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Second Order Asymptotic Expansion 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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2015 (English)In: ASMDA 2015 Proceedings: 16th Applied Stochastic Models and Data Analysis International Conference with 4th Demographics 2015 Workshop, 30 June – 4 July 2015 University of Piraeus, Greece / [ed] C. H. Skiadas, ISAST: International Society for the Advancement of Science and Technology , 2015, p. 37-52Conference paper, Published paper (Refereed)
##### Abstract [en]

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

ISAST: International Society for the Advancement of Science and Technology , 2015. p. 37-52
##### Keywords [en]

financial market, mean reversion volatility, asymptotic expansion, stochastic volatilities, regular perturbation, singular perturbation, european option
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:mdh:diva-33471ISBN: 978-618-5180-05-8 (print)OAI: oai:DiVA.org:mdh-33471DiVA, id: diva2:1040242
##### Conference

16th ASMDA Conference
#####

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##### Funder

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

Asset price processes with stochastic volatilities have been actively used by researchers in financial mathematics for valuing derivative securities. This type of models allows characterizing the uncertainties in the asset price process in financial markets. In a recent paper Chiarella and Ziveyi analyzed a model with two stochastic volatilities of mean reversion type with one variable changing fast and the other changing slowly. They used method of characteristics to solve the obtained partial differential equation and determine the price of an American option. Fouque et al presented also a similar model in which the volatility of the underlying asset is governed by two diffusion processes which are not of mean reversion type. They developed a first-order asymptotic expansion for the European option price via a perturbation method.

In this chapter we consider the model given in Chiarella and Ziveyi. Instead of pricing American options we price European options by generalizing the techniques presented in Fouque et al to a more complex model with mean reverting stochastic volatility factors. We analyse both regular and singular perturbations to obtain an asymptotic expansion up to second order which can serve as an approximation for the price of non-path-dependent European options. Similar work is done in authors earlier work Canhanga et al where a first-order asymptotic expansion has been developed. Involving the second order terms has the advantage of capturing more accurately the effects of volatility smile and skew on the option pricing. Analytical approximation formula for pricing European Option is presented.

1. Asymptotic Methods for Pricing European Option in a Market Model With Two Stochastic Volatilities$(function(){PrimeFaces.cw("OverlayPanel","overlay1040251",{id:"formSmash:j_idt793:0:j_idt800",widgetVar:"overlay1040251",target:"formSmash:j_idt793:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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