A Study on the Quality of Greeks and Hedge Effect on the Path Dependent Option

Lee, Sang-Ho; Kim, Chul-Joong

Korean Journal of Financial Studies 2014;43(2):415-437.
Published online April 30, 2014.

Sang-Ho Lee, Chul-Joong Kim

경로의존형 옵션의 그릭스 추정과 헤지효과의 질적 특성에 관한 연구

이상호, 김철중

Abstract

The objective of this study is to investigate the convergence in Greeks and hedge effect with Finite Difference Approximation (FDA) and Likelihood Ratio Method (LRM) for the path dependent option which only have Monte-Carlo Simulation (MCS) for pricing. Look back Cliquet Options which have 1 and 2 underlying assets were introduced for this study. Greeks were calculated with increasing the No. of simulation from 1,024 to 1,024,000 to analyze the convergence in Greeks. Both methods showed the convergence by increasing the No. and LRM has the quality of faster convergence. Hedge periods were set from January 2, 2013 when short options contracted to August 30, to investigate the hedge effect. According to the hedge simulation, LRM showed outstanding performance than FDA and FDA have to simulate 4 times more to meet the similar performance with LRM. The result of this study indicates that LRM is superior in the convergence in Greeks and hedge effect, So LRM could save the simulation time for pricing and hedging the derivatives and outstanding hedge performance could be expected.

Key Words: 그릭스,시뮬레이션,우도비방법,유한차분근사법,헤지효과의 질적 특성,Finite Difference Approximation,Greeks,Likelihood Ratio Method,Quality of Hedge Effect,Simulation