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Approximation Methods of European Option Pricing in Multiscale Stochastic Volatility ModelPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2017 (English)In: INCPAA 2016 Proceedings: 11th International Conference on Mathematical Problems in Engineering, Aerospace, and Sciences, ICNPAA 2016, La Rochelle, France, 4 - 8 July 2016. / [ed] S. Sivasundaram, American Institute of Physics (AIP), 2017, Vol. 1798, p. 020112-1-020112-10, article id 020112Conference paper, Published paper (Refereed)
##### Abstract [en]

##### Place, publisher, year, edition, pages

American Institute of Physics (AIP), 2017. Vol. 1798, p. 020112-1-020112-10, article id 020112
##### Keyword [en]

Black-Scholes model, option pricing, Brownian motion, stochastic volatility, asymptotic expansion
##### National Category

Probability Theory and Statistics
##### Research subject

Mathematics/Applied Mathematics
##### Identifiers

URN: urn:nbn:se:mdh:diva-33474DOI: 10.1063/1.4972704ISI: 000399203000111Scopus ID: 2-s2.0-85013633019ISBN: 9780735414648 (print)OAI: oai:DiVA.org:mdh-33474DiVA, id: diva2:1040247
##### Conference

11th International Conference on Mathematical Problems in Engineering, Aerospace, and Sciences, ICNPAA 2016, La Rochelle, France, 4 - 8 July 2016.
#####

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##### Funder

Sida - Swedish International Development Cooperation Agency
Available from: 2016-10-26 Created: 2016-10-26 Last updated: 2017-09-03Bibliographically approved
##### In thesis

In the classical Black-Scholes model for financial option pricing, the asset price follows a geometric Brownian motion with constant volatility. Empirical findings such as volatility smile/skew, fat-tailed asset return distributions have suggested that the constant volatility assumption might not be realistic. A general stochastic volatility model, e.g. Heston model, GARCH model and SABR volatility model , in which the variance/volatility itself follows typically a mean-reverting stochastic process, has shown to be superior in terms of capturing the empirical facts. However in order to capture more features of the volatility smile a two-factor, of double Heston type, stochastic volatility model is more useful as shown by Christoffersen, Heston and Jacobs. We consider one specific type of such two-factor volatility models in which the volatility has multiscale mean-reversion rates. Our model contains two mean-reverting volatility processes with a fast and a slow reverting rate respectively. We consider the European option pricing problem under one type of the multiscale stochastic volatility model where the two volatility processes act as independent factors in the asset price process. The novelty in this chapter is an approximating analytical solution using asymptotic expansion method which extends the authors earlier research in Canhanga et al. In addition we propose a numerical approximating solution using Monte-Carlo simulation. For completeness and for comparison we also implement the semi-analytical solution by Chiarella and Ziveyi using method of characteristics, Fourier and bivariate Laplace transforms.

1. Asymptotic Methods for Pricing European Option in a Market Model With Two Stochastic Volatilities$(function(){PrimeFaces.cw("OverlayPanel","overlay1040251",{id:"formSmash:j_idt1116:0:j_idt1121",widgetVar:"overlay1040251",target:"formSmash:j_idt1116:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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