A piecewise model for vanilla option pricing
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- Telescopic sum representation of option prices allows for piece-wise specification of option price formula.
- Shifted Black and Bachelier formula on individual segments yield intuitive smile parametrisation.
- Resulting smile model is flexible enough to fit arbitrage-free data while allowing for additional regularisation which prevents over-fitting.
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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