Derivative pricing with virtual arbitrage

In this paper we derive an effective equation for derivative pricing which accounts for the presence of virtual arbitrage opportunities and their elimination by the market. We model the arbitrage return by a stochastic process and find an equation for the average derivative price. This is an integro-differential equation which, in the absence of the virtual arbitrage or for an infinitely fast market reaction, reduces to the Black-Scholes equation. Explicit formulas are obtained for European call and put vanilla options.