Leland's approach to option pricing. The evolution of a discontinuity.

Peter Grandits, Werner Schachinger

Publication: Working/Discussion PaperWU Working Paper

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Abstract

A claim of Leland (1985) states that in the presence of transaction costs a call option on a stock S, described by geometric Brownian motion, can be perfectly hedged using Black-Scholes delta hedging with a modified volatility. Recently Kabanov and Safarian (1997) disproved this claim, giving an explicit (up to an integral) expression of the limiting hedging error, which appears to be strictly negative and depends on the path of the stock price only via the stock price at expiry ST . We prove in this paper that the limiting hedging error, considered as a function of ST, exhibits a removable discontinuity at the exercise price. Furthermore, we provide a quantitative result describing the evolution of the discontinuity, which shows that its precursors can very well be observed also in cases of reasonable length of revision intervals. (author's abstract)

Publication series

SeriesReport Series SFB "Adaptive Information Systems and Modelling in Economics and Management Science"
Number26

WU Working Paper Series

  • Report Series SFB \Adaptive Information Systems and Modelling in Economics and Management Science\

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