A piecewise model for vanilla option pricing

Sebastian Schlenrickh

Journal of Computational Finance

Abstract: We propose a simple static model for the arbitrage-free pricing of call and put options. The model captures the volatility smile and continues to use the classical Black and Bachelier formulas. The key idea of the model is a telescopic sum representation of option prices. We use the model to interpolate and extrapolate option prices or corresponding implied volatilities. It could also act as a building block for exotic derivative pricing methods and data-driven volatility market generators.

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