Approximate hedging with constant proportional transaction costs in financial markets with jumps

Thai Nguyen (1) , Serguei Pergamenschchikov (2)

1 Universität Ulm - Ulm University [Ulm, Allemagne]
2 LMRS - Laboratoire de Mathématiques Raphaël Salem

We study the problem of option replication under constant proportional transaction costs in models where stochastic volatility and jumps are combined to capture the mar-ket's important features. Assuming some mild condition on the jump size distribution we show that transaction costs can be approximately compensated by applying the Leland adjusting volatility principle and the asymptotic property of the hedging error due to discrete readjustments is characterized. In particular, the jump risk can be approximately eliminated and the results established in continuous diffusion models are recovered. The study also confirms that for the case of constant trading cost rate, the approximate results established by Kabanov and Safarian (2009) and by Pergamenschikov (2003) are still valid in jump-diffusion models with deterministic volatility using the classical Leland parameter.

Mots clés: transaction costs; Leland strategy; jump models; stochastic volatility; approxi- mate hedging; limit theorem; super-hedging

Domaines: Probabilités [math.PR]

Thai Nguyen, Serguei Pergamenschchikov. Approximate hedging with constant proportional transaction costs in financial markets with jumps. SIAM Theory of Probability and its Applications, 2019. ⟨hal-02334930⟩