Leland's approach to option pricing: The evolution of a discontinuity (Q2757318)

The paper studies a particular hedging strategy, due to Leland, in the Black-Scholes model with transaction costs. It was shown by \textit{Yu. M. Kabanov} and \textit{M. M. Safarian} [Finance Stoch. 1, 239-250 (1997; Zbl 0911.90027)] that there is a hedging error, i.e. the difference between the value of the hedging portfolio and that of option, moreover this error has a limit as the number of rebalancing times increases to infinity. In this paper it is shown that the hedging error as a function of stock at maturity has a jump discontinuity at the strike. It is also shown that the influence of this discontinuity is felt when \(S_T-K=O(n^{-1/4})\). The latter statement is described by a quantitative result describing the evolution of this discontinuity.