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Option Pricing and Replication with Transactions Costs

Authors

  • HAYNE E. LELAND

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    • School of Business Administration, University of California. The author thanks Richard Grinold, Mark Rubinstein, Jay Shanken, and Frederic Sipiere for discussion on this topic, and the referee for suggestions. Any remaining errors can be credited exclusively to the author.


ABSTRACT

Transactions costs invalidate the Black-Scholes arbitrage argument for option pricing, since continuous revision implies infinite trading. Discrete revision using Black-Scholes deltas generates errors which are correlated with the market, and do not approach zero with more frequent revision when transactions costs are included. This paper develops a modified option replicating strategy which depends on the size of transactions costs and the frequency of revision. Hedging errors are uncorrelated with the market and approach zero with more frequent revision. The technique permits calculation of the transactions costs of option replication and provides bounds on option prices.

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