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Arbitrage-Free Interval and Dynamic Hedging in an Illiquid Market
Zhaojun Yang * #,Jinqiang Yang
Hunan University
*Correspondence author
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Funding: 国家社科基金,湖南大学985工程经济开放与贸易发展（No.06BJL022,）
Opened online: 4 May 2009
Accepted by: none
Citation: Zhaojun Yang,Jinqiang Yang.Arbitrage-Free Interval and Dynamic Hedging in an Illiquid Market[OL]. [ 4 May 2009] http://en.paper.edu.cn/en_releasepaper/content/31917
 
 
This paper provides two modified pricing PDEs for a general European option under liquidity risk, by which two modified hedges are derived. It is shown that the hedge errors of the two modified hedges approach zero as the trading time interval converges to zero inclusive of liquidity costs. An arbitrage-free interval is identified and in contrast to transaction costs, the liquidity cost is proved to be finite even if trading is continuous. Numerical results are presented on option pricing and the moments of hedge errors with both Black-Scholes hedge and one of the two modified hedges. The results indicate that under liquidity risk, the modified option hedge developed in this paper is much superior to the Black-Scholes hedge. The bigger the liquidity risk, the more significant the advantages. In fact, the modified hedge leads to not only a much less hedge error but also to a lower replication costs than the classical Black-Scholes hedge.
Keywords:Liquidity Modelling;Liquidity Costs;Arbitrage-Free Interval;Modified Hedge
 
 
 

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