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Perturbation Methods for Pricing European Options in a Model with Two Stochastic VolatilitiesPrimeFaces.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}); 2015 (English)In: New Trends in Stochastic Modelling and Data Analysis / [ed] Raimondo Manca, Sally McClean, Christos H Skiadas, ISAST , 2015, 199-210 p.Chapter in book (Refereed)
##### Abstract [en]

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

ISAST , 2015. 199-210 p.
##### Keyword [en]

financial market, mean reversion volatility, risk-neutral measure, partial differential equation, regular perturbation, singular perturbation, European option
##### National Category

Probability Theory and Statistics
##### Research subject

Mathematics/Applied Mathematics
##### Identifiers

URN: urn:nbn:se:mdh:diva-33472ISBN: 978-618-5180-06-5 (print)ISBN: 978-618-5180-10-2 (print)OAI: oai:DiVA.org:mdh-33472DiVA: diva2:1040244
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##### Funder

Sida - Swedish International Development Cooperation Agency
Available from: 2016-10-26 Created: 2016-10-26 Last updated: 2016-12-13Bibliographically approved
##### In thesis

Financial models have to reflect the characteristics of markets in which they are developed to be able to predict the future behavior of a financial system. The nature of most trading environments is characterized by uncertainties which are expressed in mathematical models in terms of volatilities. In contrast to the classical Black-Scholes model with constant volatility, our model includes one fast-changing and another slow-changing stochastic volatilities of mean-reversion type. The different changing frequencies of volatilities can be interpreted as the effects of weekends and effects of seasons of the year (summer and winter) on the asset price.

We perform explicitly the transition from the real-world to the risk-neutral probability measure by introducing market prices of risk and applying Girsanov Theorem. To solve the boundary value problem for the partial differential equation that corresponds to the case of a European option, we perform both regular and singular multiscale expansions in fractional powers of the speed of mean-reversion factors. We then construct an approximate solution given by the two-dimensional Black-Scholes model plus some terms that expand the results obtained by Black and Scholes.

1. Asymptotic Methods for Pricing European Option in a Market Model With Two Stochastic Volatilities$(function(){PrimeFaces.cw("OverlayPanel","overlay1040251",{id:"formSmash:j_idt704:0:j_idt708",widgetVar:"overlay1040251",target:"formSmash:j_idt704:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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