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Implied Volatility Surface Approximation under a Two-Factor Stochastic Volatility Model
Mälardalen University, School of Education, Culture and Communication.
Mälardalen University, School of Education, Culture and Communication.
2018 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis
Abstract [en]

Due to recent research disproving old claims in financial mathematics such as constant volatility in option prices, new approaches have been incurred to analyze the implied volatility, namely stochastic volatility models. The use of stochastic volatility in option pricing is a relatively new and unexplored field of research with a lot of unknowns, where new answers are of great interest to anyone practicing valuation of derivative instruments such as options. With both single and two-factor stochastic volatility models containing various correlation structures with respect to the asset price and differing mean-reversions of variance the question arises as to how these values change their more observable counterpart: the implied volatility. Using the semi-analytical formula derived by Chiarella and Ziveyi, we compute European call option prices. Then, through the Black–Scholes formula, we solve for the implied volatility by applying the bisection method. The implied volatilities obtained are then approximated using various models of regression where the models’ coefficients are determined through the Moore–Penrose pseudo-inverse to produce implied volatility surfaces for each selected pair of correlations and mean-reversion rates. Through these methods we discover that for different mean-reversions and correlations the overall implied volatility varies significantly and the relationship between the strike price, time to maturity, implied volatility are transformed.

Place, publisher, year, edition, pages
2018. , p. 32
Keywords [en]
Implied Volatility; Stochastic Volatility; Implied Volatility Surfaces; European Options;Moore-Penrose Inverse;
National Category
Mathematics
Identifiers
URN: urn:nbn:se:mdh:diva-40039OAI: oai:DiVA.org:mdh-40039DiVA, id: diva2:1223668
Subject / course
Mathematics/Applied Mathematics
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Available from: 2018-06-28 Created: 2018-06-25 Last updated: 2018-06-28Bibliographically approved

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CiteExportLink to record
Permanent link

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Citation style
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
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Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
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  • Other locale
More languages
Output format
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