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Numerical Methods on European Options Second Order Asymptotic Expansions for Multiscale Stochastic VolatilityPrimeFaces.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}); PrimeFaces.cw("SelectBooleanButton","widget_formSmash_j_idt226",{id:"formSmash:j_idt226",widgetVar:"widget_formSmash_j_idt226",onLabel:"Hide others and affiliations",offLabel:"Show others and affiliations"});
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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, 2017, Vol. 1798, p. 020035-1-020035-10, article id 020035Conference paper, Published paper (Refereed)
##### Abstract [en]

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

2017. Vol. 1798, p. 020035-1-020035-10, article id 020035
##### Keywords [en]

stochastic volatilities, European option, asymptotic expansion
##### National Category

Probability Theory and Statistics
##### Research subject

Mathematics/Applied Mathematics
##### Identifiers

URN: urn:nbn:se:mdh:diva-33473DOI: 10.1063/1.4972627ISI: 000399203000035Scopus ID: 2-s2.0-85013660646ISBN: 9780735414648 (print)OAI: oai:DiVA.org:mdh-33473DiVA, id: diva2:1040245
##### 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 AgencyAvailable from: 2016-10-26 Created: 2016-10-26 Last updated: 2017-09-03Bibliographically approved
##### In thesis

After Black-Scholes proposed a model for pricing European Option in 1973, Cox, Ross and Rubinstein in 1979, and Heston in 1993, showed that the constant volatility assumption in the Black-Scholes model was one of the main reasons for the model to be unable to capture some market details. Instead of constant volatilities, they introduced non-constant volatilities to the asset dynamic modeling. In 2009, Christoffersen empirically showed "why multi-factor stochastic volatility models work so well". Four years later, Chiarella and Ziveyi solved the model proposed by Christoffersen. They considered an underlying asset whose price is governed by two factor stochastic volatilities of mean reversion type. Applying Fourier transforms, Laplace transforms and the method of characteristics they presented an approximate formula for pricing American option.The huge calculation involved in the Chiarella and Ziveyi approach motivated us to investigate another approach to compute European option prices on a Christoffersen type model. Using the first and second order asymptotic expansion method we presented a closed form solution for European option, and provided experimental and numerical studies on investigating the accuracy of the approximation formulae given by the first order asymptotic expansion. In the present chapter we will perform experimental and numerical studies for the second order asymptotic expansion and compare the obtained results with results presented by Chiarella and Ziveyi.

1. Asymptotic Methods for Pricing European Option in a Market Model With Two Stochastic Volatilities$(function(){PrimeFaces.cw("OverlayPanel","overlay1040251",{id:"formSmash:j_idt725:0:j_idt729",widgetVar:"overlay1040251",target:"formSmash:j_idt725:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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