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Pricing European Options Under Stochastic Volatilities ModelsPrimeFaces.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}); 2016 (English)In: Engineering Mathematics I: Electromagnetics, Fluid Mechanics, Material Physics and Financial Engineering / [ed] Sergei Silvestrov; Milica Rancic, Springer, 2016, 315-338 p.Chapter in book (Refereed)
##### Abstract [en]

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

Springer, 2016. 315-338 p.
##### Series

Springer Proceedings in Mathematics and Statistics, ISSN 2194-1009 ; 178
##### Keyword [en]

option pricing, European options, stochastic volatilitie, asymptotic expansion
##### National Category

Probability Theory and Statistics
##### Research subject

Mathematics/Applied Mathematics
##### Identifiers

URN: urn:nbn:se:mdh:diva-33388DOI: 10.1007/978-3-319-42082-0_18Scopus ID: 2-s2.0-85015265267ISBN: 978-3-319-42081-3 (print)ISBN: 978-3-319-42082-0 (print)OAI: oai:DiVA.org:mdh-33388DiVA: diva2:1034032
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##### Funder

Sida - Swedish International Development Cooperation Agency
Available from: 2016-10-11 Created: 2016-10-11 Last updated: 2017-09-04Bibliographically approved
##### In thesis

Interested by the volatility behavior, different models have been developed for option pricing. Starting from constant volatility model which did not succeed on capturing the effects of volatility smiles and skews; stochastic volatility models appearas a response to the weakness of the constant volatility models. Constant elasticity of volatility, Heston, Hull and White, Schöbel-Zhu, Schöbel-Zhu-Hull-Whiteand many others are examples of models where the volatility is itself a random process. Along the chapter we deal with this class of models and we present the techniques of pricing European options. Comparing single factor stochastic volatility models to constant factor volatility models it seems evident that the stochastic volatility models represent nicely the movement of the asset price and its relations with changes in the risk. However, these models fail to explain the large independent fluctuations in the volatility levels and slope. Christoffersen et al. in [4] proposed a model with two-factor stochastic volatilities where the correlation between the underlying asset price and the volatilities varies randomly. In the last section of this chapter we introduce a variation of Chiarella and Ziveyi model, which is a subclass of the model presented in [4] and we use the first order asymptotic expansion methods to determine the price of European options.

1. Asymptotic Methods for Pricing European Option in a Market Model With Two Stochastic Volatilities$(function(){PrimeFaces.cw("OverlayPanel","overlay1040251",{id:"formSmash:j_idt1390:0:j_idt1394",widgetVar:"overlay1040251",target:"formSmash:j_idt1390:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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