## Pickands Option Pricing

Sticky delta option pricing models are characterized by pricing functions that are homogeneous with respect to both the price of the underlying asset and the strike. We prove that pricing models have this property if and only if they can be written in terms of Pickands functions. We give examples of standard models, starting from the Black-Scholes formulas, and new examples of option prices. We show how to write the implied risk neutral probability of the underlying asset in terms of Pickands functions. We also show how to use them in the non parametric analysis of option prices.

Area: CS44 - Algebraic option pricing and probability: in honor of Peter Carr (Umberto Cherubini and Sabrina Mulinacci)

Keywords: Option Pricing, Sticky-Delta, Pickands functions , No-arbitrage conditions

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