Pricing of Proactive Hedging European Option with Dynamic Discrete Position Strategy

Meng Li,Xuefeng Wang,Fangfang Sun

doi:10.1155/2019/1070873

Meng Li, Xuefeng Wang + Show 1 more

Open Access

https://doi.org/10.1155/2019/1070873

Copy DOI

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.

Highlights

Exotic options, such as Asian, lookback, barrier, and passport options, have been a key focus of mathematical finance research since the late 1980s and early 1990s [1,2,3,4,5,6,7,8,9]
We build on the work of Li et al [18] by making its proactive hedging strategy discrete to increase its feasibility for practical use and derive its pricing formulas under the Geometric Fractional Brownian Motion (GFBM) assumption
Since the pricing formula derivations are very similar for call and put options, in this paper, we only present results for call options

Summary

Introduction

Exotic options, such as Asian, lookback, barrier, and passport options, have been a key focus of mathematical finance research since the late 1980s and early 1990s [1,2,3,4,5,6,7,8,9]. We focus on an exotic option that is a proactive hedging strategy bundled into the classical European option, called proactive hedging European option This exotic option has a built-in condition that requires option holders to trade the underlying asset and linearly adjust the holding position according to its price fluctuation within the option period. We build on the work of Li et al [18] by making its proactive hedging strategy discrete to increase its feasibility for practical use and derive its pricing formulas under the GFBM assumption. The intrinsic value function f(S) will include the same four terms as Lu(S) in (7), and these four terms will be further denoted as f1, f2, f3, and f4

Pricing of Proactive Hedging European Option Based on GFBM

Simulation Studies

Conclusion