Proactive Hedging European Option Pricing with a General Logarithmic Position Strategy

Lixin Qiao,Meng Li,Fangfang Sun,Xiaotuo Qiao,Xuefeng Wang,Sundarapandian Vaidyanathan

doi:10.1155/2022/4735656

Abstract

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.

Highlights

Options comprise a diverse group of indispensable trading products in the financial market, which make them effective tools for hedging risks. e options currently being traded include more than the standardized European and American options; a vast number of exotic options are being changed, combined, and derived from the standard options [1,2,3,4,5,6,7,8,9,10,11,12]. ese exotic options provide traders with more choices for outlining their trading portfolio strategies
A portfolio strategy with cheaper options is easier to execute because the option price determines the break-even threshold
For the classical European option without a proactive hedging strategy, the option holder would suffer an expected loss, L, according to equation (2), for each part of the option contract as the underlying asset prices rise from Xe to S0, for S0 > Xe

Summary

Research Article

Proactive Hedging European Option Pricing with a General Logarithmic Position Strategy. E 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. 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. 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

Introduction

Underlying Assets Prices

Xe A

Xe σ

Findings

Strategy parameters