Endogenous stochastic arbitrage bubbles and the Black–Scholes model

Mauricio Contreras G.

Physica A: Statistical Mechanics and its Applications, 2021, vol. 583, issue C

Abstract: This paper develops a model that incorporates the presence of stochastic arbitrage explicitly in the Black–Scholes equation. Here, the arbitrage is generated by a stochastic bubble, which generalizes the deterministic arbitrage model obtained in the literature (Contreras et al., 2010). It is considered to be a generic stochastic dynamic for the arbitrage bubble, and a generalized Black–Scholes equation is then derived. The resulting equation is similar to that of the stochastic volatility models, but there are no undetermined parameters as the market price of risk.

Keywords: Option pricing; Black–Scholes equation; Arbitrage bubbles; Stochastic equations (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:583:y:2021:i:c:s0378437121005963

DOI: 10.1016/j.physa.2021.126323

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