Markov type price processes modulated by stochastic indices.** / Silvestrov, D.S.; Jönsson, H.; Stenberg, F.

Research output: Book/Report › Report › Academic

TY - BOOK

T1 - Convergence of option rewards for Markov type price processes modulated by stochastic indices

AU - Silvestrov, D.S.

AU - Jönsson, H.

AU - Stenberg, F.

PY - 2008

Y1 - 2008

N2 - A general price process represented by a two-component Markov process is considered. Its first component is interpreted as a price process and the second one as an index process modulating the price component. American type options with pay-off functions, which admit power type upper bounds, are studied. Both the transition characteristics of the price processes and the pay- off functions are assumed to depend on a perturbation parameter d= 0 and to converge to the corresponding limit characteristics as d¿ 0. In the first part of the paper, asymptotically uniform skeleton approximations connecting reward functionals for continuous and discrete time models are given. In the second part of the paper, these skeleton approximations are used for getting results about the convergence of reward functionals for American type options for perturbed price processes in discrete and continuous time. Examples related to modulated exponential price processes with independent increments are given.

AB - A general price process represented by a two-component Markov process is considered. Its first component is interpreted as a price process and the second one as an index process modulating the price component. American type options with pay-off functions, which admit power type upper bounds, are studied. Both the transition characteristics of the price processes and the pay- off functions are assumed to depend on a perturbation parameter d= 0 and to converge to the corresponding limit characteristics as d¿ 0. In the first part of the paper, asymptotically uniform skeleton approximations connecting reward functionals for continuous and discrete time models are given. In the second part of the paper, these skeleton approximations are used for getting results about the convergence of reward functionals for American type options for perturbed price processes in discrete and continuous time. Examples related to modulated exponential price processes with independent increments are given.

M3 - Report

T3 - Report Eurandom

BT - Convergence of option rewards for Markov type price processes modulated by stochastic indices

PB - Eurandom

CY - Eindhoven

ER -