Option Pricing Generators

Peter Carr and Umberto Cherubini

Chapter 6 in Peter Carr Gedenkschrift:Research Advances in Mathematical Finance, 2023, pp 179-209 from World Scientific Publishing Co. Pte. Ltd.

Abstract: We characterize a class of option pricing models by their algebraic structure. Option prices are monoids, that is, operators endowed with the commutativity and associativity property and an identity element. If the price of the underlying asset is bounded, the operator corresponds to the concept of t-conorm, while if it is defined on the positive real line, the operator is a pseudo-addition. These operators have the same no-arbitrage properties as the classical option pricing models but are also associative. Each model in this class is characterized by a univariate increasing function that is defined as the generator of the model. The generator encodes a synthetic representation of the probability structure of the underlying asset. We provide no-arbitrage conditions for the generators and practical guidelines to construct them.

Keywords: Mathematical Finance; Quantitative Finance; Option Pricing; Derivatives; No Arbitrage; Asset Price Bubbles; Asset Pricing; Equilibrium; Volatility; Diffusion Processes; Jump Processes; Stochastic Integration; Trading Strategies; Portfolio Theory; Optimization; Securities; Bonds; Commodities; Futures (search for similar items in EconPapers)
JEL-codes: C02 C6 (search for similar items in EconPapers)
Date: 2023
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