Factor-Driven Option Pricing with Variable Trading Intervals

Summary

This paper extends an option pricing framework to account for trading instances that may be spaced unevenly, a feature the authors identify as relevant to option short sellers. It uses invariance principles to develop a binomial, path-dependent pricing model for complete markets in which stock price behavior depends on the log returns of an influencing market factor. The discussion covers both discrete-time and continuous-time settings.

For the discrete case, the authors also consider informed traders using a statistical arbitrage strategy with forward contracts. Numerical examples use US financial market data. The paper argues that pricing models should retain information about instantaneous mean log return, the probability of an upward stock move in each trading interval, and market microstructure characteristics. The abstract does not provide model equations, calibration details, or comparative performance evidence, so it supports understanding the proposed modeling considerations without establishing practical pricing accuracy or trading profitability.

Key ideas

• The pricing framework allows trading intervals to vary in length.
• A path-dependent binomial model links stock dynamics to a market factor’s log returns.
• The model is formulated for discrete-time and continuous-time complete markets.
• The discrete setting includes informed statistical arbitrage trading in forward contracts.
• The authors emphasize preserving return, interval-specific move probability, and microstructure information.

Tags

# Option Pricing Incorporating Factor Dynamics in Complete Markets


# Option Pricing Incorporating Factor Dynamics in Complete Markets









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.

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.