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A pricing process with stochastic volatility controlled by a semi-Markov process
Mälardalens högskola, Institutionen för matematik och fysik.ORCID-id: 0000-0002-2626-5598
Mälardalens högskola, Institutionen för matematik och fysik.
2004 (engelsk)Inngår i: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415X, Vol. 33, nr 3, s. 591-608Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [sv]

This paper is devoted to the investigation of the geometrical Brownian motion as a price process where the drift and volatility are controlled by a semi-Markov process. Conditions of risk-neutral measure are given as well as a formula for the risk-neutral price for European options. The discrete version, the binomial model controlled by a semi-Markov chain, is examined and limit theorems describing the transition from discrete time binomial to continuous time model are given. A system of partial differential equations for distribution functions of average volatility is given. Related Monte Carlo algorithms are described.

sted, utgiver, år, opplag, sider
2004. Vol. 33, nr 3, s. 591-608
HSV kategori
Identifikatorer
URN: urn:nbn:se:mdh:diva-4053DOI: 10.1081/STA-120028686ISI: 000220104900012Scopus ID: 2-s2.0-1642565874OAI: oai:DiVA.org:mdh-4053DiVA, id: diva2:120594
Tilgjengelig fra: 2006-12-12 Laget: 2006-12-12 Sist oppdatert: 2019-06-18bibliografisk kontrollert
Inngår i avhandling
1. Semi-Markov Models for Insurance and Option Rewards
Åpne denne publikasjonen i ny fane eller vindu >>Semi-Markov Models for Insurance and Option Rewards
2007 (engelsk)Doktoravhandling, med artikler (Annet vitenskapelig)
Abstract [en]

This thesis presents studies of semi-Markov models for insurance and option rewards. The thesis consists of the introduction and six papers. The introduction presents the results of the thesis in an informal way.

In paper A, a general semi-Markov reward model is presented. Recurrence relations for evaluation of higher moments of the reward process are given, as well as a backward semi-Markov reward processes are applied to insurance problems for the first time.

In paper B, models for disability insurance given in paper A are further extended. Statistical evidences of relevance of semi-Markov setting are given. Applications to profit-risk analysis for contracts are considered.

In paper C, a more detailed explanation of the algorithmic for the non-homogenous backward semi-Markov reward process is given. Two algorithmic approaches to solve the problem in an iterative manner are given. One of the algorithms is presented in a pseudo-code.

In paper D, the geometrical Brownian motion with drift and volatility controlled by a semi-Markov processes is considered as a price process in option valuation. The discrete version is examined and limit theorems describing the transition from discrete to continuous time are given. Monte-Carlo algorithms are described.

In paper E, a general price process represented by a two-component Markov process is considered. American 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 and to converge to the corresponding limits. Results about the convergence of reward functionals for American options are presented.

In paper F, convergence for option rewards when the price processes are perturbed exponential Lévy type process controlled by semi-Markov indices is studied. Both European and American type options with pay-off functions which admit power type upper bounds are considered. The paper continues research started in paper D and gives a key example for paper E.

sted, utgiver, år, opplag, sider
Institutionen för matematik och fysik, 2007
Serie
Mälardalen University Press Dissertations, ISSN 1651-4238 ; 38
Emneord
semi-Markov process, discrete time, insurance, actuarial, higher order reward, disability, variance, skewness, kurtosis, reward process, stochastic volatility, controlling semi-Markov process, Monte Carlo algorithm, convergence, optimal stopping, skeleton approximation, regime switching, semi-Markov modulated, European option, American option, Lévy process.
HSV kategori
Forskningsprogram
Matematik/tillämpad matematik
Identifikatorer
urn:nbn:se:mdh:diva-170 (URN)978-91-85485-33-8 (ISBN)
Disputas
2007-01-26, Gamma, Hus U, Högskoleplan , Mälardalens högskola, Västerås, 13:15
Opponent
Veileder
Tilgjengelig fra: 2006-12-12 Laget: 2006-12-12

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