Please use this identifier to cite or link to this item: doi:10.22028/D291-30269
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Title: Arbitrage-free interpolation of call option prices
Author(s): Bender, Christian
Thiel, Matthias
Language: English
Title: Statistics and Risk Modeling
Startpage: 1
Endpage: 24
Publisher/Platform: De Gruyter Oldenbourg
Year of Publication: 2020
Publikation type: Journal Article
Abstract: In this paper, we introduce a new interpolation method for call option prices and implied volatilities with respect to the strike, which first generates, for fixed maturity, an implied volatility curve that is smooth and free of static arbitrage. Our interpolation method is based on a distortion of the call price function of an arbitrage-free financial “reference” model of one’s choice. It reproduces the call prices of the reference model if the market data is compatible with the model. Given a set of call prices for different strikes and maturities, we can construct a call price surface by using this one-dimensional interpolation method on every input maturity and interpolating the generated curves in the maturity dimension. We obtain the algorithm of N. Kahalé [An arbitrage-free interpolation of volatilities, Risk 17 2004, 5, 102–106] as a special case, when applying the Black–Scholes model as reference model.
DOI of the first publication: 10.1515/strm-2018-0026
URL of the first publication: https://www.degruyter.com/view/j/strm.ahead-of-print/strm-2018-0026/strm-2018-0026.xml
Link to this record: hdl:20.500.11880/28712
http://dx.doi.org/10.22028/D291-30269
ISSN: 2196-7040
0721-2631
2193-1402
Date of registration: 17-Feb-2020
Faculty: MI - Fakultät für Mathematik und Informatik
Department: MI - Mathematik
Professorship: MI - Prof. Dr. Christian Bender
Collections:UniBib – Die Universitätsbibliographie

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