  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.
