On the Mean-Variance Tradeoff in Option Replication with Transactions Costs

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Abstract
This paper analyzes the tradeoff between cost and risk of discretely rebalanced option hedges in the presence of transactions costs. I present closed form solutions for expected hedging error, transactions costs, and variance of the cash flow from a time-based hedging strategy similar to that analyzed by Leland (1985). Furthermore, I characterize the cost and risk of a move-based hedging strategy without resorting to Monte Carlo simulations. All results are sufficiently general to accommodate the use of a transactions costs adjusted hedging volatility and an asset rate of return that differs from the risk-free rate of return.

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