Option Pricing Incorporating Factor Dynamics in Complete Markets

TL;DR

This paper extends option pricing models to incorporate factor dynamics and variably-spaced trading, using invariance principles to develop a new binomial path-dependent model applicable to discrete and continuous markets, supported by numerical examples.

Contribution

It introduces a novel binomial path-dependent option pricing model that accounts for factor dynamics and variable trading intervals, enhancing existing models with new invariance principle applications.

Findings

Model captures market microstructure features

Numerical examples validate the approach

Supports importance of instantaneous mean log-return

Abstract

Using the Donsker-Prokhorov invariance principle we extend the Kim-Stoyanov-Rachev-Fabozzi option pricing model to allow for variably-spaced trading instances, an important consideration for short-sellers of options. Applying the Cherny-Shiryaev-Yor invariance principles, we formulate a new binomial path-dependent pricing model for discrete- and continuous-time complete markets where the stock price dynamics depends on the log-return dynamics of a market influencing factor. In the discrete case, we extend the results of this new approach to a financial market with informed traders employing a statistical arbitrage strategy involving trading of forward contracts. Our findings are illustrated with numerical examples employing US financial market data. Our work provides further support for the conclusion that any option pricing model must preserve valuable information on the instantaneous mean log-return, the probability of the stock's upturn movement (per trading interval), and other market microstructure features.