Pricing of Proactive Hedging European Option with Dynamic Discrete Position Strategy

Abstract

Proactive hedging European option is an exotic option for hedgers in the options market proposed recently by Wang et al. It extends the classical European option by requiring option holders to continuously trade in underlying assets according to a predesigned trading strategy, to proactively hedge part of the potential risk from underlying asset price changes. To generalize this option design for practical application, in this study, a proactive hedging option with discrete trading strategy is developed and its pricing formula is deducted assuming the underlying asset price follows Geometric Fractional Brownian Motion. Simulation studies show that proactive hedging option with discrete trading strategy still enjoys strong price advantage compared to the classical European option for majority of parameter space. The observed price advantage is stronger when the underlying asset has more volatility or when the asset price follows closer to Geometric Brownian Motion. Additionally, we found that a higher frequency trading strategy has stronger price advantage if there is no trading cost. The findings in this research strongly facilitate the practical application of the proactive hedging option, making this lower-cost trading tool more feasible.

Put Options with Linear Investment for Hull-White Interest Rates

“…), a feasible discrete variant is in order. Recently Li et al [8] proposed a discretized method for the Call Option under the classical Black-Scholes with linear investment strategy. A feasible market implementation for our Hull-White pricing model will be presented in a forthcoming paper.…”

Proactive Hedging European Option Pricing with a General Logarithmic Position Strategy

“…Assuming risk-neutral conditions, i.e., μ � r, then, for any two time points t 1 andt 2 where 0 ≤ t 1 ≤ t 2 ≤ T, the relationship between S(t 1 ) and S(t 2 ) can be obtained from equation (17) such that…”

“…For example, the trading behavior of traders is discontinuous, and therefore, it does not always satisfy the assumed continuous function. Li et al improved the continuous linear function to establish a discrete linear dynamic position strategy [17], although a nonlinear dynamic position strategy might be more suitable for obtaining cheaper options. In an extreme case, if a buyer is purchasing the underlying asset with all of the capital at one time at the exercise price, then the risk exposure of the underlying asset would be completely covered, and the theoretical price of the option will be zero.…”