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Numerical Studies on Asymptotics of European Option under 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_idt385",{id:"formSmash:j_idt385",widgetVar:"widget_formSmash_j_idt385",onLabel:"Hide others and affiliations",offLabel:"Show others and affiliations"});
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2015 (English)In: ASMDA 2015 Proceedings: 16th Applied Stochastic Models and Data Analysis International Conference with 4th Demographics 2015 Workshop / [ed] Christos H Skiadas, ISAST: International Society for the Advancement of Science and Technology , 2015, p. 53-66Conference paper, Published paper (Refereed)
##### Abstract [en]

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

ISAST: International Society for the Advancement of Science and Technology , 2015. p. 53-66
##### Keywords [en]

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

Probability Theory and Statistics
##### Research subject

Mathematics/Applied Mathematics
##### Identifiers

URN: urn:nbn:se:mdh:diva-29936ISBN: 978-618-5180-05-8 (print)OAI: oai:DiVA.org:mdh-29936DiVA, id: diva2:882730
##### Conference

16th Applied Stochastic Models and Data Analysis International Conference (ASMDA2015) with Demographics 2015 Workshop, 30 June – 4 July 2015, University of Piraeus, Greece
#####

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##### Funder

Sida - Swedish International Development Cooperation AgencyAvailable from: 2015-12-15 Created: 2015-12-15 Last updated: 2016-10-28Bibliographically approved
##### In thesis

Multiscale stochastic volatilities models relax the constant volatility assumption from Black-Scholes option pricing model. Such model can capture the smile and skew of volatilities and therefore describe more accurately the movements of the trading prices. Christoffersen et al. [3] presented a model where the underlying priceis governed by two volatility components, one changing fast and another changing slowly. Chiarella and Ziveyi [2] transformed Christoffersen’s model and computed an approximate formula for pricing American options. They used Duhamel’s principle to derive an integral form solution of the boundary value problem associated to the option price. Using method of characteristics, Fourier and Laplace transforms, they obtained with good accuracy the American options prices. In a previous research of the authors (Canhanga et al. [1]), a particular case of Chiarella and Ziveyi [2] model is used for pricing of European options. The novelty of this earlier work is to present an asymptotic expansion for the option price. The present paper provides experimental and numerical studies on investigating the accuracy of the approximation formulae given by this asymptotic expansion. We present also a procedure for calibrating the parameters produced by our first-order asymptotic approximation formulae. Our approximated option prices will be compared to the approximation obtained by Chiarella and Ziveyi [2].

1. Canhanga B., Malyarenko, A., Ni, Y. and Silvestrov S. Perturbation methods for pricing European options in a model with two stochastic volatilities. 3rd SMTDA Conference Proceedings. 11-14 June 2014, Lisbon Porturgal, C. H. Skiadas (Ed.) 489-500 (2014).

2. Chiarella, C, and Ziveyi, J. American option pricing under two stochastic volatility processes. J. Appl. Math. Comput. 224:283–310 (2013).

3. Christoffersen, P.; Heston, S.; Jacobs, K. The shape and term structure of the index option smirk: why multifactor stochastic volatility models work so well. Manage. Sci. 55 (2) 1914-1932; (2009).

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2. Asymptotic Methods for Pricing European Option in a Market Model With Two Stochastic Volatilities$(function(){PrimeFaces.cw("OverlayPanel","overlay1040251",{id:"formSmash:j_idt1466:1:j_idt1470",widgetVar:"overlay1040251",target:"formSmash:j_idt1466:1:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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