Option Pricing with an Exponential Effect Function

We consider option hedging and pricing for a large agent. The large agent affects the market’s demand-supply equilibrium and, therefore, the market prices of financial instruments. By assuming a specific large agent’s effect function for the underlying asset we derive the corresponding effect function for call options on that asset. As we show, the price of a call option in our model is the solution to a Black-Scholes partial differential equation with a modified terminal condition. Finally we estimate our model parameters from option market data and compare our model with other large agent models.