Approximate hedging problem with transaction costs in stochastic volatility markets

Huu Thai Nguyen (1) , Serguei Pergamenchtchikov (1)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem

This paper investigates the problem of hedging European call options using Leland's strategy in stochastic volatility markets with transaction costs. Introducing a new form for the enlarged volatility in Leland's algorithm, we establish a limit theorem and determine a convergence rate for the hedging error. This provides a suggestion to release the underhedging property pointed out by Kabanov and Safarian (1997). Possibilities to improve the convergence rate and lower the option price inclusive transaction costs are also discussed.

Mots clés: Leland strategy; transaction costs; quantile hedging; limit theorem

Domaines: Probabilités [math.PR]; Finance quantitative [q-fin.CP]

Huu Thai Nguyen, Serguei Pergamenchtchikov. Approximate hedging problem with transaction costs in stochastic volatility markets. 2012. ⟨hal-00747689v1⟩