APPROXIMATE HEDGING PROBLEM WITH TRANSACTION COSTS IN STOCHASTIC VOLATILITY MARKETS. (30th June 2015)

• Record Type: Journal Article
• Authors: Nguyen, Thai Huu; Pergamenshchikov, Serguei
• Is Part Of: Mathematical finance. Volume 27:Number 3(2017:Jul.)
• Page Start: 832
• Page End: 865
• Publication Date: 2015-06-30
• Subjects: Leland strategy -- transaction costs -- stochastic volatility -- quantile hedging -- approximate hedging -- high‐frequency markets; Business mathematics -- Periodicals; 332
• DOI: 10.1111/mafi.12094
• Languages: English
• ISSNs: 0960-1627

Abstract

Abstract : This paper studies the problem of option replication in general stochastic volatility markets with transaction costs, using a new specification for the volatility adjustment in Leland's algorithm. We prove several limit theorems for the normalized replication error of Leland's strategy, as well as that of the strategy suggested by Lépinette. The asymptotic results obtained not only generalize the existing results, but also enable us to fix the underhedging property pointed out by Kabanov and Safarian. We also discuss possible methods to improve the convergence rate and to reduce the option price inclusive of transaction costs.