MODIFIED LELAND'S STRATEGY FOR A CONSTANT TRANSACTION COSTS RATE

In 1985 Leland suggested an approach to price contingent claims under proportional transaction costs. Its main idea is to use the classical Black–Scholes formula with a suitably adjusted volatility for a periodical revision of the portfolio whose terminal value approximates the pay‐off. Unfortunatel...

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Published in:Mathematical finance 2012-10, Vol.22 (4), p.741-752
Main Author: Lepinette, Emmanuel
Format: Article
Language:English
Subjects:
approximate hedging
Approximation
Black-Scholes formula
Leland's strategy
Mathematical models
Mathematics
Probability
Securities markets
Statistical analysis
Stochastic models
Studies
Transaction costs
Volatility
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description In 1985 Leland suggested an approach to price contingent claims under proportional transaction costs. Its main idea is to use the classical Black–Scholes formula with a suitably adjusted volatility for a periodical revision of the portfolio whose terminal value approximates the pay‐off. Unfortunately, if the transaction costs rate does not depend on the number of revisions, the approximation error does not converge to zero as the frequency of revisions tends to infinity. In the present paper, we suggest a modification of Leland’s strategy ensuring that the approximation error vanishes in the limit.
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subjects approximate hedging
Approximation
Black-Scholes formula
Leland's strategy
Mathematical models
Mathematics
Probability
Securities markets
Statistical analysis
Stochastic models
Studies
Transaction costs
Volatility
title MODIFIED LELAND'S STRATEGY FOR A CONSTANT TRANSACTION COSTS RATE
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