Option Pricing in Ornstein-Uhlenbeck Position Process: The Application in the Impact of Price Limits

Abstract

This research employs the Ornstein Uhlenbeck position process as an alternative underlying stochastic process for stock prices in markets where frictional elements are present. We derive a analytical formula for call option prices together with the hedging parameters in closed-form. We conduct sensitivity analysis to explore how this pricing model differs from the traditional Black-Scholes. Our numerical results suggest that, the impact of the frictional elements in the long term would actually be less significant. Our numerical results also show that when the underlying asset stock is highly volatile, the presence of frictional elements in the market would in fact amplifies the deviation in option prices between our model and that of the traditional Black-Scholes model.