APPROXIMATE HEDGING PROBLEM WITH TRANSACTION COSTS IN STOCHASTIC VOLATILITY MARKETS

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...

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Published inMathematical finance Vol. 27; no. 3; pp. 832 - 865
Main Authors Nguyen, Thai Huu, Pergamenshchikov, Serguei
Format Journal Article
LanguageEnglish
Published Oxford Blackwell Publishing Ltd 01.07.2017
Wiley
Subjects
Algorithms
approximate hedging
Asymptotic properties
Convergence
Cost engineering
Economic models
Errors
high‐frequency markets
Leland strategy
Marketing
Markets
Mathematics
Probability
Probability theory
Property
quantile hedging
Replication
Specification
stochastic volatility
Theorems
Transaction costs
Volatility
quantile hedging
transaction costs
Leland strategy
high-frequency markets
high frequency markets Mathematics Subject Classification : 91G20
approximate hedging
stochastic volatility
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Summary: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.
Bibliography:The second author is partially supported by Russian Science Foundation (research project No. 14‐49‐00079) and by the National Research Tomsk State University. The first author wishes to express his gratitude to the Vietnam Overseas Scholarship Program (project 322) for financial support. The authors would like to thank the two referees and editor for remarks and suggestions that have helped to improve the paper.
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ISSN:0960-1627
1467-9965
DOI:10.1111/mafi.12094