Proactive Hedging European Option Pricing with a General Logarithmic Position Strategy

This study proposes an exotic option that extends the classical European option by requiring option holders to continuously trade in underlying assets according to a predesignated trading strategy with a general logarithmic position. The pricing formula for the exotic option with a general logarithmic strategy is derived from the Black–Scholes option pricing formula, and its price advantage is compared (based on simulations) to the classical European option and to the exotic option with a linear position. By varying key parameters, we found that the exotic option with a general logarithmic position has a significant price advantage (up to 34% under certain parameter settings) over the classical European option. Moreover, the exotic option with a general logarithmic strategy can save 5.5% more of the option premium than applying a linear position strategy. Our simulation results indicate that the price advantage of this proactive hedging option with a general logarithmic strategy depends heavily on the initial amount of capital; in particular, this exotic option is more suitable for traders with limited initial amounts of capital.