Arbitrage-free interpolation of call option prices

Bender Christian () and Thiel Matthias ()
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Bender Christian: Department of Mathematics, Saarland University, Postfach 151150, 66041Saarbrücken, Germany
Thiel Matthias: Department of Mathematics, Saarland University, Postfach 151150, 66041Saarbrücken, Germany

Statistics & Risk Modeling, 2020, vol. 37, issue 1-2, 55-78

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.

Keywords: Static arbitrage; local volatility modeling; interpolation (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1515/strm-2018-0026

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