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Analytical and Nume...
Analytical and Numerical Studies on the Second Order Asymptotic Expansion Method for European Option Pricing under Two-factor Stochastic Volatilities
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- Canhanga, Betuel, 1980- (author)
- Mälardalens högskola,Utbildningsvetenskap och Matematik,Faculty of Sciences, Department of Mathematics and Computer Sciences, Eduardo Mondlane University, Maputo, Mozambique,MAM
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- Malyarenko, Anatoliy, 1957- (author)
- Mälardalens högskola,Utbildningsvetenskap och Matematik,MAM
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- Ni, Ying, 1976- (author)
- Mälardalens högskola,Utbildningsvetenskap och Matematik,MAM
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- Rancic, Milica, 1977- (author)
- Mälardalens högskola,Utbildningsvetenskap och Matematik,MAM
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- Silvestrov, Sergei, 1970- (author)
- Mälardalens högskola,Utbildningsvetenskap och Matematik,MAM
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(creator_code:org_t)
- 2017-10-11
- 2018
- English.
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In: Communications in Statistics - Theory and Methods. - : Taylor & Francis. - 0361-0926 .- 1532-415X. ; 47:6, s. 1328-1349
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http://www.tandfonli...
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https://urn.kb.se/re...
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https://doi.org/10.1...
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Abstract
Subject headings
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- The celebrated Black–Scholes model made the assumption of constant volatility but empirical studies on implied volatility and asset dynamics motivated the use of stochastic volatilities. Christoffersen in 2009 showed that multi-factor stochastic volatilities models capture the asset dynamics more realistically. Fouque in 2012 used it to price European options. In 2013 Chiarella and Ziveyi considered Christoffersen's ideas and introduced an asset dynamics where the two volatilities of the Heston type act separately and independently on the asset price, and using Fourier transform for the asset price process and double Laplace transform for the two volatilities processes, solved a pricing problem for American options. This paper considers the Chiarella and Ziveyi model and parameterizes it so that the volatilities revert to the long-run-mean with reversion rates that mimic fast(for example daily) and slow(for example seasonal) random effects. Applying asymptotic expansion method presented by Fouque in 2012, we make an extensive and detailed derivation of the approximation prices for European options. We also present numerical studies on the behavior and accuracy of our first and the second order asymptotic expansion formulas.
Subject headings
- NATURVETENSKAP -- Matematik -- Sannolikhetsteori och statistik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Probability Theory and Statistics (hsv//eng)
- NATURVETENSKAP -- Matematik -- Beräkningsmatematik (hsv//swe)
- NATURAL SCIENCES -- Mathematics -- Computational Mathematics (hsv//eng)
Keyword
- stochastic volatility
- option pricing
- asymptotic expansion
- Mathematics/Applied Mathematics
- matematik/tillämpad matematik
Publication and Content Type
- ref (subject category)
- art (subject category)
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