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Option Pricing Generators

In: Peter Carr Gedenkschrift Research Advances in Mathematical Finance

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  • Peter Carr
  • Umberto Cherubini

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.

Suggested Citation

  • Peter Carr & Umberto Cherubini, 2023. "Option Pricing Generators," World Scientific Book Chapters, in: Robert A Jarrow & Dilip B Madan (ed.), Peter Carr Gedenkschrift Research Advances in Mathematical Finance, chapter 6, pages 179-209, World Scientific Publishing Co. Pte. Ltd..
    • Handle: RePEc:wsi:wschap:9789811280306_0006
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    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;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling

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