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Connecting Financial Prices, Options, and Trading Strategies to Likelihood Theory

Article arXiv papers · Author: Arnold Janssen et al.
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Summary

This paper relates arbitrage-free price processes to filtered likelihood processes from statistical experiments. It describes how options can be interpreted through statistical tests, with some option prices expressed in terms of test power. The framework connects financial pricing concepts with methods from the likelihood theory developed by Le Cam.

The authors outline how changes in test power can help derive Delta and Gamma trading strategies in certain cases, and how statistical reasoning can approximate continuous-time strategies discretely. They also link Ito-style financial models to hazard-based survival models and identify a statistical counterpart for geometric fractional Brownian motion. The document is a conceptual overview of these correspondences; it does not provide empirical performance results or establish that the derived strategies are profitable in practice.

Key ideas

  • Arbitrage-free price processes can be represented using filtered likelihood processes.
  • Options are connected to statistical tests, and some prices relate to test power.
  • In special cases, test-power dynamics can support strategies for deriving Delta and Gamma.
  • Statistical arguments can be used to approximate continuous-time trading strategies discretely.
  • Ito-type models and geometric fractional Brownian motion have counterparts in statistical likelihood models.

Tags

StatisticsOptionsDerivatives pricingRisk management
Full text
# Statistical likelihood methods in finance


# Statistical likelihood methods in finance









It is known from previous work of the authors that non-negative arbitrage free price processes in finance can be described in terms of filtered likelihood processes of statistical experiments and vice versa. The present paper summarizes and outlines some similarities between finance and the statistical likelihood theory of Le Cam. Options are linked to statistical tests of the underlying experiments. In particular, some price formulas for options are expressed by the power of related tests. In special cases the dynamics of power functions for filtered likelihood processes can be used to establish trading strategies which lead to formulas for the Greeks Delta and Gamma. Moreover statistical arguments are then used to establish a discrete approximation of continuous time trading strategies. It is explained that Ito type financial models correspond to hazard based survival models in statistics. Also price processes given by a geometric fractional Brownian motion have a statistical counterpart in terms of the likelihood theory of Gaussian statistical experiments.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.