Regularization and analytic option pricing under $\alpha$-stable distribution of arbitrary asymmetry

Abstract

We consider a non-Gaussian option pricing model, into which the underlying log-price is assumed to be driven by an $\alpha$-stable distribution. We remove the a priori divergence of the model by introducing a Mellin regularization for the Lévy propagator. Using distributional and ${\mathbb{C}}^n$ tools, we derive an analytic closed formula for the option price, valid for any stability $\alpha \in ]1,2]$ and any asymmetry. This formula is very efficient and recovers previous cases (Black-Scholes, Carr-Wu); we calibrate the formula on market datas, make numerical tests, and discuss its many interesting properties.

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References in corpus (4)

• Option Pricing Beyond Black-Scholes Based on Double-Fractional Diffusion
• Option Pricing from Path Integral for Non-Gaussian Fluctuations. Natural Martingale and Application to Truncated Lévy Distributions
• Green function of the double fractional Fokker-Planck equation: Path integral and stochastic differential equations
• Non-Gaussian analytic option pricing: a closed formula for the Lévy-stable model

Cited by in corpus (1)

• Volatility Smile as Relativistic Effect