Trader behavior and hedging feedback in the stock pinning phenomena

This paper uses a model of market price dynamics based upon trader behavior to explore the phenomena of stock pinning. A stock is said to pin when it trades at or near an option strike price at expiration. We model value traders, who trade in reference to a perceived true value, and hedge traders, who employ a Black-Scholes based dynamic strategy to hedge their position in options. The actual order process of these traders is modeled explicitly as a conditional compound Poisson process. We take diffusion limits, leading to an Ito stochastic differential equation model of market price dynamics that captures important market features. Preliminary numerical simulations indicate that the pinning phenomena are tied to the hedging activity used to offset positions in options.